I am analyzing case-control data with conditional logistic regression. I am using the stan_clogit() function from rstanarm. Since the stratum intercepts are conditioned out and not estimated, I understand that we do not get any predicted probabilities. I was wondering how one should assess the priors and model fit in this setting. What are the appropriate prior and posterior predictive/model-fit checks for a conditional logistic regression model?
You get the predicted joint probability for the stratum, and using loo() gives you leave-one-stratum-out.
You may find a blog post by @Solomon useful to see equations and code in Bayesian context
I tested that loo() works for stan_clogit() output, except that there was a bug when the formula includes group-specific intercepts (1 | group). I created and issue and fix PR clogit log_lik and prediction bug with group-specific terms · Issue #655 · stan-dev/rstanarm · GitHub