Exercise: Power simulation for LMM

Physical healing as a function of perceived time

Aungle and Langer (2023) investigate how perceived time influences physical healing

They used cupping to induce bruises on 33 subjects, then took a picture, waited for 28 min and took another picture
Subjective time was manipulated to feel like 14, 28, or 56 min
The pre and post pictures were presented to 25 raters who rated the amount of healing on a 10-point-scale with 0 = not at all healed, 5 = somewhat healed, 10 = completely healed
Subjects participated in all three conditions over a two week period

load("../data/healing.RData")

str(dat)

# Subject ID
dat$Subject <- factor(dat$Subject)
# Rater ID
dat$ResponseId <- factor(dat$ResponseId)

Visualize the data.
- Aggregate the data over Raters and plot the data for each subject using lattice::xyplot()
- Aggregate the data over Subjects and plot one panel for each rater
- How would you choose the random effects for a model testing healing over the three conditions
Fit the model you think fits the experimental design best
Test the effects of condition
Run a power simulation for a replication study:
- Set up a data frame containing the study design and sample size.
- Specify the minimum relevant effects.
- Set the fixed effects and variance components to plausible values.
- How many participants are required to detect the specified effect with a power of 80%?
- Recover the parameters of the model for one simulated data set.

Aungle, P., and E. Langer. 2023. “Physical Healing as a Function of Perceived Time.” Scientific Reports 13 (1): 22432. https://doi.org/10.1038/s41598-023-50009-3.