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Simulation and power analysis of generalized linear mixed models

Brandon LeBeau

University of Iowa

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Overview

1. (G)LMMs
2. Power
3. simglm package
4. Demo Shiny App!

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Linear Mixed Model (LMM)

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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

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Power Example

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)

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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.

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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.

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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.

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Demo Shiny App

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

or

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

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

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Questions?

• Twitter: @blebeau11
• Website: http://educate-r.org
• Slides: http://educate-r.org/2016/06/29/user2016.html
• GitHub: http://github.com/lebebr01