Mixed effects logistic regression with repeated measures and binary outcome

Question

I have an experimental array with a binary dependent variable. Each subject belongs to 1 of 3 groups. Each subject answers 10 questions, 5 of which belong to category A and 5 of which belong to category B. My goal is to examine the interaction between the group level and the category as well to examine the group and categories main effects. I'm using the glmer function from the lme4 package:

glmer(binary_outcome ~ category * group + (1|subject_ID), 
         family=binomial(link=logit))

Does this formula capture the relevant aspects of the experimental array?

Answer 1

Since each subject answers questions from both categories, you should in principle allow for the among-subject variation in category effect:

binary_outcome ~ category * group + (category|subject_ID)

A couple of technical points you should be aware of:

• you might find that the model is singular (i.e., you don't have enough information to fully estimate the among-subject variation in the category effect, which includes the variance in both categories and the correlation among categories). See e.g. the Barr et al. 2013 "keep it maximal" paper. If so, you could fall back to a random term of (1|subject_ID/category), which will be easier to estimate.
• with 10 binary responses per individual, you probably should consider using Gaussian quadrature rather than the default Laplace approximation, e.g. nAGQ=10