I would like to be able to perform a sample size calculation for an Ordinal Logistic regression with mixed effects. The proposed design would have two different tests each with 5 different items, each participant does both tests and each item. (i.e. wide format data would be: ten columns of data - five for test 1 and five for test 2. Each row is a different participant). The dependent variable is ordered categorical with three levels (0,1,2).
Reading information on GLMMs by Ben Bolker, Andrew Gelman, and others, I see that that it might be sensible to include 'test' as a fixed effect rather than random effect (not enough levels?), but with 'item' as a random effect?
My question is in two parts:
- Is the correct model for this type of data either a series of binomial contrasts using logistic GLMM or is an ordinal logistic GLMM possible? I cannot find information on the ordinal GLMM model and an R implementation?
- Is it possible to perform a power calculation via simulation for an ordinal GLMM or alternatively, should I do a separate power calculation for each binomial contrast?