Simulation and power analysis of generalized linear mixed models

Brandon LeBeau

2016-06-29

Overview

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

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)

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.

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 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.

shiny::runGitHub('simglm', username = 'lebebr01', subdir = 'inst/shiny_examples/demo')

devtools::install_github('lebebr01/simglm')
library(simglm)
run_shiny()

Must have following packages installed: simglm, shiny, shinydashboard, ggplot2, lme4, DT.