tag:blogger.com,1999:blog-67155987353614012372024-03-20T16:10:13.940+01:00Gregor Gorjanc (gg)About various things that cross my mindGorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.comBlogger73125tag:blogger.com,1999:blog-6715598735361401237.post-4593482679905043492015-01-15T23:16:00.000+01:002015-01-15T23:16:33.637+01:00cpumemlog: Monitor CPU and RAM usage of a process (and its children)Long time no see ...<br />
<br />
Today I pushed the cpumemlog script to GitHub <a href="https://github.com/gregorgorjanc/cpumemlog">https://github.com/gregorgorjanc/cpumemlog</a>. Read more about this useful utility at the GitHub site.Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-12294097418581647012013-12-01T23:55:00.000+01:002013-12-01T23:55:04.376+01:00Read line by line of a file in RAre you using R for data manipulation for later use with other programs, i.e., a workflow something like this:<br />
<ol>
<li>read data sets from a disk,</li>
<li>modify the data, and</li>
<li>write it back to a disk.</li>
</ol>
<div>
All fine, but of data set is really big, then you will soon stumble on memory issues. If data processing is simple and you can read only chunks, say only line by line, then the following might be useful:</div>
<div>
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## File</span>
<a href="http://inside-r.org/r-doc/base/file"><span style="color: #003399; font-weight: bold;">file</span></a> <- <span style="color: blue;">"myfile.txt"</span>
<span style="color: #666666; font-style: italic;">## Create connection</span>
con <- <a href="http://inside-r.org/r-doc/base/file"><span style="color: #003399; font-weight: bold;">file</span></a><span style="color: #009900;">(</span>description=<a href="http://inside-r.org/r-doc/base/file"><span style="color: #003399; font-weight: bold;">file</span></a><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/open"><span style="color: #003399; font-weight: bold;">open</span></a>=<span style="color: blue;">"r"</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Hopefully you know the number of lines from some other source or</span>
com <- <a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span><span style="color: blue;">"wc -l "</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/file"><span style="color: #003399; font-weight: bold;">file</span></a><span style="color: #339933;">,</span> <span style="color: blue;">" | awk '{ print $1 }'"</span><span style="color: #339933;">,</span> sep=<span style="color: blue;">""</span><span style="color: #009900;">)</span>
n <- <a href="http://inside-r.org/r-doc/base/system"><span style="color: #003399; font-weight: bold;">system</span></a><span style="color: #009900;">(</span>command=com<span style="color: #339933;">,</span> intern=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Loop over a file connection</span>
<span style="color: black; font-weight: bold;">for</span><span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:n<span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
tmp <- <a href="http://inside-r.org/r-doc/base/scan"><span style="color: #003399; font-weight: bold;">scan</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/file"><span style="color: #003399; font-weight: bold;">file</span></a>=con<span style="color: #339933;">,</span> nlines=<span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> quiet=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## do something on a line of data </span>
<span style="color: #009900;">}</span></pre>
</div>
</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a></div>
Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com2tag:blogger.com,1999:blog-6715598735361401237.post-4350903055748695042013-07-02T18:47:00.000+02:002013-07-02T18:55:45.454+02:00Parse arguments of an R scriptR can be used also as a scripting tool. We just need to add shebang in the first line of a file (script):<br />
<br />
<span style="font-family: "Courier New",Courier,monospace;">#!/usr/bin/Rscript</span><br />
<br />
and then the R code should follow.<br />
<br />
<div style="text-align: justify;">
Often we want to pass arguments to such a script, which can be collected in the script by the <span style="font-family: "Courier New",Courier,monospace;">commandArgs()</span> function. Then we need to parse the arguments and conditional on them do something. I came with a rather general way of parsing these arguments using simply these few lines:<br />
<br /></div>
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## Collect arguments</span>
<a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a> <- <a href="http://inside-r.org/r-doc/base/commandArgs"><span style="color: #003399; font-weight: bold;">commandArgs</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Default setting when no arguments passed</span>
<span style="color: black; font-weight: bold;">if</span><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a><span style="color: #009900;">)</span> < <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a> <- <a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"--help"</span><span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;">## Help section</span>
<span style="color: black; font-weight: bold;">if</span><span style="color: #009900;">(</span><span style="color: blue;">"--help"</span> %in% <a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<a href="http://inside-r.org/r-doc/base/cat"><span style="color: #003399; font-weight: bold;">cat</span></a><span style="color: #009900;">(</span><span style="color: blue;">"
The R Script
Arguments:
--arg1=someValue - numeric, blah blah
--arg2=someValue - character, blah blah
--arg3=someValue - logical, blah blah
--help - print this text
Example:
./test.R --arg1=1 --arg2="</span>output.txt<span style="color: blue;">" --arg3=TRUE <span style="color: #000099; font-weight: bold;">\n</span><span style="color: #000099; font-weight: bold;">\n</span>"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/q"><span style="color: #003399; font-weight: bold;">q</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/save"><span style="color: #003399; font-weight: bold;">save</span></a>=<span style="color: blue;">"no"</span><span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;">## Parse arguments (we expect the form --arg=value)</span>
parseArgs <- <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span> <a href="http://inside-r.org/r-doc/base/strsplit"><span style="color: #003399; font-weight: bold;">strsplit</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sub"><span style="color: #003399; font-weight: bold;">sub</span></a><span style="color: #009900;">(</span><span style="color: blue;">"^--"</span><span style="color: #339933;">,</span> <span style="color: blue;">""</span><span style="color: #339933;">,</span> x<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: blue;">"="</span><span style="color: #009900;">)</span>
argsDF <- <a href="http://inside-r.org/r-doc/base/as.data.frame"><span style="color: #003399; font-weight: bold;">as.data.frame</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/do.call"><span style="color: #003399; font-weight: bold;">do.call</span></a><span style="color: #009900;">(</span><span style="color: blue;">"rbind"</span><span style="color: #339933;">,</span> parseArgs<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a><span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
argsL <- <a href="http://inside-r.org/r-doc/base/as.list"><span style="color: #003399; font-weight: bold;">as.list</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/as.character"><span style="color: #003399; font-weight: bold;">as.character</span></a><span style="color: #009900;">(</span>argsDF$V2<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/names"><span style="color: #003399; font-weight: bold;">names</span></a><span style="color: #009900;">(</span>argsL<span style="color: #009900;">)</span> <- argsDF$V1
<span style="color: #666666; font-style: italic;">## Arg1 default</span>
<span style="color: black; font-weight: bold;">if</span><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/is.null"><span style="color: #003399; font-weight: bold;">is.null</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a>$arg1<span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<span style="color: #666666; font-style: italic;">## do something</span>
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;">## Arg2 default</span>
<span style="color: black; font-weight: bold;">if</span><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/is.null"><span style="color: #003399; font-weight: bold;">is.null</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a>$arg2<span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<span style="color: #666666; font-style: italic;">## do something</span>
<span style="color: #009900;">}</span>
<span style="color: #666666; font-style: italic;">## Arg3 default</span>
<span style="color: black; font-weight: bold;">if</span><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/is.null"><span style="color: #003399; font-weight: bold;">is.null</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/args"><span style="color: #003399; font-weight: bold;">args</span></a>$arg3<span style="color: #009900;">)</span><span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
<span style="color: #666666; font-style: italic;">## do something</span>
<span style="color: #009900;">}</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #009900;"> </span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## ... your code here ...</span></pre>
</div>
</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a><br />
<br />
It is some work, but I find it pretty neat and use it for quite a while now. I do wonder what others have come up for this task. I hope I did not miss some very general solution.<!-----><!----->Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com3tag:blogger.com,1999:blog-6715598735361401237.post-9827678654663321592012-06-06T13:38:00.000+02:002012-06-06T13:38:26.509+02:002 min HOWTO in RLots of <a href="http://www.twotorials.com/">short videos</a> on how to do several things in R.Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-39178879244615054692012-04-08T19:14:00.001+02:002012-04-08T19:14:34.218+02:00Small pedigree based mixed model example<div style="text-align: justify;">
Pedigree based mixed models (often called animal models, due to modelling animal performance) are the cornerstone of animal breeding and quantitative genetics. There are many programs that can be used for analyzing your data with these models, e.g., <a href="http://www.vsni.co.uk/software/asreml">ASREML</a>, <a href="http://nce.ads.uga.edu/~ignacy/newprograms.html">BLUPf90</a>, <a href="http://statistics.unl.edu/faculty/steve/software/matvec/">MATVEC</a>, <a href="http://www.mixblup.eu/">MiXBLUP</a> & <a href="https://portal.mtt.fi/portal/page/portal/mtt_en/mtt/research/expertise/bel/biometricalgenetics/software/MiX99">MiX99</a>, <a href="http://www4.jouy.inra.fr/gabi_eng/Our-resources/Tool-development/The-Survival-Kit">SurvivalKit</a>, PEST/VCE, <a href="http://didgeridoo.une.edu.au/km/wombat.php">WOMBAT</a>, ...). There are also R packages you can use: <a href="http://cran.r-project.org/package=pedigreemm">pedigreemm</a> and <a href="http://cran.r-project.org/package=MCMCglmm">MCMCglmm</a>. If you want to run your own program you can take the example code bellow and start from it. The code shows the essence of building the system of equations that needs to be solved on a simple example. Note that this is mean only for demonstration purposes and small scale analyses. In addition, variance components are assumed known here. In order to understand the model for this simple example a bit better the graphical model view is shown first.</div>
<a href="http://www.scribd.com/doc/88476113/Graphical-model-view-of-simple-pedigree-based-mixed-model-example" style="display: block; font-family: Helvetica, Arial, sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin-bottom: 6px; margin-left: auto; margin-right: auto; margin-top: 12px; text-align: center; text-decoration: underline;" title="View Graphical model view of simple pedigree based mixed model example on Scribd">Graphical model view of simple pedigree based mixed model example</a><iframe class="scribd_iframe_embed" data-aspect-ratio="0.633333333333333" data-auto-height="true" frameborder="0" height="600" id="doc_99624" scrolling="no" src="http://www.scribd.com/embeds/88476113/content?start_page=1&view_mode=slideshow&access_key=key-vokrg8ej1hz95wsiadw" width="100%"></iframe><br />
<b><br /></b><br />
<b>The code:</b>
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"></pre>
<pre class="r geshifilter-R" style="font-family: monospace;">
</pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #003399; font-weight: bold;"><a href="http://inside-r.org/r-doc/base/options">options</a></span><span style="color: #009900;">(</span>width=<span style="color: #cc66cc;">200</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">### --- Required packages ---</span>
<span style="color: #666666; font-style: italic;">## install.packages(pkg=c("pedigreemm", "MatrixModels"))</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"pedigreemm"</span><span style="color: #009900;">)</span> <span style="color: #666666; font-style: italic;">## pedigree functions</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"MatrixModels"</span><span style="color: #009900;">)</span> <span style="color: #666666; font-style: italic;">## sparse matrices</span>
<span style="color: #666666; font-style: italic;">### --- Data ---</span>
<span style="color: #666666; font-style: italic;">## NOTE:</span>
<span style="color: #666666; font-style: italic;">## - some individuals have one or both parents (un)known</span>
<span style="color: #666666; font-style: italic;">## - some individuals have phenotype (un)known</span>
<span style="color: #666666; font-style: italic;">## - some indididuals have repeated phenotype observations </span>
<a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a> <- <a href="http://inside-r.org/r-doc/base/data.frame"><span style="color: #003399; font-weight: bold;">data.frame</span></a><span style="color: #009900;">(</span>
individual=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">7</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
father=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
mother=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
phenotype=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">103</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">106</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">98</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">101</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">106</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">93</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">109</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
<a href="http://inside-r.org/r-doc/grDevices/group"><span style="color: #003399; font-weight: bold;">group</span></a>=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Variance components</span>
sigma2e <- <span style="color: #cc66cc;">1</span>
sigma2a <- <span style="color: #cc66cc;">3</span>
<span style="color: #009900;">(</span>h2 <- sigma2a / <span style="color: #009900;">(</span>sigma2a + sigma2e<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">### --- Setup data ---</span>
<span style="color: #666666; font-style: italic;">## Make sure each individual has only one record in pedigree</span>
ped <- <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a><span style="color: #009900;">[</span>!<a href="http://inside-r.org/r-doc/base/duplicated"><span style="color: #003399; font-weight: bold;">duplicated</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;">3</span><span style="color: #009900;">]</span>
<span style="color: #666666; font-style: italic;">## Factors (this eases buliding the design matrix considerably)</span>
<a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual <- <a href="http://inside-r.org/r-doc/base/factor"><span style="color: #003399; font-weight: bold;">factor</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$group <- <a href="http://inside-r.org/r-doc/base/factor"><span style="color: #003399; font-weight: bold;">factor</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$group<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Phenotype data</span>
dat <- <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a><span style="color: #009900;">[</span>!<a href="http://inside-r.org/r-doc/base/is.na"><span style="color: #003399; font-weight: bold;">is.na</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$phenotype<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #009900;">]</span>
<span style="color: #666666; font-style: italic;">### --- Setup MME ---</span>
<span style="color: #666666; font-style: italic;">## Phenotype vector</span>
<span style="color: #009900;">(</span>y <- dat$phenotype<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Design matrix for the "fixed" effects (group)</span>
<span style="color: #009900;">(</span>X <- model.Matrix<span style="color: #009900;">(</span> ~ <a href="http://inside-r.org/r-doc/grDevices/group"><span style="color: #003399; font-weight: bold;">group</span></a><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Design matrix for the "random" effects (individual)</span>
<span style="color: #009900;">(</span>Z <- model.Matrix<span style="color: #009900;">(</span>~ individual - <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Inverse additive relationship matrix</span>
ped2 <- <a href="http://inside-r.org/packages/cran/pedigree">pedigree</a><span style="color: #009900;">(</span>sire=ped$father<span style="color: #339933;">,</span> dam=ped$mother<span style="color: #339933;">,</span> label=ped$individual<span style="color: #009900;">)</span>
TInv <- <a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;">as</span></a><span style="color: #009900;">(</span>ped2<span style="color: #339933;">,</span> <span style="color: blue;">"sparseMatrix"</span><span style="color: #009900;">)</span>
DInv <- <a href="http://inside-r.org/r-doc/Matrix/Diagonal"><span style="color: #003399; font-weight: bold;">Diagonal</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">1</span>/Dmat<span style="color: #009900;">(</span>ped2<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
AInv <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>DInv<span style="color: #009900;">)</span> %*% TInv<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Variance ratio</span>
alpha <- sigma2e / sigma2a
<span style="color: #666666; font-style: italic;">## Mixed Model Equations (MME)</span>
<span style="color: #666666; font-style: italic;">## ... Left-Hand Side (LHS) without pedigree prior</span>
<span style="color: #009900;">(</span>LHS0 <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## ... Left-Hand Side (LHS) with pedigree prior</span>
<a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;">round</span></a><span style="color: #009900;">(</span>
<a href="http://inside-r.org/packages/cran/lhs">LHS</a> <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span> + AInv * alpha<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## ... Right-Hand Side (RHS)</span>
<span style="color: #009900;">(</span>RHS <- rBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span><span style="color: #339933;">,</span>
<a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">### --- Solutions ---</span>
<span style="color: #666666; font-style: italic;">## Solve</span>
LHSInv <- <a href="http://inside-r.org/r-doc/base/solve"><span style="color: #003399; font-weight: bold;">solve</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a><span style="color: #009900;">)</span>
sol <- LHSInv %*% RHS
<span style="color: #666666; font-style: italic;">## Standard errors</span>
se <- <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span>LHSInv<span style="color: #009900;">)</span> * sigma2e
<span style="color: #666666; font-style: italic;">## Reliabilities</span>
r2 <- <span style="color: #cc66cc;">1</span> - <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span>LHSInv<span style="color: #009900;">)</span> * alpha
<span style="color: #666666; font-style: italic;">## Accuracies</span>
r <- <a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>r2<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Printout</span>
cBind<span style="color: #009900;">(</span>sol<span style="color: #339933;">,</span> se<span style="color: #339933;">,</span> r<span style="color: #339933;">,</span> r2<span style="color: #009900;">)</span></pre>
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</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a><br />
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<br />
<b>And the transcript:</b></div>
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"></pre>
<pre class="r geshifilter-R" style="font-family: monospace;">R <a href="http://inside-r.org/r-doc/base/version"><span style="color: #003399; font-weight: bold;">version</span></a> 2.14.2 <span style="color: #009900;">(</span><span style="color: #cc66cc;">2012</span>-02-<span style="color: #cc66cc;">29</span><span style="color: #009900;">)</span>
Copyright <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/stats/C"><span style="color: #003399; font-weight: bold;">C</span></a><span style="color: #009900;">)</span> <span style="color: #cc66cc;">2012</span> The R Foundation <span style="color: black; font-weight: bold;">for</span> Statistical Computing
ISBN <span style="color: #cc66cc;">3</span>-<span style="color: #cc66cc;">900051</span>-07-<span style="color: #cc66cc;">0</span>
<a href="http://inside-r.org/r-doc/base/Platform"><span style="color: #003399; font-weight: bold;">Platform</span></a>: x86_64-pc-linux-gnu <span style="color: #009900;">(</span><span style="color: #cc66cc;">64</span>-<a href="http://inside-r.org/packages/cran/bit">bit</a><span style="color: #009900;">)</span>
R <a href="http://inside-r.org/r-doc/methods/is"><span style="color: #003399; font-weight: bold;">is</span></a> free software and comes <a href="http://inside-r.org/r-doc/base/with"><span style="color: #003399; font-weight: bold;">with</span></a> ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type <span style="color: blue;">'license()'</span> or <span style="color: blue;">'licence()'</span> <span style="color: black; font-weight: bold;">for</span> distribution details.
Natural language support but running <span style="color: black; font-weight: bold;">in</span> an English locale
R <a href="http://inside-r.org/r-doc/methods/is"><span style="color: #003399; font-weight: bold;">is</span></a> a collaborative project <a href="http://inside-r.org/r-doc/base/with"><span style="color: #003399; font-weight: bold;">with</span></a> many contributors.
Type <span style="color: blue;">'contributors()'</span> <span style="color: black; font-weight: bold;">for</span> more information and
<span style="color: blue;">'citation()'</span> on how to cite R or R packages <span style="color: black; font-weight: bold;">in</span> publications.
Type <span style="color: blue;">'demo()'</span> <span style="color: black; font-weight: bold;">for</span> some demos<span style="color: #339933;">,</span> <span style="color: blue;">'help()'</span> <span style="color: black; font-weight: bold;">for</span> on-<a href="http://inside-r.org/r-doc/stats/line"><span style="color: #003399; font-weight: bold;">line</span></a> <a href="http://inside-r.org/r-doc/utils/help"><span style="color: #003399; font-weight: bold;">help</span></a><span style="color: #339933;">,</span> or
<span style="color: blue;">'help.start()'</span> <span style="color: black; font-weight: bold;">for</span> an HTML <a href="http://inside-r.org/r-doc/base/browser"><span style="color: #003399; font-weight: bold;">browser</span></a> interface to help.
Type <span style="color: blue;">'q()'</span> to <a href="http://inside-r.org/r-doc/base/quit"><span style="color: #003399; font-weight: bold;">quit</span></a> R.
<span style="color: #009900;">[</span>Previously saved workspace restored<span style="color: #009900;">]</span>
>
> <a href="http://inside-r.org/r-doc/base/options"><span style="color: #003399; font-weight: bold;">options</span></a><span style="color: #009900;">(</span>width=<span style="color: #cc66cc;">200</span><span style="color: #009900;">)</span>
>
> <span style="color: #666666; font-style: italic;">### --- Required packages ---</span>
>
> <span style="color: #666666; font-style: italic;">## install.packages(pkg=c("pedigreemm", "MatrixModels"))</span>
>
> <a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"pedigreemm"</span><span style="color: #009900;">)</span> <span style="color: #666666; font-style: italic;">## pedigree functions</span>
Loading required package: <a href="http://inside-r.org/packages/cran/lme4">lme4</a>
Loading required package: <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a>
Loading required package: <a href="http://inside-r.org/packages/cran/lattice">lattice</a>
Attaching package: ‘<a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a>’
The following object<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/mgcv/s"><span style="color: #003399; font-weight: bold;">s</span></a><span style="color: #009900;">)</span> are masked from ‘package:<a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a>’:
<a href="http://inside-r.org/r-doc/base/det"><span style="color: #003399; font-weight: bold;">det</span></a>
Attaching package: ‘<a href="http://inside-r.org/packages/cran/lme4">lme4</a>’
The following object<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/mgcv/s"><span style="color: #003399; font-weight: bold;">s</span></a><span style="color: #009900;">)</span> are masked from ‘package:<a href="http://inside-r.org/r-doc/stats"><span style="color: #006600; font-weight: bold;">stats</span></a>’:
<a href="http://inside-r.org/r-doc/stats/AIC"><span style="color: #003399; font-weight: bold;">AIC</span></a><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/nlme/BIC"><span style="color: #003399; font-weight: bold;">BIC</span></a>
> <a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"MatrixModels"</span><span style="color: #009900;">)</span> <span style="color: #666666; font-style: italic;">## sparse matrices</span>
>
> <span style="color: #666666; font-style: italic;">### --- Data ---</span>
>
> <span style="color: #666666; font-style: italic;">## NOTE:</span>
> <span style="color: #666666; font-style: italic;">## - some individuals have one or both parents (un)known</span>
> <span style="color: #666666; font-style: italic;">## - some individuals have phenotype (un)known</span>
> <span style="color: #666666; font-style: italic;">## - some indididuals have repeated phenotype observations </span>
> <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a> <- <a href="http://inside-r.org/r-doc/base/data.frame"><span style="color: #003399; font-weight: bold;">data.frame</span></a><span style="color: #009900;">(</span>
+ individual=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">7</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ father=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ mother=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ phenotype=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">103</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">106</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">98</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">101</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">106</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">93</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">109</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ <a href="http://inside-r.org/r-doc/grDevices/group"><span style="color: #003399; font-weight: bold;">group</span></a>=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
>
> <span style="color: #666666; font-style: italic;">## Variance components</span>
> sigma2e <- <span style="color: #cc66cc;">1</span>
> sigma2a <- <span style="color: #cc66cc;">3</span>
> <span style="color: #009900;">(</span>h2 <- sigma2a / <span style="color: #009900;">(</span>sigma2a + sigma2e<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">0.75</span>
>
> <span style="color: #666666; font-style: italic;">### --- Setup data ---</span>
>
> <span style="color: #666666; font-style: italic;">## Make sure each individual has only one record in pedigree</span>
> ped <- <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a><span style="color: #009900;">[</span>!<a href="http://inside-r.org/r-doc/base/duplicated"><span style="color: #003399; font-weight: bold;">duplicated</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;">3</span><span style="color: #009900;">]</span>
>
> <span style="color: #666666; font-style: italic;">## Factors (this eases buliding the design matrix considerably)</span>
> <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual <- <a href="http://inside-r.org/r-doc/base/factor"><span style="color: #003399; font-weight: bold;">factor</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$individual<span style="color: #009900;">)</span>
> <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$group <- <a href="http://inside-r.org/r-doc/base/factor"><span style="color: #003399; font-weight: bold;">factor</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$group<span style="color: #009900;">)</span>
>
> <span style="color: #666666; font-style: italic;">## Phenotype data</span>
> dat <- <a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a><span style="color: #009900;">[</span>!<a href="http://inside-r.org/r-doc/base/is.na"><span style="color: #003399; font-weight: bold;">is.na</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/utils/example"><span style="color: #003399; font-weight: bold;">example</span></a>$phenotype<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <span style="color: #009900;">]</span>
>
> <span style="color: #666666; font-style: italic;">### --- Setup MME ---</span>
>
> <span style="color: #666666; font-style: italic;">## Phenotype vector</span>
> <span style="color: #009900;">(</span>y <- dat$phenotype<span style="color: #009900;">)</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">103</span> <span style="color: #cc66cc;">106</span> <span style="color: #cc66cc;">98</span> <span style="color: #cc66cc;">101</span> <span style="color: #cc66cc;">106</span> <span style="color: #cc66cc;">93</span> <span style="color: #cc66cc;">109</span>
>
> <span style="color: #666666; font-style: italic;">## Design matrix for the "fixed" effects (group)</span>
> <span style="color: #009900;">(</span>X <- model.Matrix<span style="color: #009900;">(</span> ~ <a href="http://inside-r.org/r-doc/grDevices/group"><span style="color: #003399; font-weight: bold;">group</span></a><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: blue;">"dsparseModelMatrix"</span>: <span style="color: #cc66cc;">7</span> x <span style="color: #cc66cc;">2</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> group2
<span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span> .
<span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">1</span> .
<span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">1</span> .
<span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">6</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">7</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">11</span> <span style="color: #cc66cc;">1</span> .
@ <a href="http://inside-r.org/r-doc/base/assign"><span style="color: #003399; font-weight: bold;">assign</span></a>: <span style="color: #cc66cc;">0</span> <span style="color: #cc66cc;">1</span>
@ <a href="http://inside-r.org/r-doc/stats/contrasts"><span style="color: #003399; font-weight: bold;">contrasts</span></a>:
$group
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <span style="color: blue;">"contr.treatment"</span>
>
> <span style="color: #666666; font-style: italic;">## Design matrix for the "random" effects (individual)</span>
> <span style="color: #009900;">(</span>Z <- model.Matrix<span style="color: #009900;">(</span>~ individual - <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: blue;">"dsparseModelMatrix"</span>: <span style="color: #cc66cc;">7</span> x <span style="color: #cc66cc;">10</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #009900;">[</span> suppressing <span style="color: #cc66cc;">10</span> column <a href="http://inside-r.org/r-doc/base/names"><span style="color: #003399; font-weight: bold;">names</span></a> ‘individual1’<span style="color: #339933;">,</span> ‘individual2’<span style="color: #339933;">,</span> ‘individual3’ ... <span style="color: #009900;">]</span><span style="color: #009900;">]</span>
<span style="color: #cc66cc;">2</span> . <span style="color: #cc66cc;">1</span> . . . . . . . .
<span style="color: #cc66cc;">3</span> . <span style="color: #cc66cc;">1</span> . . . . . . . .
<span style="color: #cc66cc;">4</span> . . <span style="color: #cc66cc;">1</span> . . . . . . .
<span style="color: #cc66cc;">5</span> . . . <span style="color: #cc66cc;">1</span> . . . . . .
<span style="color: #cc66cc;">6</span> . . . . <span style="color: #cc66cc;">1</span> . . . . .
<span style="color: #cc66cc;">7</span> . . . . . <span style="color: #cc66cc;">1</span> . . . .
<span style="color: #cc66cc;">11</span> . . . . . . . . . <span style="color: #cc66cc;">1</span>
@ <a href="http://inside-r.org/r-doc/base/assign"><span style="color: #003399; font-weight: bold;">assign</span></a>: <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
@ <a href="http://inside-r.org/r-doc/stats/contrasts"><span style="color: #003399; font-weight: bold;">contrasts</span></a>:
$individual
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <span style="color: blue;">"contr.treatment"</span>
>
> <span style="color: #666666; font-style: italic;">## Inverse additive relationship matrix</span>
> ped2 <- <a href="http://inside-r.org/packages/cran/pedigree">pedigree</a><span style="color: #009900;">(</span>sire=ped$father<span style="color: #339933;">,</span> dam=ped$mother<span style="color: #339933;">,</span> label=ped$individual<span style="color: #009900;">)</span>
> TInv <- <a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;">as</span></a><span style="color: #009900;">(</span>ped2<span style="color: #339933;">,</span> <span style="color: blue;">"sparseMatrix"</span><span style="color: #009900;">)</span>
> DInv <- <a href="http://inside-r.org/r-doc/Matrix/Diagonal"><span style="color: #003399; font-weight: bold;">Diagonal</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">1</span>/Dmat<span style="color: #009900;">(</span>ped2<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
> AInv <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>DInv<span style="color: #009900;">)</span> %*% TInv<span style="color: #009900;">)</span>
>
> <span style="color: #666666; font-style: italic;">## Variance ratio</span>
> alpha <- sigma2e / sigma2a
>
> <span style="color: #666666; font-style: italic;">## Mixed Model Equations (MME)</span>
>
> <span style="color: #666666; font-style: italic;">## ... Left-Hand Side (LHS) without pedigree prior</span>
> <span style="color: #009900;">(</span>LHS0 <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">12</span> x <span style="color: #cc66cc;">12</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #009900;">[</span> suppressing <span style="color: #cc66cc;">12</span> column <a href="http://inside-r.org/r-doc/base/names"><span style="color: #003399; font-weight: bold;">names</span></a> ‘<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span>’<span style="color: #339933;">,</span> ‘group2’<span style="color: #339933;">,</span> ‘individual1’ ... <span style="color: #009900;">]</span><span style="color: #009900;">]</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">7</span> <span style="color: #cc66cc;">3</span> . <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . . <span style="color: #cc66cc;">1</span>
group2 <span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">3</span> . . . <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . . .
individual1 . . . . . . . . . . . .
individual2 <span style="color: #cc66cc;">2</span> . . <span style="color: #cc66cc;">2</span> . . . . . . . .
individual3 <span style="color: #cc66cc;">1</span> . . . <span style="color: #cc66cc;">1</span> . . . . . . .
individual4 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . . <span style="color: #cc66cc;">1</span> . . . . . .
individual5 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . . . <span style="color: #cc66cc;">1</span> . . . . .
individual6 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . . . . <span style="color: #cc66cc;">1</span> . . . .
individual7 . . . . . . . . . . . .
individual8 . . . . . . . . . . . .
individual9 . . . . . . . . . . . .
individual10 <span style="color: #cc66cc;">1</span> . . . . . . . . . . <span style="color: #cc66cc;">1</span>
>
> <span style="color: #666666; font-style: italic;">## ... Left-Hand Side (LHS) with pedigree prior</span>
> <a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;">round</span></a><span style="color: #009900;">(</span>
+ <a href="http://inside-r.org/packages/cran/lhs">LHS</a> <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> X<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span> + AInv * alpha<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">12</span> x <span style="color: #cc66cc;">12</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #009900;">[</span> suppressing <span style="color: #cc66cc;">12</span> column <a href="http://inside-r.org/r-doc/base/names"><span style="color: #003399; font-weight: bold;">names</span></a> ‘<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span>’<span style="color: #339933;">,</span> ‘group2’<span style="color: #339933;">,</span> ‘individual1’ ... <span style="color: #009900;">]</span><span style="color: #009900;">]</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">7</span> <span style="color: #cc66cc;">3</span> . <span style="color: #cc66cc;">2.0</span> <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">1.0</span> . . . <span style="color: #cc66cc;">1.0</span>
group2 <span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">3</span> . . . <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">1.0</span> . . . .
individual1 . . <span style="color: #cc66cc;">0.5</span> <span style="color: #cc66cc;">0.2</span> -<span style="color: #cc66cc;">0.3</span> . . . . . . .
individual2 <span style="color: #cc66cc;">2</span> . <span style="color: #cc66cc;">0.2</span> <span style="color: #cc66cc;">2.8</span> -<span style="color: #cc66cc;">0.2</span> -<span style="color: #cc66cc;">0.2</span> . -<span style="color: #cc66cc;">0.3</span> . . . .
individual3 <span style="color: #cc66cc;">1</span> . -<span style="color: #cc66cc;">0.3</span> -<span style="color: #cc66cc;">0.2</span> <span style="color: #cc66cc;">2.0</span> <span style="color: #cc66cc;">0.2</span> -<span style="color: #cc66cc;">0.3</span> -<span style="color: #cc66cc;">0.3</span> . . . .
individual4 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . -<span style="color: #cc66cc;">0.2</span> <span style="color: #cc66cc;">0.2</span> <span style="color: #cc66cc;">1.6</span> -<span style="color: #cc66cc;">0.3</span> . . . . .
individual5 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . . -<span style="color: #cc66cc;">0.3</span> -<span style="color: #cc66cc;">0.3</span> <span style="color: #cc66cc;">2.1</span> <span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> . .
individual6 <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span> . -<span style="color: #cc66cc;">0.3</span> -<span style="color: #cc66cc;">0.3</span> . <span style="color: #cc66cc;">0.4</span> <span style="color: #cc66cc;">2.1</span> -<span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> . .
individual7 . . . . . . -<span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> <span style="color: #cc66cc;">0.8</span> . . .
individual8 . . . . . . -<span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> . <span style="color: #cc66cc;">1.0</span> <span style="color: #cc66cc;">0.2</span> -<span style="color: #cc66cc;">0.4</span>
individual9 . . . . . . . . . <span style="color: #cc66cc;">0.2</span> <span style="color: #cc66cc;">0.5</span> -<span style="color: #cc66cc;">0.4</span>
individual10 <span style="color: #cc66cc;">1</span> . . . . . . . . -<span style="color: #cc66cc;">0.4</span> -<span style="color: #cc66cc;">0.4</span> <span style="color: #cc66cc;">1.8</span>
>
> <span style="color: #666666; font-style: italic;">## ... Right-Hand Side (RHS)</span>
> <span style="color: #009900;">(</span>RHS <- rBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">12</span> x <span style="color: #cc66cc;">1</span> <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgeMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">716</span>
group2 <span style="color: #cc66cc;">300</span>
individual1 <span style="color: #cc66cc;">0</span>
individual2 <span style="color: #cc66cc;">209</span>
individual3 <span style="color: #cc66cc;">98</span>
individual4 <span style="color: #cc66cc;">101</span>
individual5 <span style="color: #cc66cc;">106</span>
individual6 <span style="color: #cc66cc;">93</span>
individual7 <span style="color: #cc66cc;">0</span>
individual8 <span style="color: #cc66cc;">0</span>
individual9 <span style="color: #cc66cc;">0</span>
individual10 <span style="color: #cc66cc;">109</span>
>
> <span style="color: #666666; font-style: italic;">### --- Solutions ---</span>
>
> <span style="color: #666666; font-style: italic;">## Solve</span>
> LHSInv <- <a href="http://inside-r.org/r-doc/base/solve"><span style="color: #003399; font-weight: bold;">solve</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a><span style="color: #009900;">)</span>
> sol <- LHSInv %*% RHS
>
> <span style="color: #666666; font-style: italic;">## Standard errors</span>
> se <- <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span>LHSInv<span style="color: #009900;">)</span> * sigma2e
>
> <span style="color: #666666; font-style: italic;">## Reliabilities</span>
> r2 <- <span style="color: #cc66cc;">1</span> - <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span>LHSInv<span style="color: #009900;">)</span> * alpha
>
> <span style="color: #666666; font-style: italic;">## Accuracies</span>
> r <- <a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>r2<span style="color: #009900;">)</span>
Warning <a href="http://inside-r.org/r-doc/base/message"><span style="color: #003399; font-weight: bold;">message</span></a>:
In <a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>r2<span style="color: #009900;">)</span> : NaNs produced
>
> <span style="color: #666666; font-style: italic;">## Printout</span>
> cBind<span style="color: #009900;">(</span>sol<span style="color: #339933;">,</span> se<span style="color: #339933;">,</span> r<span style="color: #339933;">,</span> r2<span style="color: #009900;">)</span>
<span style="color: #cc66cc;">12</span> x <span style="color: #cc66cc;">4</span> <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgeMatrix"</span>
se r r2
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">104.76444809</span> <span style="color: #cc66cc;">1.901479</span> <span style="color: #cc66cc;">0.6051228</span> <span style="color: #cc66cc;">0.3661736</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">4.65061921</span> <span style="color: #cc66cc;">1.376348</span> <span style="color: #cc66cc;">0.7356748</span> <span style="color: #cc66cc;">0.5412175</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">2.62685846</span> <span style="color: #cc66cc;">2.432448</span> <span style="color: #cc66cc;">0.4349528</span> <span style="color: #cc66cc;">0.1891839</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">0.77797260</span> <span style="color: #cc66cc;">1.983301</span> <span style="color: #cc66cc;">0.5821509</span> <span style="color: #cc66cc;">0.3388997</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">4.32927399</span> <span style="color: #cc66cc;">1.979138</span> <span style="color: #cc66cc;">0.5833415</span> <span style="color: #cc66cc;">0.3402874</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">1.54997883</span> <span style="color: #cc66cc;">2.316720</span> <span style="color: #cc66cc;">0.4772421</span> <span style="color: #cc66cc;">0.2277600</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">7</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">3.18706240</span> <span style="color: #cc66cc;">2.604540</span> <span style="color: #cc66cc;">0.3630701</span> <span style="color: #cc66cc;">0.1318199</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">5.07852788</span> <span style="color: #cc66cc;">2.508673</span> <span style="color: #cc66cc;">0.4046922</span> <span style="color: #cc66cc;">0.1637758</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">9</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">0.94573274</span> <span style="color: #cc66cc;">3.459904</span> <span style="color: black; font-weight: bold;">NaN</span> -<span style="color: #cc66cc;">0.1533013</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">10</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> -<span style="color: #cc66cc;">0.08765651</span> <span style="color: #cc66cc;">3.534636</span> <span style="color: black; font-weight: bold;">NaN</span> -<span style="color: #cc66cc;">0.1782121</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">11</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">2.11218764</span> <span style="color: #cc66cc;">2.511203</span> <span style="color: #cc66cc;">0.4036487</span> <span style="color: #cc66cc;">0.1629323</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">12</span><span style="color: #339933;">,</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">2.82742681</span> <span style="color: #cc66cc;">2.009539</span> <span style="color: #cc66cc;">0.5745901</span> <span style="color: #cc66cc;">0.3301538</span>
>
> <a href="http://inside-r.org/r-doc/base/proc.time"><span style="color: #003399; font-weight: bold;">proc.time</span></a><span style="color: #009900;">(</span><span style="color: #009900;">)</span>
user <a href="http://inside-r.org/r-doc/base/system"><span style="color: #003399; font-weight: bold;">system</span></a> elapsed
<span style="color: #cc66cc;">3.350</span> <span style="color: #cc66cc;">0.070</span> <span style="color: #cc66cc;">3.425</span> </pre>
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</div>
<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-67423335300021900632012-04-04T03:17:00.000+02:002012-04-04T03:17:58.543+02:00Regression - covariate adjustment<div style="text-align: justify;">
Linear regression is one of the key concepts in statistics [<a href="http://en.wikipedia.org/wiki/Simple_linear_regression">wikipedia1</a>, <a href="http://en.wikipedia.org/wiki/Linear_regression">wikipedia2</a>]. However, people are often confuse the meaning of parameters of linear regression - the intercept tells us the average value of y at x=0, while the slope tells us how much change of y can we expect on average when we change x for one unit - exactly the same as in the <a href="http://en.wikipedia.org/wiki/Linear_function">linear function</a>, though we use averages here due to noise.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Today colleague got confused with the meaning of adjusting covariate (x variable) and the effect of parameter estimates. By shifting the x scale, we also shift the point at which intercept is estimated. I made the following graph to demonstrate this point in the case of nested regression of y on x within a group factor having two levels. R code to produce this plots is shown on bottom.</div>
<a href="http://www.scribd.com/doc/87894714/Regression-covariate-adjustment" style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto; text-decoration: underline;" title="View Regression - covariate adjustment on Scribd">Regression - covariate adjustment</a><iframe class="scribd_iframe_embed" data-aspect-ratio="1" data-auto-height="true" frameborder="0" height="600" id="doc_34763" scrolling="no" src="http://www.scribd.com/embeds/87894714/content?start_page=1&view_mode=list&access_key=key-2089cd6i93nwzs81443f" width="100%"></iframe>
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<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"MASS"</span><span style="color: #009900;">)</span>
x1 <- <a href="http://inside-r.org/r-doc/MASS/mvrnorm"><span style="color: #003399; font-weight: bold;">mvrnorm</span></a><span style="color: #009900;">(</span>n=<span style="color: #cc66cc;">100</span><span style="color: #339933;">,</span> mu=<span style="color: #cc66cc;">50</span><span style="color: #339933;">,</span> Sigma=<span style="color: #cc66cc;">20</span><span style="color: #339933;">,</span> empirical=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
x2 <- <a href="http://inside-r.org/r-doc/MASS/mvrnorm"><span style="color: #003399; font-weight: bold;">mvrnorm</span></a><span style="color: #009900;">(</span>n=<span style="color: #cc66cc;">100</span><span style="color: #339933;">,</span> mu=<span style="color: #cc66cc;">70</span><span style="color: #339933;">,</span> Sigma=<span style="color: #cc66cc;">20</span><span style="color: #339933;">,</span> empirical=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
mu1 <- mu2 <- <span style="color: #cc66cc;">4</span>
b1 <- <span style="color: #cc66cc;">0.300</span>
b2 <- <span style="color: #cc66cc;">0.250</span>
y1 <- mu1 + b1 * x1 + <a href="http://inside-r.org/r-doc/stats/rnorm"><span style="color: #003399; font-weight: bold;">rnorm</span></a><span style="color: #009900;">(</span>n=<span style="color: #cc66cc;">100</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/stats/sd"><span style="color: #003399; font-weight: bold;">sd</span></a>=<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
y2 <- mu2 + b2 * x2 + <a href="http://inside-r.org/r-doc/stats/rnorm"><span style="color: #003399; font-weight: bold;">rnorm</span></a><span style="color: #009900;">(</span>n=<span style="color: #cc66cc;">100</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/stats/sd"><span style="color: #003399; font-weight: bold;">sd</span></a>=<span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
x <- <a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span>x1<span style="color: #339933;">,</span> x2<span style="color: #009900;">)</span>
xK <- x - <span style="color: #cc66cc;">60</span>
y <- <a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span>y1<span style="color: #339933;">,</span> y2<span style="color: #009900;">)</span>
g <- <a href="http://inside-r.org/r-doc/base/factor"><span style="color: #003399; font-weight: bold;">factor</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/rep"><span style="color: #003399; font-weight: bold;">rep</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> each=<span style="color: #cc66cc;">100</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/par"><span style="color: #003399; font-weight: bold;">par</span></a><span style="color: #009900;">(</span>mfrow=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> pty=<span style="color: blue;">"m"</span><span style="color: #339933;">,</span> bty=<span style="color: blue;">"l"</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>fit1n <- <a href="http://inside-r.org/r-doc/stats/lm"><span style="color: #003399; font-weight: bold;">lm</span></a><span style="color: #009900;">(</span>y ~ g + x + x:g<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## (Intercept) g2 x g2:x </span>
<span style="color: #666666; font-style: italic;">## 3.06785 2.32448 0.31967 -0.09077 </span>
<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a> <- <a href="http://inside-r.org/r-doc/stats/coef"><span style="color: #003399; font-weight: bold;">coef</span></a><span style="color: #009900;">(</span>fit1n<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span>y ~ x<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"blue"</span><span style="color: #339933;">,</span> <span style="color: blue;">"red"</span><span style="color: #009900;">)</span><span style="color: #009900;">[</span>g<span style="color: #009900;">]</span><span style="color: #339933;">,</span> ylim=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>y<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> xlim=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> cex=<span style="color: #cc66cc;">0.25</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x2<span style="color: #009900;">)</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y2<span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>v=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x2<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"gray"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>h=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y2<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"gray"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"blue"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2"</span><span style="color: #009900;">]</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"red"</span><span style="color: #009900;">)</span>
z <- <span style="color: #cc66cc;">0</span>:<a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/lines"><span style="color: #003399; font-weight: bold;">lines</span></a><span style="color: #009900;">(</span>y= <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"x"</span><span style="color: #009900;">]</span> * z <span style="color: #339933;">,</span> x=z<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"blue"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/lines"><span style="color: #003399; font-weight: bold;">lines</span></a><span style="color: #009900;">(</span>y=<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2"</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> + <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"x"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2:x"</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> * z<span style="color: #339933;">,</span> x=z<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"red"</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>fit2n <- <a href="http://inside-r.org/r-doc/stats/lm"><span style="color: #003399; font-weight: bold;">lm</span></a><span style="color: #009900;">(</span>y ~ g + xK + xK:g<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## (Intercept) g2 xK g2:xK </span>
<span style="color: #666666; font-style: italic;">## 22.24824 -3.12153 0.31967 -0.09077</span>
<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a> <- <a href="http://inside-r.org/r-doc/stats/coef"><span style="color: #003399; font-weight: bold;">coef</span></a><span style="color: #009900;">(</span>fit2n<span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span>y ~ x<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"blue"</span><span style="color: #339933;">,</span> <span style="color: blue;">"red"</span><span style="color: #009900;">)</span><span style="color: #009900;">[</span>g<span style="color: #009900;">]</span><span style="color: #339933;">,</span> ylim=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>y<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> xlim=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">0</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> cex=<span style="color: #cc66cc;">0.25</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x2<span style="color: #009900;">)</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y2<span style="color: #009900;">)</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>v=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>x2<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"gray"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>h=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y1<span style="color: #009900;">)</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/mean"><span style="color: #003399; font-weight: bold;">mean</span></a><span style="color: #009900;">(</span>y2<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"gray"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/abline"><span style="color: #003399; font-weight: bold;">abline</span></a><span style="color: #009900;">(</span>v=<span style="color: #cc66cc;">60</span><span style="color: #339933;">,</span> lty=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"gray"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">60</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"blue"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/points"><span style="color: #003399; font-weight: bold;">points</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">60</span><span style="color: #339933;">,</span> y=<a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2"</span><span style="color: #009900;">]</span><span style="color: #339933;">,</span> pch=<span style="color: #cc66cc;">19</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"red"</span><span style="color: #009900;">)</span>
z <- <span style="color: #cc66cc;">0</span>:<a href="http://inside-r.org/r-doc/base/max"><span style="color: #003399; font-weight: bold;">max</span></a><span style="color: #009900;">(</span>x<span style="color: #009900;">)</span> - <span style="color: #cc66cc;">60</span>
<a href="http://inside-r.org/r-doc/graphics/lines"><span style="color: #003399; font-weight: bold;">lines</span></a><span style="color: #009900;">(</span>y= <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"xK"</span><span style="color: #009900;">]</span> * z <span style="color: #339933;">,</span> x=z + <span style="color: #cc66cc;">60</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"blue"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/lines"><span style="color: #003399; font-weight: bold;">lines</span></a><span style="color: #009900;">(</span>y=<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"(Intercept)"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2"</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> + <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"xK"</span><span style="color: #009900;">]</span> + <a href="http://inside-r.org/r-doc/base/beta"><span style="color: #003399; font-weight: bold;">beta</span></a><span style="color: #009900;">[</span><span style="color: blue;">"g2:xK"</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> * z<span style="color: #339933;">,</span> x=z + <span style="color: #cc66cc;">60</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/col"><span style="color: #003399; font-weight: bold;">col</span></a>=<span style="color: blue;">"red"</span><span style="color: #009900;">)</span></pre>
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<a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com5tag:blogger.com,1999:blog-6715598735361401237.post-27049454418139176522012-03-31T00:37:00.001+02:002012-03-31T00:37:29.454+02:00GBLUP example in R<div style="text-align: justify;">
Shirin Amiri was asking about GBLUP (genomic BLUP) and based on her example I set up the following R script to show how GBLUP works. Note that this is the so called marker model, where we estimate allele substitution effects of the markers and not individual based model, where genomic breeding values are inferred directly. The code:</div>
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<pre class="r geshifilter-R" style="font-family: monospace;"><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"MatrixModels"</span><span style="color: #009900;">)</span>
dat <- <a href="http://inside-r.org/r-doc/base/data.frame"><span style="color: #003399; font-weight: bold;">data.frame</span></a><span style="color: #009900;">(</span> y=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">1.5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2.35</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3.4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2.31</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1.53</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
s1=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"AA"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Aa"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Aa"</span><span style="color: #339933;">,</span> <span style="color: blue;">"AA"</span><span style="color: #339933;">,</span> <span style="color: blue;">"aa"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
s2=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"Bb"</span><span style="color: #339933;">,</span> <span style="color: blue;">"BB"</span><span style="color: #339933;">,</span> <span style="color: blue;">"bb"</span><span style="color: #339933;">,</span> <span style="color: blue;">"BB"</span><span style="color: #339933;">,</span> <span style="color: blue;">"bb"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
s3=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"CC"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
s4=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"Dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"DD"</span><span style="color: #339933;">,</span> <span style="color: blue;">"dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Dd"</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
cols <- <a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span><span style="color: blue;">"s"</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> sep=<span style="color: blue;">""</span><span style="color: #009900;">)</span>
dat<span style="color: #009900;">[</span><span style="color: #339933;">,</span> cols<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/lapply"><span style="color: #003399; font-weight: bold;">lapply</span></a><span style="color: #009900;">(</span>dat<span style="color: #009900;">[</span><span style="color: #339933;">,</span> cols<span style="color: #009900;">]</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>z<span style="color: #009900;">)</span> <a href="http://inside-r.org/r-doc/base/as.integer"><span style="color: #003399; font-weight: bold;">as.integer</span></a><span style="color: #009900;">(</span>z<span style="color: #009900;">)</span> - <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
lambda <- <span style="color: #cc66cc;">1</span>
<span style="color: #009900;">(</span>y <- dat$y<span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>X <- model.Matrix<span style="color: #009900;">(</span>y ~ <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>Z <- model.Matrix<span style="color: #009900;">(</span>y ~ -<span style="color: #cc66cc;">1</span> + s1 + s2 + s3 + s4<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
XX <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span>
XZ <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span>
ZZ <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #009900;">)</span>
Xy <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span>
Zy <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span>
<span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a> <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span>XX<span style="color: #339933;">,</span> XZ<span style="color: #009900;">)</span><span style="color: #339933;">,</span>
cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;">t</span></a><span style="color: #009900;">(</span>XZ<span style="color: #009900;">)</span><span style="color: #339933;">,</span> ZZ + <a href="http://inside-r.org/r-doc/Matrix/Diagonal"><span style="color: #003399; font-weight: bold;">Diagonal</span></a><span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>ZZ<span style="color: #009900;">)</span><span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> * lambda<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>RHS <- rBind<span style="color: #009900;">(</span>Xy<span style="color: #339933;">,</span>
Zy<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>sol <- <a href="http://inside-r.org/r-doc/base/solve"><span style="color: #003399; font-weight: bold;">solve</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a><span style="color: #339933;">,</span> RHS<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #009900;">(</span>GEBV <- Z %*% sol<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span></pre>
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And the transcript:<br />
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<pre class="r geshifilter-R" style="font-family: monospace;">R <a href="http://inside-r.org/r-doc/base/version"><span style="color: #003399; font-weight: bold;">version</span></a> 2.14.2 <span style="color: #009900;">(</span><span style="color: #cc66cc;">2012</span>-02-<span style="color: #cc66cc;">29</span><span style="color: #009900;">)</span>
Copyright <span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/stats/C"><span style="color: #003399; font-weight: bold;">C</span></a><span style="color: #009900;">)</span> <span style="color: #cc66cc;">2012</span> The R Foundation <span style="color: black; font-weight: bold;">for</span> Statistical Computing
ISBN <span style="color: #cc66cc;">3</span>-<span style="color: #cc66cc;">900051</span>-07-<span style="color: #cc66cc;">0</span>
<a href="http://inside-r.org/r-doc/base/Platform"><span style="color: #003399; font-weight: bold;">Platform</span></a>: x86_64-pc-linux-gnu <span style="color: #009900;">(</span><span style="color: #cc66cc;">64</span>-<a href="http://inside-r.org/packages/cran/bit">bit</a><span style="color: #009900;">)</span>
R <a href="http://inside-r.org/r-doc/methods/is"><span style="color: #003399; font-weight: bold;">is</span></a> free software and comes <a href="http://inside-r.org/r-doc/base/with"><span style="color: #003399; font-weight: bold;">with</span></a> ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type <span style="color: blue;">'license()'</span> or <span style="color: blue;">'licence()'</span> <span style="color: black; font-weight: bold;">for</span> distribution details.
Natural language support but running <span style="color: black; font-weight: bold;">in</span> an English locale
R <a href="http://inside-r.org/r-doc/methods/is"><span style="color: #003399; font-weight: bold;">is</span></a> a collaborative project <a href="http://inside-r.org/r-doc/base/with"><span style="color: #003399; font-weight: bold;">with</span></a> many contributors.
Type <span style="color: blue;">'contributors()'</span> <span style="color: black; font-weight: bold;">for</span> more information and
<span style="color: blue;">'citation()'</span> on how to cite R or R packages <span style="color: black; font-weight: bold;">in</span> publications.
Type <span style="color: blue;">'demo()'</span> <span style="color: black; font-weight: bold;">for</span> some demos<span style="color: #339933;">,</span> <span style="color: blue;">'help()'</span> <span style="color: black; font-weight: bold;">for</span> on-<a href="http://inside-r.org/r-doc/stats/line"><span style="color: #003399; font-weight: bold;">line</span></a> <a href="http://inside-r.org/r-doc/utils/help"><span style="color: #003399; font-weight: bold;">help</span></a><span style="color: #339933;">,</span> or
<span style="color: blue;">'help.start()'</span> <span style="color: black; font-weight: bold;">for</span> an HTML <a href="http://inside-r.org/r-doc/base/browser"><span style="color: #003399; font-weight: bold;">browser</span></a> interface to help.
Type <span style="color: blue;">'q()'</span> to <a href="http://inside-r.org/r-doc/base/quit"><span style="color: #003399; font-weight: bold;">quit</span></a> R.
>
> <a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"MatrixModels"</span><span style="color: #009900;">)</span>
Loading required package: <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a>
Loading required package: <a href="http://inside-r.org/packages/cran/lattice">lattice</a>
Attaching package: ‘<a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a>’
The following object<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/mgcv/s"><span style="color: #003399; font-weight: bold;">s</span></a><span style="color: #009900;">)</span> are masked from ‘package:<a href="http://inside-r.org/r-doc/base"><span style="color: #006600; font-weight: bold;">base</span></a>’:
<a href="http://inside-r.org/r-doc/base/det"><span style="color: #003399; font-weight: bold;">det</span></a>
Attaching package: ‘MatrixModels’
The following object<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/mgcv/s"><span style="color: #003399; font-weight: bold;">s</span></a><span style="color: #009900;">)</span> are masked from ‘package:<a href="http://inside-r.org/r-doc/stats"><span style="color: #006600; font-weight: bold;">stats</span></a>’:
getCall
>
> dat <- <a href="http://inside-r.org/r-doc/base/data.frame"><span style="color: #003399; font-weight: bold;">data.frame</span></a><span style="color: #009900;">(</span> y=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: #cc66cc;">1.5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2.35</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3.4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2.31</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1.53</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ s1=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"AA"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Aa"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Aa"</span><span style="color: #339933;">,</span> <span style="color: blue;">"AA"</span><span style="color: #339933;">,</span> <span style="color: blue;">"aa"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ s2=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"Bb"</span><span style="color: #339933;">,</span> <span style="color: blue;">"BB"</span><span style="color: #339933;">,</span> <span style="color: blue;">"bb"</span><span style="color: #339933;">,</span> <span style="color: blue;">"BB"</span><span style="color: #339933;">,</span> <span style="color: blue;">"bb"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ s3=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"cc"</span><span style="color: #339933;">,</span> <span style="color: blue;">"CC"</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ s4=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"Dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"DD"</span><span style="color: #339933;">,</span> <span style="color: blue;">"dd"</span><span style="color: #339933;">,</span> <span style="color: blue;">"Dd"</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
>
> cols <- <a href="http://inside-r.org/r-doc/base/paste"><span style="color: #003399; font-weight: bold;">paste</span></a><span style="color: #009900;">(</span><span style="color: blue;">"s"</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> sep=<span style="color: blue;">""</span><span style="color: #009900;">)</span>
> dat<span style="color: #009900;">[</span><span style="color: #339933;">,</span> cols<span style="color: #009900;">]</span> <- <a href="http://inside-r.org/r-doc/base/lapply"><span style="color: #003399; font-weight: bold;">lapply</span></a><span style="color: #009900;">(</span>dat<span style="color: #009900;">[</span><span style="color: #339933;">,</span> cols<span style="color: #009900;">]</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/function"><span style="color: #003399; font-weight: bold;">function</span></a><span style="color: #009900;">(</span>z<span style="color: #009900;">)</span> <a href="http://inside-r.org/r-doc/base/as.integer"><span style="color: #003399; font-weight: bold;">as.integer</span></a><span style="color: #009900;">(</span>z<span style="color: #009900;">)</span> - <span style="color: #cc66cc;">1</span><span style="color: #009900;">)</span>
>
> lambda <- <span style="color: #cc66cc;">1</span>
>
> <span style="color: #009900;">(</span>y <- dat$y<span style="color: #009900;">)</span>
<span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span> <span style="color: #cc66cc;">1.50</span> <span style="color: #cc66cc;">2.35</span> <span style="color: #cc66cc;">3.40</span> <span style="color: #cc66cc;">2.31</span> <span style="color: #cc66cc;">1.53</span>
> <span style="color: #009900;">(</span>X <- model.Matrix<span style="color: #009900;">(</span>y ~ <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: blue;">"dsparseModelMatrix"</span>: <span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">1</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span>
<span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">1</span>
@ <a href="http://inside-r.org/r-doc/base/assign"><span style="color: #003399; font-weight: bold;">assign</span></a>: <span style="color: #cc66cc;">0</span>
@ <a href="http://inside-r.org/r-doc/stats/contrasts"><span style="color: #003399; font-weight: bold;">contrasts</span></a>:
named <a href="http://inside-r.org/r-doc/base/list"><span style="color: #003399; font-weight: bold;">list</span></a><span style="color: #009900;">(</span><span style="color: #009900;">)</span>
> <span style="color: #009900;">(</span>Z <- model.Matrix<span style="color: #009900;">(</span>y ~ -<span style="color: #cc66cc;">1</span> + s1 + s2 + s3 + s4<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/utils/data"><span style="color: #003399; font-weight: bold;">data</span></a>=dat<span style="color: #339933;">,</span> sparse=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: blue;">"dsparseModelMatrix"</span>: <span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">4</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
s1 s2 s3 s4
<span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span> . <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">1</span>
<span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">1</span> . <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">2</span>
<span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">2</span> . .
<span style="color: #cc66cc;">5</span> . . <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">1</span>
@ <a href="http://inside-r.org/r-doc/base/assign"><span style="color: #003399; font-weight: bold;">assign</span></a>: <span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">4</span>
@ <a href="http://inside-r.org/r-doc/stats/contrasts"><span style="color: #003399; font-weight: bold;">contrasts</span></a>:
named <a href="http://inside-r.org/r-doc/base/list"><span style="color: #003399; font-weight: bold;">list</span></a><span style="color: #009900;">(</span><span style="color: #009900;">)</span>
>
> XX <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #009900;">)</span>
> XZ <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> Z<span style="color: #009900;">)</span>
> ZZ <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #009900;">)</span>
>
> Xy <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>X<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span>
> Zy <- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span>Z<span style="color: #339933;">,</span> y<span style="color: #009900;">)</span>
>
> <span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a> <- rBind<span style="color: #009900;">(</span>cBind<span style="color: #009900;">(</span>XX<span style="color: #339933;">,</span> XZ<span style="color: #009900;">)</span><span style="color: #339933;">,</span>
+ cBind<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;">t</span></a><span style="color: #009900;">(</span>XZ<span style="color: #009900;">)</span><span style="color: #339933;">,</span> ZZ + <a href="http://inside-r.org/r-doc/Matrix/Diagonal"><span style="color: #003399; font-weight: bold;">Diagonal</span></a><span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/dim"><span style="color: #003399; font-weight: bold;">dim</span></a><span style="color: #009900;">(</span>ZZ<span style="color: #009900;">)</span><span style="color: #009900;">[</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span> * lambda<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">5</span> sparse <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgCMatrix"</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> s1 s2 s3 s4
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">6</span> <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">5</span>
s1 <span style="color: #cc66cc;">6</span> <span style="color: #cc66cc;">11</span> <span style="color: #cc66cc;">8</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">5</span>
s2 <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">8</span> <span style="color: #cc66cc;">10</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">3</span>
s3 <span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">7</span> <span style="color: #cc66cc;">5</span>
s4 <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">8</span>
>
> <span style="color: #009900;">(</span>RHS <- rBind<span style="color: #009900;">(</span>Xy<span style="color: #339933;">,</span>
+ Zy<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">1</span> <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgeMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">11.09</span>
s1 <span style="color: #cc66cc;">13.37</span>
s2 <span style="color: #cc66cc;">10.82</span>
s3 <span style="color: #cc66cc;">8.81</span>
s4 <span style="color: #cc66cc;">12.18</span>
>
> <span style="color: #009900;">(</span>sol <- <a href="http://inside-r.org/r-doc/base/solve"><span style="color: #003399; font-weight: bold;">solve</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/packages/cran/lhs">LHS</a><span style="color: #339933;">,</span> RHS<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">1</span> <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgeMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>
<span style="color: #009900;">(</span>Intercept<span style="color: #009900;">)</span> <span style="color: #cc66cc;">1.65468864</span>
s1 <span style="color: #cc66cc;">0.05223443</span>
s2 <span style="color: #cc66cc;">0.08655678</span>
s3 -<span style="color: #cc66cc;">0.05223443</span>
s4 <span style="color: #cc66cc;">0.45586081</span>
>
> <span style="color: #009900;">(</span>GEBV <- Z %*% sol<span style="color: #009900;">[</span>-<span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span><span style="color: #009900;">)</span>
<span style="color: #cc66cc;">5</span> x <span style="color: #cc66cc;">1</span> <a href="http://inside-r.org/r-doc/Matrix/Matrix"><span style="color: #003399; font-weight: bold;">Matrix</span></a> of <a href="http://inside-r.org/r-doc/base/class"><span style="color: #003399; font-weight: bold;">class</span></a> <span style="color: blue;">"dgeMatrix"</span>
<span style="color: #009900;">[</span><span style="color: #339933;">,</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">]</span>
<span style="color: #cc66cc;">1</span> <span style="color: #cc66cc;">0.6468864</span>
<span style="color: #cc66cc;">2</span> <span style="color: #cc66cc;">0.6289744</span>
<span style="color: #cc66cc;">3</span> <span style="color: #cc66cc;">0.9117216</span>
<span style="color: #cc66cc;">4</span> <span style="color: #cc66cc;">0.2775824</span>
<span style="color: #cc66cc;">5</span> <span style="color: #cc66cc;">0.3513919</span>
>
> <a href="http://inside-r.org/r-doc/base/proc.time"><span style="color: #003399; font-weight: bold;">proc.time</span></a><span style="color: #009900;">(</span><span style="color: #009900;">)</span>
user <a href="http://inside-r.org/r-doc/base/system"><span style="color: #003399; font-weight: bold;">system</span></a> elapsed
<span style="color: #cc66cc;">2.330</span> <span style="color: #cc66cc;">0.070</span> <span style="color: #cc66cc;">2.412</span> </pre>
</div>
</div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com6tag:blogger.com,1999:blog-6715598735361401237.post-80808908050444740962011-09-28T14:50:00.000+02:002011-09-28T14:50:20.147+02:00Polyploidy in sugarcane<div style="text-align: justify;">While reading <a href="http://www.warwick.ac.uk/statsdept/user-2011/">UseR conference</a> abstracts I came across this sentence: "Sugarcane is polypoid, i.e., has 8 to 14 copies of every chromosome, with individual alleles in varying numbers." Vau! This generates really complex genotype system. Say we have biallelic gene with alleles being A and B. In diploids the possible genotypes are AA, AB, and BB. Given the above sentence in sugarcane possible genotypes are any permutation of A's and B's in a series of 8 to 14 alleles. I am not sure if 9, 11, and 13 are also allowed, that is having even number of chromosomes. In any case such permutations result in really large numbers!</div><div style="text-align: justify;"><br />
</div><div style="text-align: justify;">Thinking about this a bit further it appears that the whole system is not that complex once we realize that genotyping does not tell as about the order of alleles (we can not distinguish between AB and BA), which simplifies from all possible permutations to all possible combinations, e.g., for biallelic gene in tetraploids this would correspond to 5 combinations and 16 permutations.</div><div style="text-align: justify;"><br />
</div><div style="text-align: justify;"></div><div style="text-align: justify;">Bellow is an R snippet that shows how to enumerate all possible combinations or permutations<br />
<br />
</div><div><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## Load package having nice combinatorial functions</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>package=<span style="color: blue;">"gtools"</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Specify alleles - just two for simplicity</span>
alleles <- <a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span><span style="color: blue;">"A"</span><span style="color: #339933;">,</span> <span style="color: blue;">"B"</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## Possible genotypes for diploids</span>
combinations<span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>alleles<span style="color: #009900;">)</span><span style="color: #339933;">,</span> r=<span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> v=alleles<span style="color: #339933;">,</span> repeats.allowed=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## [,1] [,2]</span>
<span style="color: #666666; font-style: italic;">## [1,] "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [2,] "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [3,] "B" "B" </span>
<span style="color: #666666; font-style: italic;">## Possible genotypes for tetraploids</span>
combinations<span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>alleles<span style="color: #009900;">)</span><span style="color: #339933;">,</span> r=<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> v=alleles<span style="color: #339933;">,</span> repeats.allowed=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>ž
<span style="color: #666666; font-style: italic;">## [,1] [,2] [,3] [,4]</span>
<span style="color: #666666; font-style: italic;">## [1,] "A" "A" "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [2,] "A" "A" "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [3,] "A" "A" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## [4,] "A" "B" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## [5,] "B" "B" "B" "B" </span>
permutations<span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>alleles<span style="color: #009900;">)</span><span style="color: #339933;">,</span> r=<span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> v=alleles<span style="color: #339933;">,</span> repeats.allowed=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## [,1] [,2] [,3] [,4]</span>
<span style="color: #666666; font-style: italic;">## [1,] "A" "A" "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [2,] "A" "A" "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [3,] "A" "A" "B" "A" </span>
<span style="color: #666666; font-style: italic;">## [4,] "A" "A" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## [5,] "A" "B" "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [6,] "A" "B" "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [7,] "A" "B" "B" "A" </span>
<span style="color: #666666; font-style: italic;">## [8,] "A" "B" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## [9,] "B" "A" "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [10,] "B" "A" "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [11,] "B" "A" "B" "A" </span>
<span style="color: #666666; font-style: italic;">## [12,] "B" "A" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## [13,] "B" "B" "A" "A" </span>
<span style="color: #666666; font-style: italic;">## [14,] "B" "B" "A" "B" </span>
<span style="color: #666666; font-style: italic;">## [15,] "B" "B" "B" "A" </span>
<span style="color: #666666; font-style: italic;">## [16,] "B" "B" "B" "B" </span>
<span style="color: #666666; font-style: italic;">## Possible genotypes for 8-14 ploids</span>
<a href="http://inside-r.org/r-doc/stats/spectrum"><span style="color: #003399; font-weight: bold;">spectrum</span></a> <- <a href="http://inside-r.org/r-doc/base/seq"><span style="color: #003399; font-weight: bold;">seq</span></a><span style="color: #009900;">(</span>from=<span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span> to=<span style="color: #cc66cc;">14</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/by"><span style="color: #003399; font-weight: bold;">by</span></a>=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span>
nS <- <a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/stats/spectrum"><span style="color: #003399; font-weight: bold;">spectrum</span></a><span style="color: #009900;">)</span>
retC <- <a href="http://inside-r.org/r-doc/base/vector"><span style="color: #003399; font-weight: bold;">vector</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mode"><span style="color: #003399; font-weight: bold;">mode</span></a>=<span style="color: blue;">"list"</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a>=nS<span style="color: #009900;">)</span>
retP <- <a href="http://inside-r.org/r-doc/base/vector"><span style="color: #003399; font-weight: bold;">vector</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/mode"><span style="color: #003399; font-weight: bold;">mode</span></a>=<span style="color: blue;">"list"</span><span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a>=nS<span style="color: #009900;">)</span>
<span style="color: black; font-weight: bold;">for</span><span style="color: #009900;">(</span>i <span style="color: black; font-weight: bold;">in</span> <span style="color: #cc66cc;">1</span>:nS<span style="color: #009900;">)</span> <span style="color: #009900;">{</span>
retC<span style="color: #009900;">[</span><span style="color: #009900;">[</span>i<span style="color: #009900;">]</span><span style="color: #009900;">]</span> <- combinations<span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>alleles<span style="color: #009900;">)</span><span style="color: #339933;">,</span> r=<a href="http://inside-r.org/r-doc/stats/spectrum"><span style="color: #003399; font-weight: bold;">spectrum</span></a><span style="color: #009900;">[</span>i<span style="color: #009900;">]</span><span style="color: #339933;">,</span> v=alleles<span style="color: #339933;">,</span> repeats.allowed=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
retP<span style="color: #009900;">[</span><span style="color: #009900;">[</span>i<span style="color: #009900;">]</span><span style="color: #009900;">]</span> <- permutations<span style="color: #009900;">(</span>n=<a href="http://inside-r.org/r-doc/base/length"><span style="color: #003399; font-weight: bold;">length</span></a><span style="color: #009900;">(</span>alleles<span style="color: #009900;">)</span><span style="color: #339933;">,</span> r=<a href="http://inside-r.org/r-doc/stats/spectrum"><span style="color: #003399; font-weight: bold;">spectrum</span></a><span style="color: #009900;">[</span>i<span style="color: #009900;">]</span><span style="color: #339933;">,</span> v=alleles<span style="color: #339933;">,</span> repeats.allowed=<span style="color: black; font-weight: bold;">TRUE</span><span style="color: #009900;">)</span>
<span style="color: #009900;">}</span>
combC <- <a href="http://inside-r.org/r-doc/base/sapply"><span style="color: #003399; font-weight: bold;">sapply</span></a><span style="color: #009900;">(</span>retC<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/nrow"><span style="color: #003399; font-weight: bold;">nrow</span></a><span style="color: #009900;">)</span>
combP <- <a href="http://inside-r.org/r-doc/base/sapply"><span style="color: #003399; font-weight: bold;">sapply</span></a><span style="color: #009900;">(</span>retP<span style="color: #339933;">,</span> <a href="http://inside-r.org/r-doc/base/nrow"><span style="color: #003399; font-weight: bold;">nrow</span></a><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/cbind"><span style="color: #003399; font-weight: bold;">cbind</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/stats/spectrum"><span style="color: #003399; font-weight: bold;">spectrum</span></a><span style="color: #339933;">,</span> combC<span style="color: #339933;">,</span> combP<span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## spectrum combC combP</span>
<span style="color: #666666; font-style: italic;">## [1,] 8 9 256</span>
<span style="color: #666666; font-style: italic;">## [2,] 10 11 1024</span>
<span style="color: #666666; font-style: italic;">## [3,] 12 13 4096</span>
<span style="color: #666666; font-style: italic;">## [4,] 14 15 16384</span></pre></div></div><a href="http://www.inside-r.org/pretty-r" title="Created by Pretty R at inside-R.org">Created by Pretty R at inside-R.org</a></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-54364632141048268812011-08-12T00:58:00.002+02:002013-08-13T16:28:15.086+02:00Setup up the inverse of additive relationship matrix in R<div style="text-align: justify;">
<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="4f8242d3-61bb-47f7-91a1-5735cc58e475" ginger_sofatware_uiphraseguid="31e4f939-5384-4519-9fb4-17f24e96624c" grcontextid="Additive genetic covariance:0">Additive genetic covariance</span> between individuals is one of the key concepts in <a href="http://en.wikipedia.org/wiki/Quantitative_genetics">(quantitative) genetics</a>. When doing the prediction of additive genetic values for pedigree members, we need the inverse of the so called numerator relationship matrix (NRM) or simply <b>A</b>. <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ed6e1979-2daa-4cd5-8917-64a4b46ab78a" ginger_sofatware_uiphraseguid="5c70fa58-612f-452d-8ca7-366e620e4ca5" grcontextid="Matrix:0">Matrix</span> <b>A</b> has off-diagonal entries equal to <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="06ecc7bf-312f-47fd-83a2-55c6ad9ab1b0" ginger_sofatware_uiphraseguid="5c70fa58-612f-452d-8ca7-366e620e4ca5" grcontextid="numerator:1">numerator</span> of <a href="http://en.wikipedia.org/wiki/Sewall_Wright">Wright</a>'s relationship coefficient and diagonal elements equal to 1 + inbreeding coefficient. I have blogged before about setting up such inverse in R using <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="bc74c083-b161-4ae0-b0c9-36e2974ad424" ginger_sofatware_uiphraseguid="ceffb02b-eb75-441b-881a-4aec7f0cca89" grcontextid="routine:0">routine</span> from the <a href="http://ggorjan.blogspot.com/2010/12/asreml-r-storing-inverse-as-matrix.html">ASReml-R program</a> or importing the inverse from the <a href="http://ggorjan.blogspot.com/2008/07/cfc-program-contribution-inbreeding-f.html">CFC program</a>. However, this is not the only way to "skin this cat" in R. I am aware of the following attempts to provide this feature in R for various things (the list is probably incomplete and I would grateful if you point me to other implementations):</div>
<div style="text-align: justify;">
</div>
<ul>
<li><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c5ac9d58-5452-48cb-b203-03fd872e038b" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="pedigree R package:0"><a href="http://cran.r-project.org/web/packages/pedigree/index.html">pedigree</a> R package</span> has function <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c55134b7-091e-4a9f-94b3-ba734c0eeaf3" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="makeA:1">makeA</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="54ef0db4-ba10-4f91-8043-76461efafd27" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:2">(</span>)</span> and <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6c80e36e-78e4-4bae-a3fa-30f712e9a8be" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="makeAinv:3">makeAinv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d3633e25-e401-4b9c-8f3d-8c523e10d05b" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:4">(</span>)</span> with obvious meanings; there is also <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="bef6c80f-2610-44f1-ac85-1542b8c0c933" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="calcG:5">calcG</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5085ae06-beb0-4138-9c4e-f43df2268d03" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:6">(</span>)</span> if you have a lot of marker data instead of pedigree information; there are also some other very handy functions <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c184cddb-2503-4545-8d00-f01e96916642" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="calcInbreeding:7">calcInbreeding</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ca68a7db-3255-46ef-8c31-9606599d5ff5" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:8">(</span>)</span>, <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d6a3917b-bd0f-40fc-bbb8-14c230e5e7eb" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="orderPed:9">orderPed</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="877041f4-6635-40c9-80fa-cf9826adb2b4" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:10">(</span>)</span>, <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="66c91248-9e79-45e8-95e1-1735cfffa0aa" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="trimPed:11">trimPed</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="bbd5256b-aaf6-4b43-9177-af436f0a0a48" ginger_sofatware_uiphraseguid="cf90fa5e-1002-420d-88d1-0f03342b9286" grcontextid="(:12">(</span>)</span>, etc.</li>
<li><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a 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href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"></a><a href="http://cran.r-project.org/web/packages/pedigree/index.html"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="fb640858-04a7-4038-b0bd-48f92e657eff" ginger_sofatware_uiphraseguid="280f6cb8-9e91-43fa-b156-857efaca912d" grcontextid="pedigreemm:0"></span></a><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0f81a7ea-af02-439b-97e4-d9ffdca3e72f" ginger_sofatware_uiphraseguid="280f6cb8-9e91-43fa-b156-857efaca912d" grcontextid="pedigreemm R package:1"><a href="http://cran.r-project.org/web/packages/pedigree/index.html"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="fb640858-04a7-4038-b0bd-48f92e657eff" ginger_sofatware_uiphraseguid="280f6cb8-9e91-43fa-b156-857efaca912d" grcontextid="pedigreemm:0">pedigreemm</span></a> R package</span> does not have <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="371bdeef-a622-489c-b917-66d220c832df" ginger_sofatware_uiphraseguid="280f6cb8-9e91-43fa-b156-857efaca912d" grcontextid="direct implementation:2">direct implementation</span> to get <b>A</b> inverse, but has all the needed ingredients, which makes the package even more interesting</li>
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href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a 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href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html"></a><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6b43d0c5-2ad4-47e5-8c33-779c0d225294" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="MCMCglmm R package:0"><a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html">MCMCglmm</a> R package</span> has <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f9f60e1c-a09f-4ab9-95be-837e902f73c1" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="function inverseA:1">function <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">inverseA</span></span><span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a4a034e0-c152-4f7a-b923-c12e1bc18310" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="(:2">(</span>)</span> which works with pedigree or <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f59e4ff2-bd6b-412d-b27a-98462fb117eb" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="phlyo:3">phlyo</span> objects; there are also handy functions such as <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a2962868-b6ec-4fd2-ba19-27ef6ee30d13" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="prunePed:4">prunePed</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="55de74c0-191f-4ddf-ae2f-29489497d9d9" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="(:5">(</span>)</span>, <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="1f6e6a1a-98e5-42a6-a43d-a2417baff353" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="rbv:6">rbv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7abf1297-3b4b-4bed-bc8f-d32b387cc196" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="(:7">(</span>)</span>, <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">sm2asreml<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8e70a974-3106-4ca6-968b-3732d2dc6aac" ginger_sofatware_uiphraseguid="c52e8164-9e77-4713-90c4-ff0c1c502c08" grcontextid="(:8">(</span>)</span>, etc.</li>
<li><a href="http://cran.r-project.org/web/packages/kinship/index.html"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3bb534d2-d5ce-4f52-acde-ec86150d10bd" ginger_sofatware_uiphraseguid="526144d3-8ea4-4252-bead-e3053fc28a25" grcontextid="kinship:0">kinship</span></a> and <a href="http://cran.r-project.org/web/packages/kinship2/index.html">kinship2</a> R packages have function <span class="Apple-style-span" style="font-family: 'Courier New', Courier, monospace;">kinship<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3aaeb51b-02e3-4c9b-a681-9ff8d667d9af" ginger_sofatware_uiphraseguid="526144d3-8ea4-4252-bead-e3053fc28a25" grcontextid="(:1">(</span>)</span> to <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="60433450-1292-4afd-b049-af84a2745dc5" ginger_sofatware_uiphraseguid="526144d3-8ea4-4252-bead-e3053fc28a25" grcontextid="setup kinship matrix:2">setup kinship matrix</span>, which is equal to the half of <b>A</b>; there are also nice functions for plotting pedigrees etc. (<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8d2c0ee1-327f-43af-a1fc-dc6b153461d6" ginger_sofatware_uiphraseguid="69e88601-5ce3-4de0-a6ba-cd2ce90833b4" grcontextid="see:0">see</span> also <a href="http://ggorjan.blogspot.com/2010/06/drawing-pedigree-examples-using-kinship.html">here</a>)</li>
<li><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6cc3cfe5-d889-4639-9da5-9f7f1ab137e8" ginger_sofatware_uiphraseguid="a63088fd-cd5a-40ec-9764-2d726ab167ab" grcontextid="see:0">see</span> also a series of <a href="http://www.ansci.wisc.edu/morota/R/relmat.html">R scripts</a> for relationship matrices </li>
</ul>
<div style="text-align: justify;">
As I described <a href="http://ggorjan.blogspot.com/2010/12/asreml-r-storing-inverse-as-matrix.html">before</a>, the interesting thing is that setting up <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ca18c911-4359-4d9e-8916-23f0c4386c1a" ginger_sofatware_uiphraseguid="7d055b29-6d9e-4488-ba0f-6f9c1e835f71" grcontextid="inverse:0">inverse</span> of <b>A</b> is easier and cheaper than setting up A and inverting it. This is very important for large applications. This is an old result using the following matrix theory. We can decompose <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d595fea0-3dad-4fbb-bec7-d09c36b7d187" ginger_sofatware_uiphraseguid="7c6fd696-9ae4-4f84-88db-2bdac1235636" grcontextid="symmetric positive definite matrix:0">symmetric positive definite matrix</span> as <b>A</b> = <b>LU</b> = <b>LL</b>'<b> </b>(Cholesky decomposition) or as <b>A</b> = <b>LDU</b> = <b>LDL</b>' (Generalized Cholesky decomposition), where <b>L</b> (<b>U</b>) is lower (upper) triangular, and <b>D</b> is <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7d804baa-61d9-4562-a491-dcbce1a52fd2" ginger_sofatware_uiphraseguid="7c6fd696-9ae4-4f84-88db-2bdac1235636" grcontextid="diagonal matrix:1">diagonal matrix</span>. Note that <b>L</b> and <b>U</b> in previous two equations are not the same thing (<b>L</b> from Cholesky is not equal to <b>L</b> from Generalized Cholesky decomposition)! Sorry for sloppy notation. In order to confuse you even more note that Henderson usually wrote <b>A</b> = <b>TDT</b>'. We can even do <b><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="4cbbc97d-09b4-4530-ae07-0c739949dee9" ginger_sofatware_uiphraseguid="fb1db044-55e1-4fea-987c-94c32e480e3c" grcontextid="A:0">A</span></b> = <b>LSSU</b>, where <b>S</b> diagonal is equal to the square root of <b>D</b> diagonal. This can get us back to <b>A</b> = <b>LU</b> = <b>LL</b>' as <b>LSSU</b> = <b>LSSL</b>' = <b>LS</b><b>S</b>'<b>L</b>' = <b>LS</b>(<b>LS</b>)'<b> = L</b>'<b>L</b> (be ware of sloppy notation)! The inverse rule says that inv(<b>A</b>) = inv(<b>LDU</b>) = inv(<b>U</b>) inv(<b>D</b>) inv(<b>L</b>) = inv(<b>L</b>)' inv(<b>D</b>) inv(<b>L</b>) = inv(<b>L</b>)' inv(<b>S</b>) inv(<b>S</b>) inv(<b>L</b>). I thank to <a href="http://stat.ethz.ch/people/maechler">Martin Maechler</a> for pointing out to the last (obviously) bit to me. In Henderson's notation this would be <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5c02e229-71f1-440b-ad38-68c09da930b8" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:0">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="10c549c5-bfc3-4a19-a53f-7d317e38a2fd" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:1">(</span><b>A</b>) = <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e3c31bc3-818d-4978-a15d-9b56361ceb04" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:2">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8aa41a66-95dd-4fab-b123-037b39345e43" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:3">(</span><b>T</b>)' <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="954c449c-b806-4b94-ad9a-576a13f5bcb5" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:4">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="008dca05-85e7-4649-99a9-95d5b8be63f9" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:5">(</span><b>D</b>) <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="86c587d1-c897-4e87-8e92-7c7772c1f930" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:6">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="dc106441-e629-430f-9226-1aaefe95db51" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:7">(</span><b>T</b>) = <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="2a7a9465-7b46-4d0b-9ea5-165d539a5a30" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:8">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d686ad43-6566-4049-96c5-bea760941407" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:9">(</span><b>T</b>)' <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="92a8e4dd-ac97-4af4-9b13-b94f1542b6a5" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:10">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="33ea773a-6009-4b4b-af47-1d66490b258a" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:11">(</span><b>S</b>) <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d503c0e1-4c10-40cf-93f0-970eae1273ba" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:12">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e2947084-846d-4b94-a6eb-3efcc2a7c606" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:13">(</span><b>S</b>) <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="dacdf8d2-769c-4ee6-bb78-cb121f3ea3f4" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="inv:14">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0bbef89d-978b-4c6d-92d8-6ddb37db98b7" ginger_sofatware_uiphraseguid="07c89417-df35-4ac0-b619-36bfefb2d6cf" grcontextid="(:15">(</span><b>T</b>) Uf ... The important bit is that with<b> </b>NRM (aka <b>A</b>) <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b321afac-3317-4bde-b0c8-e6fbd57b946d" ginger_sofatware_uiphraseguid="0126163f-69b1-473b-b718-acade914da22" grcontextid="inv:0">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a7708597-c33b-4814-9300-42790cc8854a" ginger_sofatware_uiphraseguid="0126163f-69b1-473b-b718-acade914da22" grcontextid="(:1">(</span><b>L</b>) has nice simple structure - it shows the directed graph of additive genetic values in pedigree, while <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="916eecdc-954b-49a8-b8b4-0a5428368f70" ginger_sofatware_uiphraseguid="0126163f-69b1-473b-b718-acade914da22" grcontextid="inv:2">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="825d2bf5-9346-4f10-ae59-af81104c8f61" ginger_sofatware_uiphraseguid="0126163f-69b1-473b-b718-acade914da22" grcontextid="(:3">(</span><b>D</b>) tells us about the precision (inverse variance) of additive genetic values given the additive genetic values of parents and therefore depends on knowledge of parents and their inbreeding (the more they are inbred less variation can we expect in their progeny). Both <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5b7f8c92-b4d5-4132-8fed-e29db7c049fe" ginger_sofatware_uiphraseguid="aad40df8-8963-4337-ab65-a6d0742ac606" grcontextid="inv:0">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="889892c8-292e-4a08-a370-bdc91b3f1a38" ginger_sofatware_uiphraseguid="aad40df8-8963-4337-ab65-a6d0742ac606" grcontextid="(:1">(</span><b>L</b>) and <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="44410d07-0afe-4dec-9b3a-6118f56e5cdd" ginger_sofatware_uiphraseguid="aad40df8-8963-4337-ab65-a6d0742ac606" grcontextid="inv:2">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d8819e28-dfe1-44b1-a005-02558dd1ebb9" ginger_sofatware_uiphraseguid="aad40df8-8963-4337-ab65-a6d0742ac606" grcontextid="(:3">(</span><b>D</b>) are easier to <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b900f916-f36c-47d6-90b1-4c000c80ec7d" ginger_sofatware_uiphraseguid="aad40df8-8963-4337-ab65-a6d0742ac606" grcontextid="setup:4">setup</span>.</div>
<br />
<div style="text-align: justify;">
Packages <a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html">MCMCglmm</a> and <a href="http://cran.r-project.org/web/packages/pedigree/index.html">pedigree</a> give us <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0741fee8-ae18-4020-9767-83e59f2b2059" ginger_sofatware_uiphraseguid="4cfb79c9-990b-4049-aded-0257809351b0" grcontextid="inv:0">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ba7fcf76-b474-498f-8b9a-dc7f7ddd95ce" ginger_sofatware_uiphraseguid="4cfb79c9-990b-4049-aded-0257809351b0" grcontextid="(:1">(</span><b>A</b>) directly (we can also get <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b34de3c7-e4ce-4d87-92b7-956bef46d500" ginger_sofatware_uiphraseguid="4cfb79c9-990b-4049-aded-0257809351b0" grcontextid="inv:2">inv</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d7ab43ad-6d9a-46e9-8c02-df9c6277e545" ginger_sofatware_uiphraseguid="4cfb79c9-990b-4049-aded-0257809351b0" grcontextid="(:3">(</span><b>D</b>) in <a href="http://cran.r-project.org/web/packages/MCMCglmm/index.html">MCMCglmm</a>), but <a href="http://cran.r-project.org/web/packages/pedigreemm/index.html"><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="963906c4-527a-421e-8181-9bcb642aca6d" ginger_sofatware_uiphraseguid="4cfb79c9-990b-4049-aded-0257809351b0" grcontextid="pedigreemm:4">pedigreemm</span></a> enables us to play around with the above matrix algebra and graph theory. First we need a small example pedigree. Bellow is an example with 10 members and there is also some inbreeding and some individuals have both, one, or no parents known. It is hard to see inbreeding directly from the table, but we will improve that later (see also <a href="http://ggorjan.blogspot.com/2010/06/drawing-pedigree-examples-using-kinship.html">here</a>).</div>
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<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="80dbfaa5-81e4-42b6-b7f7-f921d18a1cda" ginger_sofatware_uiphraseguid="1f09bf59-56c2-493c-b7e7-35d987fba1a4" grcontextid="ped:0">ped</span> <- <a href="http://inside-r.org/r-doc/base/data.frame"><span style="color: #003399; font-weight: bold;">d<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="aaa1e07f-ddd1-41b0-aa0e-6b667da77172" ginger_sofatware_uiphraseguid="1f09bf59-56c2-493c-b7e7-35d987fba1a4" grcontextid=".:1">a</span>ta.fr<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="01a603cc-d004-4518-b5f0-28a7d2b4f812" ginger_sofatware_uiphraseguid="1f09bf59-56c2-493c-b7e7-35d987fba1a4" grcontextid="(:2">a</span>me</span></a><span style="color: #009900;">(</span> i<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b7bf75fe-b6ff-4f19-b62f-001d361bdd5f" ginger_sofatware_uiphraseguid="1f09bf59-56c2-493c-b7e7-35d987fba1a4" grcontextid="(:3">d</span>=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">7</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">10</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
fid=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">4</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">5</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">8</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span>
mid=<a href="http://inside-r.org/r-doc/base/c"><span style="color: #003399; font-weight: bold;">c</span></a><span style="color: #009900;">(</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">3</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">6</span><span style="color: #339933;">,</span> <span style="color: black; font-weight: bold;">NA</span><span style="color: #339933;">,</span> <span style="color: #cc66cc;">9</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span></pre>
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Now we will create an object of a pedigree class and show the <b>A</b> = <b>U</b>'<b>U</b> stuff:</div>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## inst<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="be47a817-b89b-4d24-9393-3a59ab70cde6" ginger_sofatware_uiphraseguid="26e14926-2899-4f30-a1e0-40a6225b437d" grcontextid=".:0">a</span>ll.packa<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7be0a506-d3fb-4e72-9052-ac16d26b0b31" ginger_sofatware_uiphraseguid="26e14926-2899-4f30-a1e0-40a6225b437d" grcontextid="(:1">g</span>es(pkg<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5df44902-9a72-40cf-8f1c-4f354d7170d5" ginger_sofatware_uiphraseguid="26e14926-2899-4f30-a1e0-40a6225b437d" grcontextid="pedigreemm:2">s="pedigre</span>emm</span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; 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font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="483bfdd2-52b1-4dd0-9266-3b019e5dfee7" ginger_sofatware_uiphraseguid="546ce5a7-3418-431d-8545-22a9583c9c6e" grcontextid="(:1">a</span>ry</span></a><span style="color: #009900;">(</span>packag<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f10fedef-22bb-4729-8b7b-2c12d6711de3" ginger_sofatware_uiphraseguid="546ce5a7-3418-431d-8545-22a9583c9c6e" grcontextid="pedigreemm:2">e=<span style="color: blue;">"pedigre</span></span><span style="color: blue;">emm"</span><span style="color: #009900;">)</span>
ped2 <- <a href="http://inside-r.org/r-doc/base/with"><span style="color: #003399; font-weight: bold;">with</span></a><span style="color: #009900;">(</span>ped<span style="color: #339933;">,</span> <a href="http://inside-r.org/packages/cran/pedigree">pedigree</a><span style="color: #009900;">(</span>sire=fid<span style="color: #339933;">,</span> dam=mid<span style="color: #339933;">,</span> label=id<span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="609e3d6b-d435-48af-b8f1-6d010a024f03" ginger_sofatware_uiphraseguid="7d280fc9-4d1c-4717-a639-21dd7cf95561" grcontextid="relfactor:0">
U <- </span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="860ac4bf-d165-4bc9-9c00-8c1cec892af7" ginger_sofatware_uiphraseguid="7d280fc9-4d1c-4717-a639-21dd7cf95561" grcontextid="(:1">r</span>elfactor<span style="color: #009900;">(</span>pe<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="2cb6f819-44e1-4e18-852a-010909dd8228" ginger_sofatware_uiphraseguid="c2a1d7e7-5ca5-4696-a28e-021ed83be847" grcontextid="crossprod:1"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="55afa27d-3d7e-4374-96b4-817eeb2155ea" ginger_sofatware_uiphraseguid="c2a1d7e7-5ca5-4696-a28e-021ed83be847" grcontextid=";:0">d</span>2<span style="color: #009900;">)</span>
A &lt</span>;- <a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0efdbbef-a53a-484b-a52d-6e20efd6829f" ginger_sofatware_uiphraseguid="c2a1d7e7-5ca5-4696-a28e-021ed83be847" grcontextid="(:2">c</span>ro<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="402ec9a0-619a-49da-9847-8a449182f822" ginger_sofatware_uiphraseguid="81372184-c40d-4339-8231-3eec0e6531c4" grcontextid="round:0">sspro</span>d</span></a><span style="color: #009900;">(</span>U<span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="62fb67cb-7318-42f3-abff-474c4ad53513" ginger_sofatware_uiphraseguid="81372184-c40d-4339-8231-3eec0e6531c4" grcontextid="(:1">)</span></span>
<a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;">round</span></a><span style="color: #009900;">(</span>U<span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 sparse Matri<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="bd6e4517-aaa4-494a-bea8-9676865366d6" ginger_sofatware_uiphraseguid="5268c439-bee4-4de6-b396-529a9d304114" grcontextid="dtCMatrix:0">x of clas</span>s "dtCMatrix" </span>
<span style="color: #666666; font-style: italic;">## [1,] 1 . 0.50 . 0.25 0.25 0.25 0.25 . 0.12</span>
<span style="color: #666666; font-style: italic;">## [2,] . 1 0.50 0.50 0.50 0.75 0.62 0.62 . 0.31</span>
<span style="color: #666666; font-style: italic;">## [3,] . . 0.71 . 0.35 0.35 0.35 0.35 . 0.18</span>
<span style="color: #666666; font-style: italic;">## [4,] . . . 0.87 0.43 . 0.22 0.22 . 0.11</span>
<span style="color: #666666; font-style: italic;">## [5,] . . . . 0.71 . 0.35 0.35 . 0.18</span>
<span style="color: #666666; font-style: italic;">## [6,] . . . . . 0.71 0.35 0.35 . 0.18</span>
<span style="color: #666666; font-style: italic;">## [7,] . . . . . . 0.64 . . . </span>
<span style="color: #666666; font-style: italic;">## [8,] . . . . . . . 0.64 . 0.32</span>
<span style="color: #666666; font-style: italic;">## [9,] . . . . . . . . 1 0.50</span>
<span style="color: #666666; font-style: italic;">## [10,] . . . . . . . . . 0.66</span></pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b62cd907-4ba1-4a3d-8ca2-793ff9e1df24" ginger_sofatware_uiphraseguid="8ee25fab-6959-4626-94a0-f178bdca1af4" grcontextid="chol:0">To c</span>hec<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f6eb6bbe-fe02-46a2-a200-ebf00364d30f" ginger_sofatware_uiphraseguid="8ee25fab-6959-4626-94a0-f178bdca1af4" grcontextid="(:1">k</span></span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;">U<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7c9642a0-881b-4fda-bde6-e8f08099bc73" ginger_sofatware_uiphraseguid="77d07d95-7b57-4bd1-926d-b36c3c67b863" grcontextid="round:0"> - ch</span>ol(<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="cae8bad8-6832-42f1-aed6-c7332199a42d" ginger_sofatware_uiphraseguid="77d07d95-7b57-4bd1-926d-b36c3c67b863" grcontextid="(:1">A</span>)
<span style="color: #003399; font-weight: bold;">
</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #003399; font-weight: bold;"><a href="http://inside-r.org/r-doc/base/round">round</a></span><span style="color: #009900;">(</span>A<span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 sparse Matri<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5d82b3ce-d887-4210-95f3-cac0714d2b90" ginger_sofatware_uiphraseguid="4d98c707-4f83-45a0-982e-18a8d73e1a45" grcontextid="dsCMatrix:0">x of clas</span>s "dsCMatrix" </span>
<span style="color: #666666; font-style: italic;">## [1,] 1.00 . 0.50 . 0.25 0.25 0.25 0.25 . 0.12</span>
<span style="color: #666666; font-style: italic;">## [2,] . 1.00 0.50 0.50 0.50 0.75 0.62 0.62 . 0.31</span>
<span style="color: #666666; font-style: italic;">## [3,] 0.50 0.50 1.00 0.25 0.62 0.75 0.69 0.69 . 0.34</span>
<span style="color: #666666; font-style: italic;">## [4,] . 0.50 0.25 1.00 0.62 0.38 0.50 0.50 . 0.25</span>
<span style="color: #666666; font-style: italic;">## [5,] 0.25 0.50 0.62 0.62 1.12 0.56 0.84 0.84 . 0.42</span>
<span style="color: #666666; font-style: italic;">## [6,] 0.25 0.75 0.75 0.38 0.56 1.25 0.91 0.91 . 0.45</span>
<span style="color: #666666; font-style: italic;">## [7,] 0.25 0.62 0.69 0.50 0.84 0.91 1.28 0.88 . 0.44</span>
<span style="color: #666666; font-style: italic;">## [8,] 0.25 0.62 0.69 0.50 0.84 0.91 0.88 1.28 . 0.64</span>
<span style="color: #666666; font-style: italic;">## [9,] . . . . . . . . 1.0 0.50</span>
<span style="color: #666666; font-style: italic;">## [10,] 0.12 0.31 0.34 0.25 0.42 0.45 0.44 0.64 <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="56981447-d9c0-4fc2-b4bf-13e6b1b75474" ginger_sofatware_uiphraseguid="87162bce-dee1-4e3d-a447-1ad610dc361c" grcontextid="ote:0">0.5</span> </span></pre>
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<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5b711b0c-da35-4456-913c-930c1331124d" ginger_sofatware_uiphraseguid="73933fea-66e4-4dd3-960c-c5abd7a989a0" grcontextid="m:0">p</span>edigreem</div>
<div style="text-align: justify;">
m package uses Matrix classes in order to store only what we need to store, e.g., matrix <b>U</b> is triangula<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8016614a-57c0-44dc-8428-e37b750a84c3" ginger_sofatware_uiphraseguid="73933fea-66e4-4dd3-960c-c5abd7a989a0" grcontextid="dtCMatrix:1">r (t in "</span>dtCMatrix") and matrix <b>A</b> is symmetri<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6984fa24-a145-473a-9eff-7cd2f424e327" ginger_sofatware_uiphraseguid="73933fea-66e4-4dd3-960c-c5abd7a989a0" grcontextid="dsCMatrix:2">c (s in "</span>dsCMatrix"). To show the generalized Cholesky <b>A</b> = <b>LDU</b> (or using Henderson notation <b>A</b> = <b>T</b><b></b><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5c78fa52-cf89-4211-90b1-e95bae379408" ginger_sofatware_uiphraseguid="83253e90-cf79-48f7-9193-bdf867b441f8" grcontextid="gchol:0"><b>DT</b>') </span>we <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="79a00836-770a-442f-9297-b2912e44a46f" ginger_sofatware_uiphraseguid="83253e90-cf79-48f7-9193-bdf867b441f8" grcontextid="(:1">u</span>se gchol<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e1f81c71-decc-49b7-b2b9-ddf1383e957c" ginger_sofatware_uiphraseguid="83253e90-cf79-48f7-9193-bdf867b441f8" grcontextid="bdsmatrix:2">() from t</span>he <a href="http://cran.r-project.org/web/packages/bdsmatrix/index.html">bdsmatrix</a><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="00be7097-7949-42d0-b3af-2804c7c1f408" ginger_sofatware_uiphraseguid="05818056-cce2-436e-a83a-9f159291ffec" grcontextid="Matrix T:0"> R packa</span>ge. Matrix <b>T</b> shows the "flow" <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="1e02a3f6-0787-4dd8-8995-78e29a3473ba" ginger_sofatware_uiphraseguid="05818056-cce2-436e-a83a-9f159291ffec" grcontextid="pedigree:1">of genes</span> in pedigree.</div>
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<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">#<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="845f986c-8598-4c33-b1fd-fb08deb4b86b" ginger_sofatware_uiphraseguid="59d2c190-2152-4ea0-b3bb-0a5989c9d9ad" grcontextid=".:0">#</span> install<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="1c39ef08-2576-4761-983a-ac61cb237c34" ginger_sofatware_uiphraseguid="59d2c190-2152-4ea0-b3bb-0a5989c9d9ad" grcontextid="(:1">.</span>pac<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="dabd91d0-3ab7-43ea-84be-d0ca98aae5f8" ginger_sofatware_uiphraseguid="59d2c190-2152-4ea0-b3bb-0a5989c9d9ad" grcontextid="bdsmatrix:2">kages(pkg</span>s="<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="63f96452-2fa1-4b9a-a6dd-70021fd6cef4" ginger_sofatware_uiphraseguid="ef6a8629-821a-40c5-95c8-d28116415a17" grcontextid="library:0">bdsmatr</span>ix"<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="83087f95-a106-4aa0-85b9-ad00cedf8db2" ginger_sofatware_uiphraseguid="ef6a8629-821a-40c5-95c8-d28116415a17" grcontextid="(:1">)</span></span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">libra</span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="91dd36a6-bbe9-46d2-9422-0a96020900f0" ginger_sofatware_uiphraseguid="ef6a8629-821a-40c5-95c8-d28116415a17" grcontextid="bdsmatrix:2"><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">ry</span></a><span style="color: #009900;">(</span>packag</span>e=<span style="color: blue;">"bds<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="488c6f10-2f7d-4454-9f3c-462fa5a418f8" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid="tmp:0">mat</span>r</span><span style="color: blue;">ix"</span><span style="color: #009900;"></span><span style="color: #009900;"></span><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5cf41478-da5f-425c-9acf-8f0c95ea0b69" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid="gchol:2"><span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="2d2a2a38-b44f-44c9-abd3-377052ac5ce6" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid=";:1">)</span></span>
tmp</span> &l<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="68c4d931-8f9d-4d83-ba3c-ae8262bc5402" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid="(:3">t</span>;-<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="1eb173ce-4b69-4362-ac8b-2685b9981e00" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid=".:4"> </span>gchol<span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6a722fea-751d-405f-abad-7a9582bc5bb4" ginger_sofatware_uiphraseguid="625f66a7-aec7-4cfc-b1cd-05b4c650a86f" grcontextid="(:5">a</span>s.matrix</span></a><span style="color: #009900;"></span><span style="color: #009900;">(</span><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3f20a1c2-ed04-4432-8cc1-0bd117e3f142" ginger_sofatware_uiphraseguid="8ffcb2ed-a79a-4c27-a404-6c3b66266802" grcontextid="diag:1"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="22211329-0138-4671-b2df-d9012061171b" ginger_sofatware_uiphraseguid="8ffcb2ed-a79a-4c27-a404-6c3b66266802" grcontextid=";:0">A</span><span style="color: #009900;">)</span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;">)</span>
</span><a href="http://inside-r.org/r-doc/stats/D"><span style="color: #003399; font-weight: bold;">D</span></a><a href="http://inside-r.org/r-doc/stats/D"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/stats/D"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/stats/D"><span style="color: #003399; font-weight: bold;"></span></a> &<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="28f731b0-0e13-4c20-acd9-7b4f075ce145" ginger_sofatware_uiphraseguid="8ffcb2ed-a79a-4c27-a404-6c3b66266802" grcontextid="(:2">l</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="843b0262-aecc-4366-9c52-5fca3eb467a1" ginger_sofatware_uiphraseguid="8ffcb2ed-a79a-4c27-a404-6c3b66266802" grcontextid="tmp:3">t;-</span> <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span>tmp<span style="color: #009900;">)</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="52f3fdc1-a0bd-4865-8f83-00cd1fc59a8b" ginger_sofatware_uiphraseguid="bc2b7215-70c0-4d8b-a434-f08c7680cc59" grcontextid="(:0">
</span><span style="color: #009900;">(</span>T<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d9087f61-6805-44c2-b721-d4df2ebd9ece" ginger_sofatware_uiphraseguid="bc2b7215-70c0-4d8b-a434-f08c7680cc59" grcontextid=".:1"> </span><- <a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="de2de7d8-e0af-4ce9-8bdc-e66067116a91" ginger_sofatware_uiphraseguid="bc2b7215-70c0-4d8b-a434-f08c7680cc59" grcontextid="(:2">a</span></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a 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href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;">s.ma</span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: 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bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;"></span></a><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="94cf6ac0-cadc-4373-966e-55e5ab0fd3b5" ginger_sofatware_uiphraseguid="bc2b7215-70c0-4d8b-a434-f08c7680cc59" grcontextid="dtCMatrix:4"><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;">tri</span></a><a href="http://inside-r.org/r-doc/base/as.matrix"><span style="color: #003399; font-weight: bold;">x</span></a><span style="color: #009900;">(</span>tmp<span style="color: #009900;">)</span></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #339933;">,</span> <span style="color: blue;">"dtCMatrix"</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 sparse Matri<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="607927e5-7975-4a3a-9522-222bfd227f9d" ginger_sofatware_uiphraseguid="5a8aba79-845c-4b39-854d-07f2e53c0578" grcontextid="dtCMatrix:0">x of clas</span>s "dtCMatrix" </span>
<span style="color: #666666; font-style: italic;">## [1,] 1.000 . . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [2,] . 1.0000 . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [3,] 0.500 0.5000 1.00 . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [4,] . 0.5000 . 1.000 . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [5,] 0.250 0.5000 0.50 0.500 1.00 . . . . .</span>
<span style="color: #666666; font-style: italic;">## [6,] 0.250 0.7500 0.50 . . 1.00 . . . .</span>
<span style="color: #666666; font-style: italic;">## [7,] 0.250 0.6250 0.50 0.250 0.50 0.50 1 . . .</span>
<span style="color: #666666; font-style: italic;">## [8,] 0.250 0.6250 0.50 0.250 0.50 0.50 . 1.0 . .</span>
<span style="color: #666666; font-style: italic;">## [9,] . . . . . . . . 1.0 .</span>
<span style="color: #666666; font-style: italic;">## [10,] 0.125 0.3125 0.25 0.125 0.25 0.25 . 0.5 <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="84695493-87d3-47c9-93f4-c064eb36e51e" ginger_sofatware_uiphraseguid="3bca10e4-9f03-4313-b168-041511ff0d64" grcontextid="chec:0">0.5 </span>1</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">
</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">##<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="72ae4016-68e5-4191-b5b2-1606ad6cff1e" ginger_sofatware_uiphraseguid="97a0ab77-4117-406c-8b71-350fc80f3ba8" grcontextid="lt:0"> T</span>o chec</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">k</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">L </span></pre>
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<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ee024acd-a76a-4cd4-8ed3-03798c062436" ginger_sofatware_uiphraseguid="a68eea08-7924-4433-965a-557db02c159b" grcontextid="diag:0"><pre class="r geshifilter-R" style="font-family: monospace;">&</pre>
<pre class="r geshifilter-R" style="font-family: monospace;">lt;</pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3fc6d277-0905-4059-87cf-ba048283aacb" ginger_sofatware_uiphraseguid="a68eea08-7924-4433-965a-557db02c159b" grcontextid="(:1">-</span><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8695320f-05d8-452a-8a38-b4c79b2273b8" ginger_sofatware_uiphraseguid="a68eea08-7924-4433-965a-557db02c159b" grcontextid="sqrt:2"> T %</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="347065dd-2935-46a7-b297-305dbb7cb52b" ginger_sofatware_uiphraseguid="a68eea08-7924-4433-965a-557db02c159b" grcontextid="(:3">*</span>% <a href="http://inside-r.org/r-doc/base/diag"><span style="color: #003399; font-weight: bold;">diag</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">s<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="efff3d21-b700-4f06-a913-82bfae1b4b10" ginger_sofatware_uiphraseguid="9032d88e-3daa-449e-8a86-882afdc557e9" grcontextid="(:0">q</span>rt</span></a><span style="color: #009900;">(</span>D<span style="color: #009900;">)</span><span class="Apple-style-span" style="color: #009900;">)</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">L - t(U)</span></pre>
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Now the <b>A</b> inver<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8f3e3574-dd7a-412c-8e1b-487a35c5daee" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:0">s</span>e par<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="580e08fc-ce77-4514-9352-20f5c5bc5738" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:1">t (</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="42caefd2-40d7-4637-9f6b-68e979a21197" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:2">i</span>nv(<b>A</b><b></b><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="596f08c5-70c1-4bf6-98af-f5a6a51d1ffd" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:3">) =</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ac4a9992-b0f0-431b-9607-f69a38a7996b" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:4"> </span>inv<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a201a570-314e-45f9-9481-cee52f27b555" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:5">(<b>T</b>)</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="853f6d26-bd8c-41ed-957d-733685fa0286" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:6">'</span> inv(<b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><b></b><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6d6bb2e0-09ec-4cf4-ab6d-a61414d33017" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:7"><b>D</b><b></b>) </span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6de61fe2-cba4-4237-9d16-628a1c46ca66" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:8">i</span>nv(<b>T</b><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ade1fc56-69a6-4418-811b-38e4491d1856" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:9">) =</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b99a05a5-ef70-4ac0-9dd6-1e7716b278a4" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:10"> </span>inv<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="73d16b43-705c-4697-8171-16e516c8a933" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:11">(<b></b><b>T</b>)</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="fbfdc0c3-a39c-4ee2-b553-01114834743e" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:12">'</span> in<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ef224c8b-31a2-4720-bfca-152196df5326" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="inv:13">v(<b>S</b></span><b></b><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0c0b2eaa-7b3e-46b6-b020-2724d4626e98" ginger_sofatware_uiphraseguid="a179c6fb-5e21-42ea-ae73-fa4caf35477f" grcontextid="(:14">)</span> inv(<b>S</b>) inv(<b>T</b>) using Henderson's notation, note that ). The nice<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="9a9df74e-748f-425d-b585-a3f685f54f6c" ginger_sofatware_uiphraseguid="66ca3c07-a34d-4faf-9f37-5c808007d7a0" grcontextid="pedigreemm:0"> thing is </span>that pedigreemm authors provided funct<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="8724445b-ea20-4dad-925c-e01b9bce1d31" ginger_sofatware_uiphraseguid="66ca3c07-a34d-4faf-9f37-5c808007d7a0" grcontextid="inv:1">ion</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7c06b09f-5c3e-4f55-a6a3-fac27c7af47d" ginger_sofatware_uiphraseguid="66ca3c07-a34d-4faf-9f37-5c808007d7a0" grcontextid="(:2">s</span> to get<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3a7960c6-79dd-4eab-91f6-38fd1a6afc5a" ginger_sofatware_uiphraseguid="aafc185d-a3b0-41b7-8c76-aa2388038303" grcontextid="TInv:0"> inv</span>(<b>T</b>) and <b>D</b><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="1464e01c-1dc2-4386-adc8-52c659f27004" ginger_sofatware_uiphraseguid="aafc185d-a3b0-41b7-8c76-aa2388038303" grcontextid="(:1">.</span><br />
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #009900;">(</span>TIn<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3725905f-82d2-4d52-b84f-91cf077c9d5f" ginger_sofatware_uiphraseguid="aafc185d-a3b0-41b7-8c76-aa2388038303" grcontextid="sparseMatrix:2">v <- <a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;">as</span></a><span style="color: #009900;">(</span>p</span>ed2<span style="color: #339933;">,</span> <span style="color: blue;">"sparseMatrix"</span><span style="color: #009900;">)</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 sparse<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3ed0629b-cfd4-4b25-80b6-a95c3e02e4cf" ginger_sofatware_uiphraseguid="1288b5e7-55ed-48f7-81b9-ce20f72d6a30" grcontextid="dtCMatrix:0"> Matrix o</span>f c<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c6f345a1-3855-453a-b049-107a8a3024c0" ginger_sofatware_uiphraseguid="1288b5e7-55ed-48f7-81b9-ce20f72d6a30" grcontextid="unitriangular:1">lass "dtCMatr</span>ix" (unitriangular) </span>
<span style="color: #666666; font-style: italic;">## 1 1.0 . . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## 2 . 1.0 . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## 3 -0.5 -0.5 1.0 . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## 4 . -0.5 . 1.0 . . . . . .</span>
<span style="color: #666666; font-style: italic;">## 5 . . -0.5 -0.5 1.0 . . . . .</span>
<span style="color: #666666; font-style: italic;">## 6 . -0.5 -0.5 . . 1.0 . . . .</span>
<span style="color: #666666; font-style: italic;">## 7 . . . . -0.5 -0.5 1 . . .</span>
<span style="color: #666666; font-style: italic;">## 8 . . . . -0.5 -0.5 . 1.0 . .</span>
<span style="color: #666666; font-style: italic;">## 9 . . . . . . . . 1.0 .</span>
<span style="color: #666666; font-style: italic;">## 10 . . . . . <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0de6d99d-62e6-41b9-a233-ff261ff035b5" ginger_sofatware_uiphraseguid="28369770-be3a-4733-a289-17e7698e18c5" grcontextid="round:0">. .</span> -0<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="284c8e07-6cdf-40a3-80ca-15f5a98e853c" ginger_sofatware_uiphraseguid="28369770-be3a-4733-a289-17e7698e18c5" grcontextid="(:1">.</span>5 -0.5 1</span>
<a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;">round</span></a><span style="color: #009900;">(</span>D<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d9e08979-f08f-4378-8767-2c5c8f8314e6" ginger_sofatware_uiphraseguid="28369770-be3a-4733-a289-17e7698e18c5" grcontextid="(:2">I</span>nv <-<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="501e358f-e4af-477b-b56e-9898e66886b5" ginger_sofatware_uiphraseguid="28369770-be3a-4733-a289-17e7698e18c5" grcontextid="(:3"> </span><a href="http://inside-r.org/r-doc/Matrix/Diagonal"><span style="color: #003399; font-weight: bold;">Diagonal</span></a><span style="color: #009900;">(</span>x=<span style="color: #cc66cc;">1</span>/Dmat<span style="color: #009900;">(</span>ped2<span style="color: #009900;">)</span><span style="color: #009900;">)</span><span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 diago<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a4a66e7c-113f-43e9-8ddd-d990cba4b2be" ginger_sofatware_uiphraseguid="e2662379-220b-4b74-8453-4cca3fb1b77e" grcontextid="ddiMatrix:0">nal matri</span>x of class "ddiMatrix"</span>
<span style="color: #666666; font-style: italic;">## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]</span>
<span style="color: #666666; font-style: italic;">## [1,] 1 . . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [2,] . 1 . . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [3,] . . 2 . . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [4,] . . . 1.33 . . . . . .</span>
<span style="color: #666666; font-style: italic;">## [5,] . . . . 2 . . . . .</span>
<span style="color: #666666; font-style: italic;">## [6,] . . . . . 2 . . . .</span>
<span style="color: #666666; font-style: italic;">## [7,] . . . . . . 2.46 . . .</span>
<span style="color: #666666; font-style: italic;">## [8,] . . . . . . . 2.46 . .</span>
<span style="color: #666666; font-style: italic;">## [9,] . . . . . . . . 1 .</span>
<span style="color: #666666; font-style: italic;">## [10,] . . . . . . . <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="14d4b1ec-388f-4ce6-95ec-080546d07a56" ginger_sofatware_uiphraseguid="b2561df4-cc70-4e1e-91b9-b52b7ceb64d4" grcontextid="round:0"> . </span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="23210369-e49b-4ee6-9370-b5111c373f6a" ginger_sofatware_uiphraseguid="b2561df4-cc70-4e1e-91b9-b52b7ceb64d4" grcontextid="(:1"> </span> <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="06f15c0d-5c80-4b66-a26d-5083cf53fd63" ginger_sofatware_uiphraseguid="b2561df4-cc70-4e1e-91b9-b52b7ceb64d4" grcontextid="(:2"> </span>. 2.33</span>
<a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;">round</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;">t</span></a><span style="color: #009900;">(</span>T<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b4661571-a4f4-4bc0-a71c-768970df8a4c" ginger_sofatware_uiphraseguid="b2561df4-cc70-4e1e-91b9-b52b7ceb64d4" grcontextid="TInv:3">Inv<span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;">)</span></span><span style="color: #009900;"></span><span style="color: #009900;"></span> %*% DInv %*% TInv<span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span>
<span style="color: #666666; font-style: italic;">## 10 x 10 spa<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a60272b1-79e2-460d-947e-7e3ccd44831e" ginger_sofatware_uiphraseguid="a8f299d0-bbd8-440c-b994-1eff24367644" grcontextid="dgCMatrix:0">rse Matri</span>x of class "</span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a9bb8c51-52f4-407b-bb95-a77f3b74cf82" ginger_sofatware_uiphraseguid="0f8c57f3-a4a7-4b1d-b9e5-a28b18167cd7" grcontextid="round:0"><span style="color: #666666; font-style: italic;">dgC</span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;">Ma</span></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="a7132a35-5c93-4255-9ca7-2f3e4b7e7e22" ginger_sofatware_uiphraseguid="0f8c57f3-a4a7-4b1d-b9e5-a28b18167cd7" grcontextid="(:1">t</span></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; 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<span style="color: #666666; font-style: italic;">#</span><span style="color: #666666; font-style: italic;"># .</span></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; 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font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="4a9c91a2-c679-40e8-b571-1afea35f5eed" ginger_sofatware_uiphraseguid="0f8c57f3-a4a7-4b1d-b9e5-a28b18167cd7" grcontextid="(:5">u</span>nd</span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/round"><span style="color: #003399; font-weight: bold;"></span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">crossprod</span></a><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>DInv<span style="color: #009900;">)</span> %*% TInv<span style="color: #009900;">)</span><span style="color: #339933;">,</span> digits=<span style="color: #cc66cc;">2</span><span style="color: #009900;">)</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## 10 x 10 spa<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c850715c-f8cc-4365-a907-6ce7178560f2" ginger_sofatware_uiphraseguid="077c4637-6867-4cdf-b456-36007e03fc89" grcontextid="dsCMatrix:0">rse Matri</span>x of class "dsCMatrix"</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## [1,] 1.5 0.50 -1.0 . . . . . . . </span>
<span style="color: #666666; font-style: italic;">## [2,] 0.5 2.33 -0.5 -0.67 . -1.00 . . . . </span>
<span style="color: #666666; font-style: italic;">## [3,] -1.0 -0.50 3.0 0.50 -1.00 -1.00 . . . . </span>
<span style="color: #666666; font-style: italic;">## [4,] . -0.67 0.5 1.83 -1.00 . . . . . </span>
<span style="color: #666666; font-style: italic;">## [5,] . . -1.0 -1.00 3.23 1.23 -1.23 -1.23 . . </span>
<span style="color: #666666; font-style: italic;">## [6,] . -1.00 -1.0 . 1.23 3.23 -1.23 -1.23 . . </span>
<span style="color: #666666; font-style: italic;">## [7,] . . . . -1.23 -1.23 2.46 . . . </span>
<span style="color: #666666; font-style: italic;">## [8,] . . . . -1.23 -1.23 . 3.04 0.58 -1.16</span>
<span style="color: #666666; font-style: italic;">## [9,] . . . . . . . 0.58 1.58 -1.16</span>
<span style="color: #666666; font-style: italic;">## [10,] . . . . . . . -1.1<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="844fa925-0132-4cd0-9bef-cb18eeb26ab8" ginger_sofatware_uiphraseguid="67fa9ad8-1027-4a9b-a4f6-a4b1d53241fb" grcontextid="o:0">6</span> -<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b23381a2-8871-4e6a-b3b1-6d24fb4d048f" ginger_sofatware_uiphraseguid="456db685-be2e-4145-8a21-e17cd24fc4bd" grcontextid="heck:0">1.16</span></span></pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"></span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="57bd4c50-7684-4b98-bb3d-6b1faca9c90d" ginger_sofatware_uiphraseguid="9d7dd07a-7e2f-4684-8d52-ea4df6920acc" grcontextid="so:0"> </span>2</span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3f77ee55-74bf-4286-bd0f-dcab7f4667b8" ginger_sofatware_uiphraseguid="929ef739-54de-456c-aa37-444ba16d5003" grcontextid="ve:0">.3</span></span></pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">3</span></pre>
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</span></pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="Apple-style-span" style="color: black; font-style: normal;"></span></span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="Apple-style-span" style="color: black; font-style: normal;"></span></span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="Apple-style-span" style="color: black; font-style: normal;"></span></span></pre>
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;"><span class="Apple-style-span" style="color: black; font-style: normal;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="cf99f0f5-b823-4208-98cf-b8480629b806" ginger_sofatware_uiphraseguid="5e720bb1-80ec-4d8a-b30e-021ae254ae74" grcontextid="(:3">)</span> - </span></span><span style="color: #003399; font-weight: bold;"><a href="http://inside-r.org/r-doc/base/crossprod">crossprod</a></span><span style="color: #009900;">(</span><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>DInv<span style="color: #009900;">)</span> %*% TInv<span style="color: #009900;">)</span></pre>
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The <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="b9c61ea1-d2f4-4b2c-958b-9b99e14994c5" ginger_sofatware_uiphraseguid="783195a3-19c2-4bbf-ae0c-3e84aab9f9b7" grcontextid="crossprod:0">second me</span>thod (using crossprod) is preferred as <span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="bdd0592d-3091-4a84-a40d-6c669dd05224" ginger_sofatware_uiphraseguid="783195a3-19c2-4bbf-ae0c-3e84aab9f9b7" grcontextid="symmetric matrix:1">it leads directl</span>y <span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="19f188f5-43f2-4478-b6c1-34bc776d05ff" ginger_sofatware_uiphraseguid="783195a3-19c2-4bbf-ae0c-3e84aab9f9b7" grcontextid="dsCMatrix:2">to symmet</span>ric matrix (dsCMatrix<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c56bba7e-f63a-4d08-8e81-2cee353076e8" ginger_sofatware_uiphraseguid="783195a3-19c2-4bbf-ae0c-3e84aab9f9b7" grcontextid="upper or lower triangle:3">), which stores only up</span>per or lower triangle. And mak<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="ad2fd34e-3dbc-4ab9-aafe-96216e362a28" ginger_sofatware_uiphraseguid="60762634-5a99-4340-8f74-b092c01d564c" grcontextid="crossprod:0">e sure yo</span>u d<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="354415a2-88f2-41d5-b724-72bdb2af72de" ginger_sofatware_uiphraseguid="60762634-5a99-4340-8f74-b092c01d564c" grcontextid="(:1">o</span> not do <span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">c</span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; 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white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="75148a51-4d7c-419a-acf3-24ab51c7bc7f" ginger_sofatware_uiphraseguid="60762634-5a99-4340-8f74-b092c01d564c" grcontextid="(:3">p</span>ro</span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;"></span></a></span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/crossprod"><span style="color: #003399; font-weight: bold;">d</span></a><span style="color: #009900;">(</span>TInv %*% </span><span class="Apple-style-span" style="font-family: monospace; white-space: pre;"><a href="http://inside-r.org/r-doc/base/sqrt"><span style="color: #003399; font-weight: bold;">sqrt</span></a><span style="color: #009900;">(</span>DInv<span style="color: #009900;">)</span></span><span class="Apple-style-span" style="color: #009900; font-family: monospace; white-space: pre;">)</span> as it is the wrong order of matrices.</div>
<br />
<div style="text-align: justify;">
As promised we will display (plot<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="2855c83e-95ea-4ac5-9f2a-ef092801f7a9" ginger_sofatware_uiphraseguid="f95d1a93-5f99-4a38-9cc3-88f868e72c2b" grcontextid="conversion functions:0">) pedigree by use of</span> conversion functions of matrix objects to graph objects using the following code. Two examples are provided us<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="80481d31-3d8c-4a26-9193-7a9ac554b94d" ginger_sofatware_uiphraseguid="b335fd24-f80f-4847-8246-6ba3a19a286a" grcontextid="igraph:0">ing th</span>e graph and igraph packages. The former doe<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="779d559c-b352-46b7-8e76-90093347fe24" ginger_sofatware_uiphraseguid="5e0b6a96-de8a-4f5b-94f9-5c31e7b52e2c" grcontextid="on:0">s </span>a very good job on this examp<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="4ac0e943-3076-4e58-bfae-9a50f58b02f5" ginger_sofatware_uiphraseguid="5e0b6a96-de8a-4f5b-94f9-5c31e7b52e2c" grcontextid="igraph:1">le, bu</span>t otherwise igraph seems to have much nicer support for editing etc.</div>
<br />
<div style="overflow: auto;">
<div class="geshifilter">
<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## source("http://www.bioconductor<span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d48be0e7-1bf0-4ed1-8350-a53b258776ef" ginger_sofatware_uiphraseguid="9a687280-e768-4f15-a444-32c529d0ae0e" grcontextid="biocLite:0">.org/bio</span>cLi<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="6e8f70ee-7218-489f-a2c5-bc39aa55f8fc" ginger_sofatware_uiphraseguid="9a687280-e768-4f15-a444-32c529d0ae0e" grcontextid="(:1">t</span>e.R")</span>
<span style="color: #666666; font-style: italic;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="39f54164-00b4-4896-b0a0-19d85d477489" ginger_sofatware_uiphraseguid="9a687280-e768-4f15-a444-32c529d0ae0e" grcontextid="(:2">#</span># biocLite(pkgs=c("g<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="9e926786-e394-4e81-969b-fbc116d466af" ginger_sofatware_uiphraseguid="b1ba2f03-fe04-4494-813f-bee8bfe76dc7" grcontextid="library:0">raph", </span>"Rg<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f6625ccb-d4f4-49d3-a38d-72d46f761a53" ginger_sofatware_uiphraseguid="b1ba2f03-fe04-4494-813f-bee8bfe76dc7" grcontextid="(:1">r</span>aphviz"))</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">libr</span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">ary</span></a><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7a8309e5-05f5-4178-8e47-ccdf9a00971e" ginger_sofatware_uiphraseguid="a34cec67-8f3a-4576-93e5-959c0bc99263" grcontextid="library:0"><span style="color: #009900;">(</span>packag</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="372af232-b586-48f3-bd64-bd1c781acffc" ginger_sofatware_uiphraseguid="a34cec67-8f3a-4576-93e5-959c0bc99263" grcontextid="(:1">e</span>=<span style="color: blue;">"</span><span style="color: blue;">graph"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">library</span></a><span style="color: #009900;">(</span>pac<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="d5038c6b-89d3-4520-a32c-bdd29715d8ee" ginger_sofatware_uiphraseguid="ce781b91-2aea-4b93-9818-ef43789e931d" grcontextid="g:0">k</span>age=<span style="color: blue;">"R<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="44785626-01c7-4828-b157-dddd06d60248" ginger_sofatware_uiphraseguid="ce781b91-2aea-4b93-9818-ef43789e931d" grcontextid="(:1">g</span>r<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="52894a5c-4222-4032-bded-a33434a3a459" ginger_sofatware_uiphraseguid="ce781b91-2aea-4b93-9818-ef43789e931d" grcontextid="(:2">a</span>phviz"</span><span style="color: #009900;">)</span>
g <- <a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/methods/as"><span style="color: #003399; 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font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/t"><span style="color: #003399; font-weight: bold;"></span></a><span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="66ee10a6-da00-49c2-a3ac-ac45c249fae1" ginger_sofatware_uiphraseguid="f999cf9c-9772-4aa1-b154-e154e19c1e5c" grcontextid="(:1">(</span></span>TInv<span style="color: #009900;">)</span><span style="color: #009900;"></span><span style="color: #339933;">,</span> <span style="color: blue;">"grap<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="c84f3d4a-fc08-46b6-b91a-0c701a087901" ginger_sofatware_uiphraseguid="4a95a995-282b-43fd-beb7-2b474b68742b" grcontextid=".:0">h</span>"</span><span style="color: #009900;">)</span>
<a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;">plot</span></a><span style="color: #009900;">(</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="90b784bf-e91c-4c32-9e53-4a93dad28b5b" ginger_sofatware_uiphraseguid="4a95a995-282b-43fd-beb7-2b474b68742b" grcontextid="(:1">g</span><span style="color: #009900;">)</span></pre>
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<pre class="r geshifilter-R" style="font-family: monospace;"><span style="color: #666666; font-style: italic;">## in<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="5e62d511-e562-4f55-8396-12f515dd7d47" ginger_sofatware_uiphraseguid="4a95a995-282b-43fd-beb7-2b474b68742b" grcontextid="igraph:2">stall.</span>pac<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="2ade467b-41fd-4930-a306-cd392b5f02ba" ginger_sofatware_uiphraseguid="88e8044d-fc3e-4335-8d4d-37c54986c7d7" grcontextid="library:0">kages(p</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="eea66f85-161c-40a8-a917-39dbf8ae5d2d" ginger_sofatware_uiphraseguid="88e8044d-fc3e-4335-8d4d-37c54986c7d7" grcontextid="(:1">k</span>gs="igrap</span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; font-style: italic;"></span><span style="color: #666666; 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font-style: italic;">h")</span>
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font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;">bra</span></a><a href="http://inside-r.org/r-doc/base/library"><span style="color: #003399; font-weight: bold;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="30acaf6a-cec3-48f3-b4db-80cc5094e6dd" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid="i:0">r</span>y</span></a><span style="color: #009900;">(</span><span style="color: #009900;"></span>pa<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="815a735d-7125-4105-a54d-6cee99db66f6" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid="igraph:2"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="3406c23b-58c8-49bc-9f1c-e0b01766461f" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid=";:1">c</span>kage=</span><span style="color: blue;">"ig</span><span style="color: blue;"></span><span style="color: blue;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="982e9bbb-548a-421c-a003-611b30575c6f" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid=".:3">r</span>ap</span><span style="color: blue;"></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="cec43e40-a367-4096-96bc-d767e8f7ed4f" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid="graphNEL:5"><span style="color: blue;">h"</span><span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="cc9e6dd0-0ef8-4e7f-9ffa-bb643e5cf5c1" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid=".:4">)</span></span>
i &l</span>t;-<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e2b8755e-099e-452a-a0c9-b82af9122a7e" ginger_sofatware_uiphraseguid="7847dd48-e19d-41fa-b58f-708a183bc91e" grcontextid="(:6"> </span>igraph.from.g<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e7b39de8-a4ef-4e9c-8703-ed53fb96452a" ginger_sofatware_uiphraseguid="1b06c6dd-aeb6-441f-963e-7a7cde8e9a8e" grcontextid="(:0">r</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f4d375c8-460b-400a-9d1d-ba791f58095e" ginger_sofatware_uiphraseguid="1b06c6dd-aeb6-441f-963e-7a7cde8e9a8e" grcontextid="i:1">a</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="85619a3b-1bf1-4059-834c-6ec8a79300e1" ginger_sofatware_uiphraseguid="1b06c6dd-aeb6-441f-963e-7a7cde8e9a8e" grcontextid="):2">p</span>hNEL<span style="color: #009900;">(</span>graphNEL=g<span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="4e8ecf56-44d3-4ef3-b027-06fd6bfe39c0" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid="plot:0"><span style="color: #009900;">)</span><span style="color: #009900;"></span><span style="color: #009900;"></span>
V<span style="color: #009900;"></span><span style="color: #009900;">(</span></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span style="color: #009900;"></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="e1412731-131e-40fb-925c-50cbf46c72af" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid="(:1">i</span><span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f62e5371-a6e1-4d5b-b429-a68005e59779" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid="i:2">)</span></span>$label <- <span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;">1</span>:<span style="color: #cc66cc;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="f0f668f0-29c1-4002-8b54-836adcd84a80" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid=".:3">1</span></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: #cc66cc;"></span><span style="color: 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font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/plot"><span style="color: #003399; font-weight: bold;"></span></a><span style="color: #009900;"><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="7391c235-f73b-4491-ae10-1a77b7506b8d" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid=".:5">(</span></span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0cfc07c9-4fcb-475f-92c2-dd2712ce7ca7" ginger_sofatware_uiphraseguid="74b0001f-6d11-4d67-8f67-760b16bfae04" grcontextid="kawai:6">i<span style="color: #339933;">,</span><span style="color: #339933;"></span><span style="color: #339933;"></span><span style="color: #339933;"></span> <a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;">la</span></a></span><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;"></span></a><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;">yo</span></a><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;"></span></a><span class="GINGER_SOFATWARE_noSuggestion GINGER_SOFATWARE_correct" ginger_sofatware_markguid="cb5e0f92-dcb2-43f3-9537-13177ac94eaa" ginger_sofatware_uiphraseguid="d64ad29a-05d7-471a-9907-3e905ba75f91" grcontextid="tkplot:0"><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;">u</span></a><a href="http://inside-r.org/r-doc/graphics/layout"><span style="color: #003399; font-weight: bold;">t</span></a>=lay</span>out<span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="703116a0-9cc5-4ee2-bd9a-65ba7ce1b55f" ginger_sofatware_uiphraseguid="d64ad29a-05d7-471a-9907-3e905ba75f91" grcontextid="(:1">.</span><span class="GINGER_SOFATWARE_correct" ginger_sofatware_markguid="0f593eb2-af97-4e8e-b34a-1ec5c7e48a61" ginger_sofatware_uiphraseguid="d64ad29a-05d7-471a-9907-3e905ba75f91" grcontextid="i:2">k</span>amada.kawai<span style="color: #009900;">)</span>
## tkplot<span style="color: #009900;">(</span>i<span style="color: #009900;">)</span></pre>
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Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com1tag:blogger.com,1999:blog-6715598735361401237.post-72964568744196698372011-04-15T00:33:00.003+02:002011-04-15T01:24:43.618+02:00gRain: genetics example<div style="text-align: justify;"><a href="http://cran.r-project.org/web/packages/gRain/">gRain</a> is an R package for "probability propagation in graphical independence networks, also known as probabilistic expert systems (which includes Bayesian networks as a special case)". This package caught my attention because some genetic models can be seen as graphical models, which is a broader class of models encompassing <a href="http://en.wikipedia.org/wiki/Bayesian_network">Bayesian networks</a> or sometimes also called <a href="http://en.wikipedia.org/wiki/Directed_acyclic_graph">Directed Acyclic graphs (DAGs)</a>.<br /><br /></div><div style="text-align: justify;">A very simple example of DAG in genetics is to draw a pedigree of a small family (say father, mother, and child) with three nodes representing their genotype (g01, g02, and g03). Nodes are logically connected, father to child (g01 --> g03) and mother to child (g02 --> g03). Assume we observe some phenotype condition in a child and if we postulate that this phenotype is affected by genotype, we draw another connection between genotype and phenotype of a child (g03 --> p03).</div><div style="text-align: justify;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXLjO7jiFahuAvSv4x3_tqIc18gUZ5zHAMpk4rZ9MzqVsOwvBPlUDJRsbFq-JkoBPYTAOaZ2tBkGlIxc5qR0Pr4r1a-vY09bnfiQoiq-jxQD5fo53EywE0SB1FjGmHPGcSSWSzRXRfE484/s1600/DAG.png"><img style="display: block; margin: 0px auto 10px; text-align: center; cursor: pointer; width: 320px; height: 320px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXLjO7jiFahuAvSv4x3_tqIc18gUZ5zHAMpk4rZ9MzqVsOwvBPlUDJRsbFq-JkoBPYTAOaZ2tBkGlIxc5qR0Pr4r1a-vY09bnfiQoiq-jxQD5fo53EywE0SB1FjGmHPGcSSWSzRXRfE484/s320/DAG.png" alt="" id="BLOGGER_PHOTO_ID_5595574693196962546" border="0" /></a><div style="text-align: justify;">This kind of problems/models are often postulated and one might want to do some queries about the genotype of individuals given some data (observed phenotype and/or genotype). Can we do this in R? Yes, this can be neatly done with the gRain package.<br /><br /></div><div style="text-align: justify;">Before digging into the code we need to pause to see how can we describe the above model? If you have read at least some parts of Wikipedia links provided above than it should be straightforward to understand the following factorization of this simple model: p(g01, g02, g03, p03) = p(g01) p(g02) p(g03|g01, g02) p(p03|g03). The terms p(g01) and p(g02) are often called prior distributions (probabilities) of genotypes in some population. Term p(g03|g01, g02) describes probability of genotype in child (g03) given that we know the genotype of parents (g01 and g02). This is actually very simple part and often referred as transmission probability If there are only two alleles (gene variants) in population (A and a) and father is AA and mother is AA then child must also be AA or p(g03|g01=AA, g02=AA) = (1, 0, 0), where number show probability for genotype AA, Aa, and aa. The last term p(p03|g03) is often called penetrance function and tells us the conditional probability of some phenotype given the genotype data. Let us assume that we are interested in some binary condition, which is under very very large influence of genotype, but expressed primarily in individuals with genotype aa. Bellow is R code for specifying such a model with some additional details skipped in the text.<br /></div><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family:monospace;"><span style="color: rgb(102, 102, 102); font-style: italic;">## Set of genotype values</span><br />geno <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(0, 0, 255);">"AA"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"Aa"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"aa"</span><span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Prior allele frequencies in (founder) population</span><br />PrA <span style=""><-</span> <span style="color: rgb(204, 102, 204);">2</span><span style="">/</span><span style="color: rgb(204, 102, 204);">3</span><br /><span style="color: rgb(0, 153, 0);">(</span>Pra <span style=""><-</span> <span style="color: rgb(204, 102, 204);">1</span> <span style="">-</span> PrA<span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Prior genotype frequencies in (founder) population - according to Hardy-Weinberg's law</span><br /><span style="color: rgb(0, 153, 0);">(</span>gP <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span>PrA<span style="">*</span>PrA<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">2</span><span style="">*</span>PrA<span style="">*</span>Pra<span style="color: rgb(51, 153, 51);">,</span> Pra<span style="">*</span>Pra<span style="color: rgb(0, 153, 0);">)</span><span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Genotype frequencies in children given the genotype of parents - according to Mendel's law </span><br />gM_AA_AA <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">1</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_AA_Aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_AA_aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(0, 153, 0);">)</span><br /><br />gM_Aa_AA <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_Aa_Aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">4</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">4</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_Aa_aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(0, 153, 0);">)</span><br /><br />gM_aa_AA <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_aa_Aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">/</span><span style="color: rgb(204, 102, 204);">2</span><span style="color: rgb(0, 153, 0);">)</span><br />gM_aa_aa <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="color: rgb(0, 153, 0);">)</span><br /><br />gM <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span>gM_AA_AA<span style="color: rgb(51, 153, 51);">,</span> gM_AA_Aa<span style="color: rgb(51, 153, 51);">,</span> gM_AA_aa<span style="color: rgb(51, 153, 51);">,</span><br />gM_Aa_AA<span style="color: rgb(51, 153, 51);">,</span> gM_Aa_Aa<span style="color: rgb(51, 153, 51);">,</span> gM_Aa_aa<span style="color: rgb(51, 153, 51);">,</span><br />gM_aa_AA<span style="color: rgb(51, 153, 51);">,</span> gM_aa_Aa<span style="color: rgb(51, 153, 51);">,</span> gM_aa_aa<span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Set of phenotype values</span><br />phen <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(0, 0, 255);">"OK"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"NOK"</span><span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Error rate (= 1 - penetrance)</span><br />e <span style=""><-</span> <span style="color: rgb(204, 102, 204);">0.01</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Phenotype frequencies in individual given the genotype of individual - penetrance</span><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## OK NOK</span><br />p <span style=""><-</span> <a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(204, 102, 204);">1</span><span style="">-</span>e<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="">+</span>e<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(102, 102, 102); font-style: italic;">## AA</span><br /><span style="color: rgb(204, 102, 204);">1</span><span style="">-</span>e<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">0</span><span style="">+</span>e<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(102, 102, 102); font-style: italic;">## Aa</span><br /><span style="color: rgb(204, 102, 204);">0</span><span style="">+</span>e<span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(204, 102, 204);">1</span><span style="">-</span>e<span style="color: rgb(0, 153, 0);">)</span> <span style="color: rgb(102, 102, 102); font-style: italic;">## aa</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Graph - joint distribution</span><br />g01 <span style=""><-</span> cptable<span style="color: rgb(0, 153, 0);">(</span><span style="">~</span>g01<span style="color: rgb(51, 153, 51);">,</span> values=gP<span style="color: rgb(51, 153, 51);">,</span> <a href="http://inside-r.org/r-doc/base/levels"><span style="color: rgb(0, 51, 153); font-weight: bold;">levels</span></a>=geno<span style="color: rgb(0, 153, 0);">)</span><br />g02 <span style=""><-</span> cptable<span style="color: rgb(0, 153, 0);">(</span><span style="">~</span>g02<span style="color: rgb(51, 153, 51);">,</span> values=gP<span style="color: rgb(51, 153, 51);">,</span> <a href="http://inside-r.org/r-doc/base/levels"><span style="color: rgb(0, 51, 153); font-weight: bold;">levels</span></a>=geno<span style="color: rgb(0, 153, 0);">)</span><br />g03 <span style=""><-</span> cptable<span style="color: rgb(0, 153, 0);">(</span><span style="">~</span>g03 <span style="">+</span> g01 <span style="">+</span> g02<span style="color: rgb(51, 153, 51);">,</span> values=gM<span style="color: rgb(51, 153, 51);">,</span> <a href="http://inside-r.org/r-doc/base/levels"><span style="color: rgb(0, 51, 153); font-weight: bold;">levels</span></a>=geno<span style="color: rgb(0, 153, 0);">)</span><br />p03 <span style=""><-</span> cptable<span style="color: rgb(0, 153, 0);">(</span><span style="">~</span>p03 <span style="">+</span> g03<span style="color: rgb(51, 153, 51);">,</span> values=p<span style="color: rgb(51, 153, 51);">,</span> <a href="http://inside-r.org/r-doc/base/levels"><span style="color: rgb(0, 51, 153); font-weight: bold;">levels</span></a>=phen<span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Compile model</span><br />plist <span style=""><-</span> compileCPT<span style="color: rgb(0, 153, 0);">(</span><a href="http://inside-r.org/r-doc/base/list"><span style="color: rgb(0, 51, 153); font-weight: bold;">list</span></a><span style="color: rgb(0, 153, 0);">(</span>g01<span style="color: rgb(51, 153, 51);">,</span> g02<span style="color: rgb(51, 153, 51);">,</span> g03<span style="color: rgb(51, 153, 51);">,</span> p03<span style="color: rgb(0, 153, 0);">)</span><span style="color: rgb(0, 153, 0);">)</span><br />g <span style=""><-</span> <a href="http://inside-r.org/packages/cran/gRain"><span style="">grain</span></a><span style="color: rgb(0, 153, 0);">(</span>plist<span style="color: rgb(0, 153, 0);">)</span><br /><a href="http://inside-r.org/r-doc/base/summary"><span style="color: rgb(0, 51, 153); font-weight: bold;">summary</span></a><span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(0, 153, 0);">)</span><br /><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Plot the model</span><br />iplot<span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(0, 153, 0);">)</span></pre></div></div></div><br /><div style="text-align: justify;">Now if we want to query our model without any observed data, but just using parameter values for this population we use the following code:<br /></div><br /><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family:monospace;"><span style="color: rgb(102, 102, 102); font-style: italic;">## Query model given parameter values (=prior)</span><br />querygrain<span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(51, 153, 51);">,</span> nodes=<a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(0, 0, 255);">"g01"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"g02"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"g03"</span><span style="color: rgb(0, 153, 0);">)</span><span style="color: rgb(0, 153, 0);">)</span></pre></div></div><br /><div style="text-align: justify;">which returns probabilities shown bellow. Not really interesting, but we should not expect much as we did not observe any data. Genotype probabilities are equal for all individuals and they are completely defined by population parameters.<br /></div><br /><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family:monospace;"><span style="">$</span>g01<br />g01<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.1111111</span><br /><br /><span style="">$</span>g02<br />g02<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.1111111</span><br /><br /><span style="">$</span>g03<br />g03<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.4444444</span> <span style="color: rgb(204, 102, 204);">0.1111111</span></pre></div></div><br /><div style="text-align: justify;">Now we can add some data and repeat the query again.<br /></div><br /><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family:monospace;">g <span style=""><-</span> setFinding<span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(51, 153, 51);">,</span> nodes=<span style="color: rgb(0, 0, 255);">"p03"</span><span style="color: rgb(51, 153, 51);">,</span> states=<span style="color: rgb(0, 0, 255);">"NOK"</span><span style="color: rgb(0, 153, 0);">)</span><br /><a href="http://inside-r.org/r-doc/base/summary"><span style="color: rgb(0, 51, 153); font-weight: bold;">summary</span></a><span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(0, 153, 0);">)</span><br /><span style="color: rgb(102, 102, 102); font-style: italic;">## Query model given parameter values (=prior) + some data</span><br />querygrain<span style="color: rgb(0, 153, 0);">(</span>g<span style="color: rgb(51, 153, 51);">,</span> nodes=<a href="http://inside-r.org/r-doc/base/c"><span style="color: rgb(0, 51, 153); font-weight: bold;">c</span></a><span style="color: rgb(0, 153, 0);">(</span><span style="color: rgb(0, 0, 255);">"g01"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"g02"</span><span style="color: rgb(51, 153, 51);">,</span> <span style="color: rgb(0, 0, 255);">"g03"</span><span style="color: rgb(0, 153, 0);">)</span><span style="color: rgb(0, 153, 0);">)</span></pre></div></div><br /><div style="text-align: justify;">Results show probability of such finding (that phenotype condition was observed) given the defined model and parameters. Probability is not really high. Further on we get updated genotype probabilities and we can see the change due to introduction of phenotype information. Now we can claim with high confidence that child has genotype aa, while there is still quite some ambiguity about genotypes of parents as there are several possible combinations of parent genotypes that would give aa genotype in child (Aa x Aa, Aa x aa, aa x Aa, and aa x aa).<br /></div><br /><div style="overflow: auto;"><div class="geshifilter"><pre class="r geshifilter-R" style="font-family: monospace;">Independence <a href="http://inside-r.org/packages/cran/network"><span style="">network</span></a><span style="">:</span> Compiled<span style="">:</span> <span style="color: rgb(0, 0, 0); font-weight: bold;">TRUE</span> Propagated<span style="">:</span> <span style="color: rgb(0, 0, 0); font-weight: bold;">TRUE</span><br />Nodes <span style="">:</span> chr <span style="color: rgb(0, 153, 0);">[</span><span style="color: rgb(204, 102, 204);">1</span><span style="">:</span><span style="color: rgb(204, 102, 204);">4</span><span style="color: rgb(0, 153, 0);">]</span> <span style="color: rgb(0, 0, 255);">"g01"</span> <span style="color: rgb(0, 0, 255);">"g02"</span> <span style="color: rgb(0, 0, 255);">"g03"</span> <span style="color: rgb(0, 0, 255);">"p03"</span><br />Number of cliques<span style="">:</span> <span style="color: rgb(204, 102, 204);">2</span><br />Maximal clique size<span style="">:</span> <span style="color: rgb(204, 102, 204);">3</span><br />Maximal <a href="http://inside-r.org/r-doc/datasets/state"><span style="color: rgb(0, 51, 153); font-weight: bold;">state</span></a> <a href="http://inside-r.org/packages/cran/space"><span style="">space</span></a> <span style="color: rgb(0, 0, 0); font-weight: bold;">in</span> cliques<span style="">:</span> <span style="color: rgb(204, 102, 204);">27</span><br />Finding<span style="">:</span><br /> variable <a href="http://inside-r.org/r-doc/datasets/state"><span style="color: rgb(0, 51, 153); font-weight: bold;">state</span></a><br /><span style="color: rgb(0, 153, 0);">[</span><span style="color: rgb(204, 102, 204);">1</span><span style="color: rgb(51, 153, 51);">,</span><span style="color: rgb(0, 153, 0);">]</span> p03 NOK<br />Pr<span style="color: rgb(0, 153, 0);">(</span>Finding<span style="color: rgb(0, 153, 0);">)</span>= <span style="color: rgb(204, 102, 204);">0.1188889</span><br /><br /><span style="">$</span>g01<br />g01<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.03738318</span> <span style="color: rgb(204, 102, 204);">0.64797508</span> <span style="color: rgb(204, 102, 204);">0.31464174</span><br /><br /><span style="">$</span>g02<br />g02<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.03738318</span> <span style="color: rgb(204, 102, 204);">0.64797508</span> <span style="color: rgb(204, 102, 204);">0.31464174</span><br /><br /><span style="">$</span>g03<br />g03<br /> AA Aa aa<br /><span style="color: rgb(204, 102, 204);">0.03738318</span> <span style="color: rgb(204, 102, 204);">0.03738318</span> <span style="color: rgb(204, 102, 204);">0.92523364</span></pre></div></div><br />This is all for the purpose of this blog post, but it should be clear that it is very easy to extend our model either with model individuals (just defined them with cptable and compile in joint model) or with other stuff (more alleles leads to more genotypes, other penetrance function, sex-linked genes, ...).Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com1tag:blogger.com,1999:blog-6715598735361401237.post-54993816981764122762011-03-15T23:32:00.001+01:002011-03-15T23:34:20.609+01:00Nice simple notes on running R in parallel by Geyer<a href="http://www.stat.umn.edu/~charlie/parallel/">Here</a>, by Charles J. Geyer.Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-4371918319360089412011-01-28T18:44:00.003+01:002011-01-28T23:53:44.007+01:00Converting strsplit() output to a data.frame<div style="text-align: justify;"><a href="http://www.r-project.org/">R</a> has a nice set of utilities to work with strings. Function <span class="Apple-style-span" style="font-family: 'courier new'; ">paste</span> is surely one among these. It can be used to "glue" several strings with optional separator. The following example shows how <span class="Apple-style-span" style="font-family: 'courier new'; ">paste</span> can be used to create a new variable in a dataset:</div><span class="Apple-style-span" style="font-family: 'courier new'; "><blockquote><pre>dat <- data.frame(x=1:5, y=letters[1:5])</pre><pre>(dat$z <- with(dat, paste(x, y, sep="-")))</pre></blockquote></span><div style="text-align: justify;">Today I was in a situation where I only had column z and wanted to reverse the action of paste. Is there a way to do it? Not directly (AFAIK), but <span class="Apple-style-span" style="font-family: 'courier new'; ">strsplit</span> seems to be quite useful for this:</div><span class="Apple-style-span" style="font-family: 'courier new'; "><blockquote><pre>(tmp <- strsplit(x=dat$z, split="-"))</pre></blockquote></span><div style="text-align: justify;">However, the output of <span class="Apple-style-span" style="font-family: 'courier new'; ">strsplit</span> is a list object with elements (vectors) by the elements of my column z and not by split components. Consequently one can not convert strsplit output easily back to a data.frame as you can test yourself with:</div><meta equiv="content-type" content="text/html; charset=utf-8"><span class="Apple-style-span" style="font-family: 'courier new'; "><blockquote><pre>as.data.frame(tmp)</pre></blockquote></span><div style="text-align: justify;">Argh. I understand that <span class="Apple-style-span" style="font-family: 'courier new'; ">strsplit</span> is meant to be very general (say we could have unequal number of components in one element, e.g., <span class="Apple-style-span" style="font-family: 'courier new'; ">c("1-a-0", "1-a")</span>), but its output is really inconvenient for transformation to a data.frame. I came up with the following solution, which seems to work nicely and is quite fast.</div><pre><span class="Apple-style-span" style="font-family: 'courier new'; "><blockquote><pre>tmp <- unlist(strsplit(dat$z, split="-"))</pre><pre>cols <- c("x2", "y2")</pre><pre>nC <- length(cols)</pre><pre>ind <- seq(from=1, by=nC, length=nrow(dat))</pre><pre>for(i in 1:nC) {</pre><pre> dat[, cols[i]] <- tmp[ind + i - 1]</pre><pre>}</pre></blockquote></span></pre><div>Does anyone have a better (more obvious) solution?</div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com20tag:blogger.com,1999:blog-6715598735361401237.post-3923308753581533512010-12-18T21:18:00.007+01:002010-12-19T14:12:05.697+01:00ASReml-R: Storing A inverse as a sparse matrix<div style="text-align: justify;">I was testing <a href="http://www.vsni.co.uk/software/asreml/">ASReml-R</a> program (an R package that links propriety ASReml binaries that can be used only with valid licence) this week and had to do some manipulations with the numerator relationship matrix (A). ASReml-R provides a function (asreml.Ainverse) that can create inverse of A directly from the pedigree as this inverse is needed in pedigree based mixed model. Bulding inverse of A directly from a pedigree is a well known result dating back to Henderson in 1970s or so. The funny thing is that it is cheaper to setup inverse of A directly than to setup up first A and then to invert it. In addition, inverse of A is very spare so it is easy/cheap to store it. Documentation for asreml.Ainverse has a tiny example of usage. Since the result of this function is a list with several elements (data.frame with "triplets" for non-zero elements of inverse of A, inbreeding coefficients, ...) example also shows how to create a matrix object in R as shown bellow:</div><div style="text-align: justify;"></div><blockquote><pre>library(package="asreml")<br />## Create test pedigree<br />ped <- data.frame( me=c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),<br /> dad=c(0, 0, 0, 1, 1, 2, 4, 5, 7, 9),<br /> mum=c(0, 0, 0, 1, 1, 2, 6, 6, 8, 9))<br />## Create inverse of A in triplet form<br />tmp <- asreml.Ainverse(pedigree=ped)$ginv<br />## Create a "proper" matrix<br />AInv <- asreml.sparse2mat(x=tmp)<br />## Print AInv<br />AInv</pre></blockquote><div style="text-align: justify;"><div style="text-align: justify;"><div style="text-align: justify;">So the inverse of A would be:</div><div style="text-align: justify;"><blockquote><pre><span class="Apple-style-span"><span class="Apple-style-span" style="font-size: x-small;"> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]<br />[1,] 5 0 0 -2 -2 0 0.0 0.0 0.000000 0.000000<br />[2,] 0 3 0 0 0 -2 0.0 0.0 0.000000 0.000000<br />[3,] 0 0 1 0 0 0 0.0 0.0 0.000000 0.000000<br />[4,] -2 0 0 3 0 1 -2.0 0.0 0.000000 0.000000<br />[5,] -2 0 0 0 3 1 0.0 -2.0 0.000000 0.000000<br />[6,] 0 -2 0 1 1 4 -2.0 -2.0 0.000000 0.000000<br />[7,] 0 0 0 -2 0 -2 4.5 0.5 -1.000000 0.000000<br />[8,] 0 0 0 0 -2 -2 0.5 4.5 -1.000000 0.000000<br />[9,] 0 0 0 0 0 0 -1.0 -1.0 4.909091 -2.909091<br />[10,] 0 0 0 0 0 0 0.0 0.0 -2.909091 2.909091</span></span></pre></blockquote></div><div style="text-align: justify;">However, this is problematic as it creates a dense matrix - zero values are also stored (you can see them). If we would have 1,000 individuals, such a matrix would consume 7.6 Mb of RAM (= (((1000 * (1000 + 1)) / 2) * 16) / 2^20). This is not a lot, but with 10,000 individuals we would already need 763 Mb of RAM, which can create some bottlenecks. A solution is to create a sparse matrix using the <a href="http://www.blogger.com/cran.r-project.org/package=Matrix">Matrix</a> R package. Luckily we have all the ingredients prepared by asreml.Ainverse function - the triplets. However, the essential R code is a bit daunting and I had to test several options before I figured it out - code from my <a href="http://ggorjan.blogspot.com/2008/07/cfc-program-contribution-inbreeding-f.html">previous post</a> helped;)</div><div style="text-align: justify;"><blockquote><pre>## Load package<br />library(package="Matrix")<br />## Number of pedigree members<br />nI <- nrow(ped)<br />## Store inverse of A in sparse form<br />AInv2 <- as(new("dsTMatrix",<br /> Dim=c(nI, nI),<br /> uplo="L",<br /> i=(as.integer(tmp$Row) - 1L),<br /> j=(as.integer(tmp$Column) - 1L),<br /> x=tmp$Ainverse),<br /> "dsCMatrix")<br />## Add row and column names - optional<br />dimnames(AInv2) <- list(attr(x=tmp, which="rowNames"),<br /> attr(x=tmp, which="rowNames"))<br />## Print AInv<br />AInv2 <br /></pre></blockquote></div><div style="text-align: justify;">And the inverse of A is now:</div><div style="text-align: justify;"><blockquote><pre>10 x 10 sparse Matrix of class "dsCMatrix"<br />[[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]<br /> <br />1 5 . . -2 -2 . . . . . <br />2 . 3 . . . -2 . . . . <br />3 . . 1 . . . . . . . <br />4 -2 . . 3 . 1 -2.0 . . . <br />5 -2 . . . 3 1 . -2.0 . . <br />6 . -2 . 1 1 4 -2.0 -2.0 . . <br />7 . . . -2 . -2 4.5 0.5 -1.000000 . <br />8 . . . . -2 -2 0.5 4.5 -1.000000 . <br />9 . . . . . . -1.0 -1.0 4.909091 -2.909091<br />10 . . . . . . . . -2.909091 2.909091</pre></blockquote></div><div style="text-align: justify;">you can clearly see the structure and it soon becomes obvious why such a storage is more efficient.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">If we want to go back from matrix to triplet form (this might be useful if we want to create a matrix for programs as ASReml) we can use the following code:</div><div style="text-align: justify;"><blockquote><pre>## Convert back to triplet form - first the matrix<br />tmp2 <- as(AInv2, "dsTMatrix")<br />## ... - now to data.frame<br />tmp3 <- data.frame(Row=tmp2@i + 1, Column=tmp2@j + 1, Ainverse=tmp2@x)<br />## Sort<br />tmp3 <- tmp3[order(tmp3$Row, tmp3$Column), ]<br />## Test that we get the same stuff<br />any((tmp[, 3] - tmp3[, 3]) > 0)<br />## ASReml-R specificities<br />attr(x=tmp3, which="rowNames") <- rownames(tmp)<br />attr(x=tmp3, which="geneticGroups") <- c(0, 0)<br /></pre></blockquote></div></div></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com4tag:blogger.com,1999:blog-6715598735361401237.post-61458725101445952512010-07-28T19:30:00.004+02:002010-07-28T19:37:59.021+02:00IPSUR book used LyX-Sweave<div style="text-align: justify;">Jay Kerns wrote a book titled "Introduction to Probability and Statistics Using R" or IPSUR for short. He has put up a <a href="http://ipsur.r-forge.r-project.org/">web site</a> for the book and Rcmdr plugin. There are at least two very important points from my side (I did not read the book, yet): 1. it is free to download (thank you Jay!!!) and 2. it was written with the help of <a href="http://sites.google.com/site/gregorgorjanc/lyx-sweave">LyX-Sweave</a>. This shows that combination of <a href="http://www.lyx.org/">LyX</a> and <a href="http://www.statistik.lmu.de/~leisch/Sweave">Sweave</a> is really powerful.</div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com2tag:blogger.com,1999:blog-6715598735361401237.post-55747066719219265952010-06-30T20:35:00.006+02:002010-06-30T22:08:01.083+02:00Drawing pedigree examples using the kinship R package<div style="text-align: justify;">I have previously provided sort of an overview about <a href="http://ggorjan.blogspot.com/2008/09/drawing-pedigrees.html">plotting the pedigrees</a>, then specifically using the <a href="http://ggorjan.blogspot.com/2009/01/drawing-pedigree-examples-using.html">Graphiviz</a>, while I have lately used the <a href="http://www.scribd.com/doc/19956842/Fitting-pedigree-based-mixed-models-in-BUGS-software">TikZ LaTeX</a> (see slides 11-15) system (see <a href="http://www.texample.net/tikz/examples/">more example</a>). The later gives great (beautiful) results, but at the cost of writing TikZ code - it is not that horible, just time consuming - the same applies to Graphviz. Is there a quick way to plot a pedigree if we already have the data in the file. It is possible to do it in R using the <a href="http://cran.r-project.org/web/packages/kinship/index.html">kinship</a> package. Here is an example:</div><blockquote>ped <- data.frame( id=c( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11),<div> fid=c( 0, 0, 0, 3, 3, 5, 3, 6, 6, 0, 9),</div><div> mid=c( 0, 0, 0, 2, 1, 4, 4, 7, 7, 0, 10),</div><div> sex=c( 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2),</div><div> aff=0)</div><div>ped[11, "aff"] <- 1</div><div><br /></div><div>library(package="kinship")</div><div>ped <- with(ped, pedigree(id=id, dadid=fid, momid=mid, sex=sex, affected=aff))</div><div>plot(ped)</div></blockquote><div style="text-align: justify;">Which gives the following result. It is not great, but it is informative and easy to do. From a practical point of implementation all pedigree members need to have both parents known or no parents known.</div><div style="text-align: center;"><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFoZrf6v_Y-3xs1-Hw3z-2p29T6spcthTZ3SRcbUr3sJvCvCQbeT9KE-kj49qFnooWEXqrAJmrgu8PCK9ZKhUteRsGFuz7FtRJKIcEy8aeLyoq5cM-yzlb1TIQMqX_zn3pymB-S4UO1oaH/s1600/kinship-pedigree.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 360px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFoZrf6v_Y-3xs1-Hw3z-2p29T6spcthTZ3SRcbUr3sJvCvCQbeT9KE-kj49qFnooWEXqrAJmrgu8PCK9ZKhUteRsGFuz7FtRJKIcEy8aeLyoq5cM-yzlb1TIQMqX_zn3pymB-S4UO1oaH/s320/kinship-pedigree.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5488660049496775090" /></a><br /></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com1tag:blogger.com,1999:blog-6715598735361401237.post-67595171905081308352010-06-29T15:14:00.004+02:002010-06-29T15:19:09.205+02:00Sweave.sh in Eclipse-StatET<div style="text-align: justify;">Sébastien Bihorel sent the following instructions on how to use my <a href="http://cran.r-project.org/contrib/extra/scripts/Sweave.sh">sweave.sh</a> shell script in <a href="http://www.walware.de/goto/statet">Eclipse-StatET</a>.</div><div><blockquote>1- First, you need to know the path to your TEXINPUTS settings. Type R CMD env |grep TEXINPUTS in a shell. In my installation (opensuse 11.2), the shell returned the following<br />TEXINPUTS=.::/usr/lib/R/share/texmf:<br /><br />2- Edit your .bashrc file (located in your home directory) and add the following statement<br />export TEXINPUTS<br /><br />3- Download Gregor Gorjanc's sweave.sh script at http://cran.r-project.org/contrib/extra/scripts/Sweave.sh. Copy it to /usr/local/bin, rename the file to sweave (mv sweave.sh sweave) and make the file executable (chmod +ax sweave) if it is not already.<br /><br />4- Open Eclipse and create a new Program in External Tools Configuration using the following settings:<br />>Main:<br />- location: /usr/local/bin/sweave<br />- working directory: ${container_loc}<br />- Arguments: -ld ${resource_loc}<br /><br />>Refresh:<br />no selection<br /><br />>Build:<br />Build before launch: checked<br />The project containing the selected resource: checked<br />Include referenced projects: checked<br /><br />>Environment: added a new variable<br />Variable: TEXINPUTS<br />Value: .:/usr/lib/R/share/texmf: <- Use here the path obtained at step 1 (for some reason you have to add .: before the path and : after. Do not use quotes around the Value) Append environment to native environment: checked >Common:<br />Local file: checked<br />Console encoding: default - inherited (UTF-8)<br />Standard Input and Ouput: Allocate console<br />Launch in background: checked<br /><br /><br />Now you should be able to see sweave as a new program in your main screen. Hope it helps<br /><br />Sebastien</blockquote><br /></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-71592166723147959802010-01-21T20:10:00.005+01:002010-07-31T18:03:08.857+02:00R AnalyticFlow<a href="http://www.ef-prime.com/products/ranalyticflow_en/index.html">R AnalyticFlow</a> seems to be a nice tool to have a good overview over the analysis. The same kind of mode is available in <a href="http://www.ailab.si/orange/">Orange</a> and <a href="http://www.sas.com/technologies/bi/query_reporting/guide/">SAS Enterprise Guide</a>. I have not tried it yet, though. Does anyone have any experiences with it?<div><br /></div><div>Update on 2010-07-31: there is also <a href="http://www.red-r.org">Red-R</a>, which is a "sort of mixture" of R and <a href="http://www.ailab.si/orange/">Orange</a>.<br /><br /><div style="text-align: center;"><a href="http://www.ef-prime.com/products/ranalyticflow_en/index.html">R AnalyticFlow</a><br /><a href="http://www.ailab.si/orange/"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 252px; height: 190px;" src="http://www.ef-prime.com/products/ranalyticflow/img/screen2_en.jpg" alt="" border="0" />Orange</a><br /></div><div style="text-align: center;"><a href="http://www.sas.com/technologies/bi/query_reporting/guide/"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 95%;" src="http://www.ailab.si/orange/snaps/lr-nbc-nomogram.gif" alt="" border="0" />SAS Enterprise Guide</a></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.sas.com/resources/screenshot/sas-enterprise-guide-1-thumb.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 230px; height: 186px;" src="http://www.sas.com/resources/screenshot/sas-enterprise-guide-1-thumb.jpg" alt="" border="0" /></a><br /></div></div><br /><br /><object width="90%"><param name="movie" value="http://www.youtube.com/v/QyjOlAd1fF8&color1=0xb1b1b1&color2=0xd0d0d0&hl=en_US&feature=player_embedded&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowScriptAccess" value="always"></param><embed src="http://www.youtube.com/v/QyjOlAd1fF8&color1=0xb1b1b1&color2=0xd0d0d0&hl=en_US&feature=player_embedded&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" allowScriptAccess="always" width="90%" ></embed></object>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com11tag:blogger.com,1999:blog-6715598735361401237.post-60671087027336271622009-12-13T21:16:00.003+01:002009-12-13T21:27:49.816+01:00Galton's quincunx in R<div style="text-align: justify;"><a href="http://ablejec.nib.si/">Andrej Blejec</a> has a very nice R <a href="http://ablejec.nib.si/R/quincunx.pdf">demo</a> of Galton's quincunx (<a href="http://www.bun.kyoto-u.ac.jp/%7Esuchii/quinc.html">link1</a>, <a href="http://en.wikipedia.org/wiki/Bean_machine">link2</a>). It is a bit tedious to copy the code from PDF to R console, but it is worth the effort as the demo simulation clearly shows the nature of quincunx. After a bit of search I also found a similar function <a href="http://bm2.genes.nig.ac.jp/RGM2/R_current/library/animation/man/quincunx.html">quincunx</a> in the <a href="http://cran.r-project.org/web/packages/animation">animation</a> R package by Yihui Xi. </div><br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://mathworld.wolfram.com/images/eps-gif/GaltonBoard_1000.gif"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 25%;" src="http://mathworld.wolfram.com/images/eps-gif/GaltonBoard_1000.gif" alt="" border="0" /></a> Image source: <a href="http://mathworld.wolfram.com/GaltonBoard.html">Wolfram MathWorld</a></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-45143459349008866802009-11-12T19:37:00.003+01:002009-11-12T19:46:01.060+01:00Sweave-Lyx from terminal on MacMark Heckmann writes:<br /><blockquote>In your paper "<a href="http://gregor.gorjanc.googlepages.com/lyx-sweave">Using Sweave with Lyx</a>" (great work bty) you pointed out that one can see the sweave error code when processing when starting lyx from the terminal. I just changed from Windows to Mac so that's new for me. Could you send me a few lines how to do that, that is how to operate lyx from terminal and sweave the content from the terminal.</blockquote>I am not familiar with Mac, though would be happy to own one;) Since Mac OS is build on top of some linux/unix like system you need to start the terminal (console) with shell and find the lyx binary. Perhaps something like this on my linux box (text following $ are shell commands)<br /><br /># Find the lyx binary<br />$ which lyx<br />/usr/bin/lyx<br /><br /># Start lyx from console<br />$ lyx&Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-24934757611341521042009-10-13T21:01:00.003+02:002009-10-13T21:46:02.867+02:00RExcel<div style="text-align: justify;">I am not a fan of MS Windows software. However, the reality is that majority of people use it and it is often easier for me to live with this than to convert the sorounding souls. Additionally I am find ing out lately that majority of my favourite open-source programs work on all major platforms: MS Windows, Mac, and UNIX/Linux. Then there is no problem for me to work on any of these systems. MS Excel tool is similarly very widely used by mases, but not really powerfull when it comes to data analysis. However, we must admit that it is jolly usefull for handling medium sized data and that majority of people perform analyses with Excel. For those that can not live without Excel and have some working knowledge of <a href="http://www.r-project.org">R</a> I suggest to take a look at the <a href="http://rcom.univie.ac.at/">RExcel</a> and its <a href="http://rcom.univie.ac.at/RExcelDemo">demo video</a> (28 min!). It seems to be very nicely integrated - Excel keeps tracks of all the dependencies, while R takes care of the computations. Of course you can do the same stuff in R, by reruning the script for each change, but the interactivity offered by the Excel has its own merit. Regarding the quality of graphics it is obvious that Excel plots can not match with R. But if you need some interactivity (imagine you would like to study the effect of a particular parameter on distribution density), then Excel plots are good enough.<br /></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com5tag:blogger.com,1999:blog-6715598735361401237.post-48323548919816480382009-10-02T21:09:00.004+02:002009-10-02T21:16:33.709+02:00smoothScatter in base R<div style="text-align: justify;">smoothScatter function is now available also in base R - in the recommended package graphics that is shipped with R. Originally this function was in the <a href="http://www.bioconductor.org/packages/2.3/bioc/html/geneplotter.html">genepplotter</a> package from <a href="http://www.blogger.com/www.bioconductor.org">Bioconductor</a>. I really like it since it can nicely plot large datasets. Bellow is an example figure (also available at <a href="http://addictedtor.free.fr/graphiques/RGraphGallery.php?graph=139">R Graph Gallery</a>). Simply start R and type ?smoothScatter to get familiar with this function.</div><div style="text-align: center;"><a href="http://addictedtor.free.fr/graphiques/RGraphGallery.php?graph=139"><img src="http://addictedtor.free.fr/graphiques/graphiques/graph_139.png" width="100%" height="100%" /></a></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-64338427864387769702009-09-03T09:29:00.006+02:002009-09-21T21:17:31.101+02:00Fitting lactation curves/functions in R<div style="text-align: justify;">It is quite some time ago since I wrote a set of lactation curves/functions in <a href="http://www.r-project.org/">R</a>. I put those functions in the animSci package. However, the package is in a mess for quite some time now - I was adding some new functions, but did not have time to finish the job properly. This is also the reason that package was not published. I got several inquries about the lactation functions. Therefore, I compiled the package and checked that lactation curves work as they should. The package is now published <a href="http://gregor.gorjanc.googlepages.com/software">here</a> with a warning.</div><br /><div style="text-align: justify;">The key fact to fit a particular lactation curve in R is to create a function that will take a numeric variable (days in milk) and create a design matrix that can be fed to model fitting function such as lm() or similar, e.g.,</div><br /><blockquote><pre>someFunc <- function(x, ...) ... lm(y ~ someFunc(x)) </pre></blockquote><br /><div style="text-align: justify;">It must be noted that this approach is not the most efficient for large datasets, since design matrix can be large, but this is a well known problem with using lm() in R. I implemented four lactation functions: Wood, Wilmink, Ali-Schaeffer, and Guo-Swalve, but others can be added. Bellow is the R code to run the lactation curves example on a data set of four milk traits in goats and the resulting figure. It would be interesting to compare this functions with Legendre polynomials (see <a href="http://ggorjan.blogspot.com/2009/02/fitting-legendre-orthogonal-polynomials.html">here</a>) and splines.</div><br /><blockquote><pre>## Add my repository<br />tmp <- c("http://gregor.gorjanc.googlepages.com", <br /> contrib.url(repos=getOption("repos"),<br /> type=getOption("pkgType")))<br /><br />## Install the package<br />install.packages("animSci", contriburl=tmp, dep=TRUE)<br /><br />## Load the package<br />library(package="animSci")<br /><br />## Run the lactation curve examples<br />example(topic="lactCurves")</pre></blockquote><br /><br />P.S. I got a nice <a href="http://blog.revolution-computing.com/2009/09/using-r-to-analyze-milk-yields.html">cover up</a> from David Smith.<br /><br /><a title="View Some lactation curves for milk traits in goat on Scribd" href="http://www.scribd.com/doc/19380821/Some-lactation-curves-for-milk-traits-in-goat" style="margin: 12px auto 6px; font-family: Helvetica,Arial,Sans-serif; font-style: normal; font-variant: normal; font-weight: normal; font-size: 14px; line-height: normal; font-size-adjust: none; font-stretch: normal; display: block; text-decoration: underline;">Some lactation curves for milk traits in goat</a> <object codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=9,0,0,0" id="doc_430952089625697" name="doc_430952089625697" classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" align="middle" height="500" width="100%"> <param name="movie" value="http://d.scribd.com/ScribdViewer.swf?document_id=19380821&access_key=key-1o5xkb4ut9sysadtvfw7&page=1&version=1&viewMode="> <param name="quality" value="high"> <param name="play" value="true"> <param name="loop" value="true"> <param name="scale" value="showall"> <param name="wmode" value="opaque"> <param name="devicefont" value="false"> <param name="bgcolor" value="#ffffff"> <param name="menu" value="true"> <param name="allowFullScreen" value="true"> <param name="allowScriptAccess" value="always"> <param name="salign" value=""> <embed src="http://d.scribd.com/ScribdViewer.swf?document_id=19380821&access_key=key-1o5xkb4ut9sysadtvfw7&page=1&version=1&viewMode=" quality="high" pluginspage="http://www.macromedia.com/go/getflashplayer" play="true" loop="true" scale="showall" wmode="opaque" devicefont="false" bgcolor="#ffffff" name="doc_430952089625697_object" menu="true" allowfullscreen="true" allowscriptaccess="always" salign="" type="application/x-shockwave-flash" align="middle" height="500" width="100%"></embed> </object>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-82084537341467784592009-08-07T13:31:00.002+02:002009-08-07T13:57:23.237+02:00Additive vs. dominance two-allele genetic model by DIC<div style="text-align: justify;">Two-allele model has alleles A1 and A2 and genotypes A1A1, A1A2, and A2A2. This model can be fitted using only additive effect (restricted model) or additve+dominance effect. (full model) The later model has one parameter more than the former. I was using this model lately and got weird <a href="http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/dicpage.shtml">DIC</a> results - the full model had less number of parameters. Bellow is a simulation (using R and <a href="http://www.mrc-bsu.cam.ac.uk/bugs/">BUGS</a>), that shows expected DIC results.</div><blockquote><pre>## Needed packages and functions<br />library(package="e1071")<br />library(package="doBy")<br />library(package="R2WinBUGS")<br /><br />rvalue <- function(n, p, value, mean=0, sdE=0)<br />{<br /> if(!is.matrix(value)) value <- as.matrix(value)<br /> <br /> ## Frequencies<br /> k <- length(p)<br /> q <- 1 - p<br /> P <- p * p<br /> Q <- q * q<br /> H <- 2 * p * q<br /><br /> ## Allocate matrix of arbitrary values by loci<br /> x <- matrix(data=1, nrow=n, ncol=k)<br /> y <- matrix(data=1, nrow=n, ncol=k)<br /><br /> ## Simulate arbitrary values<br /> for(i in 1:k) {<br /> x[, i] <- rdiscrete(n=n, probs=c(P[i], H[i], Q[i]))<br /> y[, i] <- value[x[, i], i]<br /> }<br /> x <- x - 1 ## convert 1:3 to 0:2, i.e., number of A1 alleles<br /><br /> ## Sum all values<br /> y <- rowSums(y)<br /><br /> ## Add mean and normal deviate (error)<br /> y <- y + rnorm(n=n, mean=mean, sd=sdE)<br /><br /> return(as.data.frame(cbind(y, x)))<br />}<br /><br />prepairData <- function(x, dominance=FALSE)<br />{<br /> ret <- list()<br /> ret$n <- nrow(x)<br /> ret$y <- x$y<br /> if(!dominance) {<br /> ret$x <- x$V2 - 1 ## scale to the mean<br /> } else {<br /> ret$x <- x$V2 + 1 ## BUGS does not allow zero indexing!<br /> }<br /> ret<br />}<br /><br />### SIMULATE DATA<br />###-----------------------------------------------------------------------<br /><br />## --- Purely additive ---<br /><br />set.seed(seed=19791123)<br /><br />## Model parameters<br />n <- 1000<br />mu <- 100<br />sigma <- 1<br />value <- c(-1, 0, 1)<br />p <- 0.5<br /><br />## Simulate<br />podatkiA <- rvalue(n=n, p=p, value=value, mean=mu, sdE=sigma)<br /><br />par(mfrow=c(2, 1))<br />hist(podatkiA$y, xlab="Phenotype")<br /><br />plot(podatkiA$y ~ jitter(podatkiA$V2), xlab="Genotype", ylab="Phenotype")<br /><br />tmpA1 <- lm(podatkiA$y ~ podatkiA$V2)<br />abline(coef(tmpA1), lwd="2", col="blue")<br />tmpA2 <- summaryBy(y ~ V2, data=podatkiA)<br />points(tmpA2$y.mean ~ tmpA2$V2, pch=19, col="red")<br /><br />## --- Additive + Dominance ---<br /><br />set.seed(seed=19791123)<br /><br />## Model parameters<br />n <- 1000<br />mu <- 100<br />sigma <- 1<br />value <- c(-1, 1, -1)<br />p <- 0.5<br /><br />## Simulate<br />podatkiD <- rvalue(n=n, p=p, value=value, mean=mu, sdE=sigma)<br /><br />par(mfrow=c(2, 1))<br />hist(podatkiD$y, xlab="Phenotype")<br /><br />plot(podatkiD$y ~ jitter(podatkiD$V2), xlab="Genotype", ylab="Phenotype")<br /><br />tmpD1 <- lm(podatkiD$y ~ podatkiD$V2)<br />abline(coef(tmpD1), lwd="2", col="blue")<br />tmpD2 <- summaryBy(y ~ V2, data=podatkiD)<br />points(tmpD2$y.mean ~ tmpD2$V2, pch=19, col="red")<br /><br />### ESTIMATE MODEL PARAMETERS AND DIC<br />###-----------------------------------------------------------------------<br /><br />modelA <- function()<br />{<br /> ## --- Additive model (regression on gene content) ---<br /> ## Phenotypes<br /> for(i in 1:n) {<br /> y[i] ~ dnorm(mu[i], tau2)<br /> mu[i] <- a + b * x[i]<br /> }<br /> ## Location prior<br /> a ~ dnorm(0, 1.0E-6) <br /> b ~ dnorm(0, 1.0E-6)<br /> ## Variance prior<br /> lsigma ~ dunif(-10, 10) ## sigma between 4.539993e-05 and 2.202647e+04<br /> tau2 <- pow(sigma, -2)<br /> sigma <- exp(lsigma)<br />}<br /><br />modelD <- function()<br />{<br /> ## --- Additive + Dominance model (genotype as a factor) ---<br /> ## Phenotypes<br /> for(i in 1:n) {<br /> y[i] ~ dnorm(mu[i], tau2)<br /> mu[i] <- g[x[i]]<br /> }<br /> ## Location prior<br /> g[1] ~ dnorm(0, 1.0E-6)<br /> g[2] ~ dnorm(0, 1.0E-6)<br /> g[3] ~ dnorm(0, 1.0E-6) <br /> ## Variance prior<br /> lsigma ~ dunif(-10, 10) ## sigma between 4.539993e-05 and 2.202647e+04<br /> tau2 <- pow(sigma, -2)<br /> sigma <- exp(lsigma)<br />}<br /><br />tmpAA <- prepairData(x=podatkiA)<br />tmpAD <- prepairData(x=podatkiA, dominance=TRUE)<br />tmpDA <- prepairData(x=podatkiD)<br />tmpDD <- prepairData(x=podatkiD, dominance=TRUE)<br /><br />initsA <- function() list(a=rnorm(n=1, mean=mu), b=rnorm(n=1), lsigma=0)<br />initsD <- function() list(g=rnorm(n=3, mean=mu), lsigma=0)<br /><br />(fitAA <- bugs(model=modelA, data=tmpAA, inits=initsA,<br /> n.chains=3, n.burnin=5000, n.iter=10000, n.thin=10,<br /> bugs.seed=19791123, parameters=c("a", "b", "sigma"),<br /> bugs.directory="C:/Programs/BUGS/WinBUGS14_orig"))<br />## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff<br />## a 99.9 0.0 99.9 99.9 100 100 100.0 1 1500<br />## b 1.0 0.0 0.9 1.0 1 1 1.1 1 1500<br />## sigma 1.0 0.0 1.0 1.0 1 1 1.0 1 400<br />## deviance 2828.3 2.4 2826.0 2826.0 2828 2829 2834.0 1 1500<br />## pD = 2.9 and DIC = 2831.2<br /><br />(fitAD <- bugs(model=modelD, data=tmpAD, inits=initsD,<br /> n.chains=3, n.burnin=5000, n.iter=10000, n.thin=10,<br /> bugs.seed=19791123, parameters=c("g", "sigma"),<br /> bugs.directory="C:/Programs/BUGS/WinBUGS14_orig"))<br />## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff<br />## g[1] 98.9 0.1 98.8 98.9 98.9 99 99.1 1 660<br />## g[2] 99.9 0.0 99.8 99.9 99.9 100 100.0 1 1500<br />## g[3] 101.0 0.1 100.8 100.9 101.0 101 101.1 1 1500<br />## sigma 1.0 0.0 1.0 1.0 1.0 1 1.0 1 1300<br />## deviance 2829.2 2.9 2826.0 2827.0 2829.0 2831 2837.0 1 1500<br />## pD = 4.0 and DIC = 2833.2<br /><br />## pD seem OK and DIC agrees with simulated data - it is worse<br />## for AD model for data following additive model<br /><br />(fitDA <- bugs(model=modelA, data=tmpDA, inits=initsA,<br /> n.chains=3, n.burnin=5000, n.iter=10000, n.thin=10,<br /> bugs.seed=19791123, parameters=c("a", "b", "sigma"),<br /> bugs.directory="C:/Programs/BUGS/WinBUGS14_orig"))<br />## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff<br />## a 100.0 0.0 99.9 100.0 100.0 100.0 100.1 1 570<br />## b 0.0 0.1 -0.1 0.0 0.0 0.1 0.2 1 1500<br />## sigma 1.4 0.0 1.3 1.4 1.4 1.4 1.5 1 1300<br />## deviance 3512.9 2.6 3510.0 3511.0 3512.0 3514.0 3520.0 1 1500<br />## pD = 3.0 and DIC = 3515.9<br /><br />(fitDD <- bugs(model=modelD, data=tmpDD, inits=initsD,<br /> n.chains=3, n.burnin=5000, n.iter=10000, n.thin=10,<br /> bugs.seed=19791123, parameters=c("g", "sigma"),<br /> bugs.directory="C:/Programs/BUGS/WinBUGS14_orig"))<br />## mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff<br />## g[1] 98.9 0.1 98.8 98.9 99.0 99 99.1 1 1500<br />## g[2] 100.9 0.1 100.8 100.9 100.9 101 101.0 1 1500<br />## g[3] 99.0 0.1 98.8 98.9 99.0 99 99.1 1 1500<br />## sigma 1.0 0.0 1.0 1.0 1.0 1 1.0 1 530<br />## deviance 2829.2 2.9 2826.0 2827.0 2829.0 2831 2837.0 1 1500<br />## pD = 4.1 and DIC = 2833.3<br /><br />## pD seems OK and DIC also agrees with the model --> dominance<br />## model is better for this dataset</pre></blockquote>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-12917040558141239292009-06-19T03:28:00.002+02:002009-06-19T03:45:13.355+02:00bugsparallel<div style="text-align: justify;"><a href="http://code.google.com/p/bugsparallel/">bugsparallel</a> is a <a href="http://metruminstitute.org">Metrum Institute</a> project to run BUGS (via R2WinBUGS) in parallel - McMC is an application, where parallel runs can be used very efficientlly. Here is the code for one <a href="http://code.google.com/p/bugsparallel/source/browse/trunk/examples/FXaExample1/FXaExample1.R">example</a> using bugsparallel.<br /><br />Some usefull links:<br /><ul><li><a href="https://eprints.kfupm.edu.sa/56806/1/56806.pdf">Rosenthal, Parallel computing and Monte Carlo algorithms</a></li><li><a href="http://www.tcd.ie/Statistics/hpcsi/presentations/005.pdf">Wilkinson, Parallel Bayesian computation</a></li></ul></div>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com0tag:blogger.com,1999:blog-6715598735361401237.post-87381409516446656202009-05-27T10:42:00.002+02:002009-05-27T10:47:32.189+02:00Embeding fonts in figures produced by RSome publishers insist that we embed (include) the fonts in each figure. Here is a set of links regarding this issue for figures produced by R:<br /><ul><li><a href="http://tolstoy.newcastle.edu.au/R/help/05/01/10779.html">http://tolstoy.newcastle.edu.au/R/help/05/01/10779.html</a></li><li><a href="https://stat.ethz.ch/pipermail/r-help/2006-October/114751.html">https://stat.ethz.ch/pipermail/r-help/2006-October/114751.html</a></li><li><a href="https://stat.ethz.ch/pipermail/r-help/2005-April/069208.html">https://stat.ethz.ch/pipermail/r-help/2005-April/069208.html</a></li><li><a href="http://tolstoy.newcastle.edu.au/R/e6/help/09/03/8065.html">http://tolstoy.newcastle.edu.au/R/e6/help/09/03/8065.html</a></li><li><a href="http://tolstoy.newcastle.edu.au/R/e5/help/08/09/1874.html">http://tolstoy.newcastle.edu.au/R/e5/help/08/09/1874.html</a></li></ul>Gorjanc Gregorhttp://www.blogger.com/profile/07815994784120702971noreply@blogger.com2