<h1>Simulation and power analysis of generalized linear mixed models</h1>
<h2>Brandon LeBeau</h2>
<h3>University of Iowa</h3>
# Overview
1. (G)LMMs
2. Power
3. `simglm` package
4. Demo Shiny App!
# Linear Mixed Model (LMM)
![](/figs/equations.png)
# Power
- Power is the ability to statistically detect a true effect (i.e. non-zero population effect).
- For simple models (e.g. t-tests, regression) there are closed form equations for generating power.
+ R has routines for these: `power.t.test, power.anova.test`
+ Gpower3
# Power Example
```r
n <- seq(4, 1000, 2)
power <- sapply(seq_along(n), function(i)
power.t.test(n = n[i], delta = .15, sd = 1, type = 'two.sample')$power)
```
![](/figs/power_plot-1.png)
# Power for (G)LMM
- Power for more complex models is not as straightforward;
+ particularly with messy real world data.
- There is software for the GLMM models to generate power:
+ Optimal Design: <http://hlmsoft.net/od/>
+ MLPowSim: <http://www.bristol.ac.uk/cmm/software/mlpowsim/>
+ Snijders, *Power and Sample Size in Multilevel Linear Models*.
# Power is hard
- In practice, power is hard.
- Need to make many assumptions on data that has not been collected.
+ Therefore, data assumptions made for power computations will likely differ from collected sample.
- A power analysis needs to be flexible, exploratory, and well thought out.
# `simglm` Overview
- `simglm` aims to simulate (G)LMMs with up to three levels of nesting (aim to add more later).
- Flexible data generation allows:
+ any number of covariates and discrete covariates
+ change random distribution
+ unbalanced data
+ missing data
+ serial correlation.
- Also has routines to generate power.
# Demo Shiny App
```r
shiny::runGitHub('simglm', username = 'lebebr01', subdir = 'inst/shiny_examples/demo')
```
or
```r
devtools::install_github('lebebr01/simglm')
library(simglm)
run_shiny()
```
- Must have following packages installed: `simglm, shiny, shinydashboard, ggplot2, lme4, DT`.
# Questions?
- Twitter: @blebeau11
- Website: <http://brandonlebeau.org>
- Slides: <http://brandonlebeau.org/2016/06/29/user2016.html>
- GitHub: <http://github.com/lebebr01>