I once read around here that with binary factors in mixed effects models (
lmer specifically), one shouldn't specify both random and fixed effects. The person went on to note that some people wouldn't combine fixed and random even for three- and four-level factors. Unfortunately, I can't recall if the person referred to random intercepts and/or random slopes in particular--what's certain is this relates to the very concept of random effects.
Does it ring true? Please take this question as from a beginner. It might as well be that obviously having both random and fixed effects doesn't make sense for a binary factor because there's nothing to control there... So, I have tried setting random intercepts and a fixed effect for a binary factor, and indeed, the model doesn't converge--yet that's little testing.
Sincerely thank you for any tips