powersim_workshop_2026/05_mixed1/exercises-pwrlmm.md

Exercise: Power simulation for longitudinal data

Risperidone vs. haloperidol and schizophrenia

dat       <- read.table("../data/moeller.csv", header = TRUE, sep = ",")
dat$id    <- factor(dat$id)
dat$treat <- factor(dat$treat, levels = c("risp", "halo"))

lattice::xyplot(pans ~ week, data = dat, groups = treat, type = c("g", "p", "a"), auto.key = TRUE)

1. Analyze the original data from moeller.csv:

   • pans: Positive and Negative Symptom Scale for schizophrenia

   • treat: medication group

     • risp: atypical neuroleptic risperidone
     • halo: conventional neuroleptic haloperidol

   • What is the sample size in each treatment group?

   • Estimate the by-group random-slope model.

   • What are the estimates for the fixed effects and variance components?

   • Interpret the interaction effect.

   • Test the interaction effect.

2. Run a power simulation for a replication study:

   • Set up a data frame containing the study design and sample size.

   • Specify the minimum relevant effect.

   • Set the fixed effects and variance components to plausible values.

   • How many participants are required for the test of the interaction to detect the specified effect with a power of 80%?

   • Recover the parameters of the by-group random-slope model for one simulated data set.

3. Create a renderable R script or an R Markdown file that includes

   • a header with title, author, date
   • at least one section head line
   • the questions from above and your answers
   • the R code, output, and plots (if any)

   Render the R or Rmd file to HTML.