Power analysis from scratch using simR (glmer) - How to specify fixed and random effects?

0
votes

I'm very new to R (psychology background) and I am trying to estimate the required sample size (no pilot data available) for a mixed model (glmer) with the fixed effect 'Time' (3 levels) and the random effects 'Site' (5 levels) and 'Participant' (n=60 at each site), with participant being nested in site. I am interested in the effect of 'time' on various 'outcome' variables. Ideally, would like to have random slopes and intercepts because we are assuming that participants have different baselines and will evolve differently over time.

I am following the Appendix S2 (power analysis from scratch) of Green & MacLeod (2015). SIMR: an R package for power analysis of generalized linear mixed models by simulation, available at: https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12504

My question is related to the specification of parameters. The paper suggests the following arbitrarily chosen values: (see https://humburg.github.io/Power-Analysis/simr_power_analysis.html)

## Intercept and slopes for intervention, time1, time2, intervention:time1, intervention:time2
fixed <- c(5, 0, 0.1, 0.2, 1, 0.9)

## Random intercepts for participants clustered by class
rand <- list(0.5, 0.1)

## residual variance
res <- 2

What I would like to know is what these numbers stand for? I understand that they represent slopes and intercepts for intervention, time1, time2 and the interactions, but why is there 6 numbers for 5 parameters? And why are there only 2 values for the random effect? In other words, how can I adapt these lines so that they reflect my model?

Thank you to anyone who could direct me to an answer or to further reading.

1
rlme4mixed-models

1 Answers

0
votes

See the equation:

y∼treatment+time+treatment×time+(1|class/id)+ϵ

There is always an intercept (fixed). The intercept is what level of Y you have with all the predictors at 0/baseline. Keep in mind that time is coded up as a factor and not a covariate.

  1. Intercept here is treatment=control and time = 0.
  2. Treatment = intervention
  3. Time = 1
  4. Time = 2
  5. Treatment = intervention*time
  6. Treatment = intervention*time2

The two random effects are random intercepts around two levels of analysis: Class and id. These two numbers are the best fitting distributions that incapsulates the random effects.

Take a look here: http://mfviz.com/hierarchical-models/