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(This article was first published on <strong><a href="http://educate-r.org//2016/06/29/user2016.html"> Educate-R - R</a></strong>, and kindly contributed to <a rel="nofollow" href="http://www.r-bloggers.com/">R-bloggers)</a> </div>
<section>
<h1>Simulation and power analysis of generalized linear mixed models</h1>
<h2>Brandon LeBeau</h2>
<h3>University of Iowa</h3>
</section>
<section>
<h1>Overview</h1>
<ol>
<li>(G)LMMs</li>
<li>Power</li>
<li><code>simglm</code> package</li>
<li>Demo Shiny App!<br>

</li>
</ol>
<section>
<h1>Linear Mixed Model (LMM)</h1>
<p><img alt="" src="http://i2.wp.com/educate-r.org/figs/equations.png?w=456" data-recalc-dims="1"></p>
</section>
<section>
<h1>Power</h1>
<ul>
<li>Power is the ability to statistically detect a true effect (i.e. non-zero population effect).</li>
<li>For simple models (e.g. t-tests, regression) there are closed form equations for generating power.
<ul>
<li>R has routines for these: <code>power.t.test, power.anova.test</code></li>
<li>Gpower3<br>

</li>
</ul>
</li>
</ul>
<section>
<h1>Power Example</h1>
<pre><code>n &lt;- seq(4, 1000, 2)
power &lt;- sapply(seq_along(n), function(i) 
  power.t.test(n = n[i], delta = .15, sd = 1, type = 'two.sample')$power)
</code></pre>
<p><img alt="" src="http://i1.wp.com/educate-r.org/figs/power_plot-1.png?w=456" data-recalc-dims="1"><br>
</section>

<section>
<h1>Power for (G)LMM</h1>
<ul>
<li>Power for more complex models is not as straightforward;
<ul>
<li>particularly with messy real world data.</li>
</ul>
</li>
<li>There is software for the GLMM models to generate power:
<ul>
<li>Optimal Design: <a target="_blank" href="http://hlmsoft.net/od/">http://hlmsoft.net/od/</a></li>
<li>MLPowSim: <a target="_blank" href="http://www.bristol.ac.uk/cmm/software/mlpowsim/">http://www.bristol.ac.uk/cmm/software/mlpowsim/</a></li>
<li>Snijders, <em>Power and Sample Size in Multilevel Linear Models</em>.<br>

</li>
</ul>
</li>
</ul>
<section>
<h1>Power is hard</h1>
<ul>
<li>In practice, power is hard.</li>
<li>Need to make many assumptions on data that has not been collected.
<ul>
<li>Therefore, data assumptions made for power computations will likely differ from collected sample.</li>
</ul>
</li>
<li>A power analysis needs to be flexible, exploratory, and well thought out.<br>

</li>
</ul>
<section>
<h1><code>simglm</code> Overview</h1>
<ul>
<li><code>simglm</code> aims to simulate (G)LMMs with up to three levels of nesting (aim to add more later).</li>
<li>Flexible data generation allows:
<ul>
<li>any number of covariates and discrete covariates</li>
<li>change random distribution</li>
<li>unbalanced data</li>
<li>missing data</li>
<li>serial correlation.</li>
</ul>
</li>
<li>Also has routines to generate power.<br>

</li>
</ul>
<section>
<h1>Demo Shiny App</h1>
<pre><code>shiny::runGitHub('simglm', username = 'lebebr01', subdir = 'inst/shiny_examples/demo')
</code></pre>
<p>or</p>
<pre><code>devtools::install_github('lebebr01/simglm')
library(simglm)
run_shiny()
</code></pre>
<ul>
<li>Must have following packages installed: <code>simglm, shiny, shinydashboard, ggplot2, lme4, DT</code>.<br>

</li>
</ul>
<section>
<h1>Questions?</h1>
<ul>
<li>Twitter: @blebeau11</li>
<li>Website: <a target="_blank" href="http://educate-r.org/">http://educate-r.org</a></li>
<li>Slides: <a target="_blank" href="http://educate-r.org/2016/06/29/user2016.html">http://educate-r.org/2016/06/29/user2016.html</a></li>
<li>GitHub: <a target="_blank" href="http://github.com/lebebr01">http://github.com/lebebr01</a><br>

</li>
</ul>
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