Conditional logit (clogit) models

Currently, projpred does not work with models estimated via stan_clogit; e.g.

example(stan_clogit, package = "rstanarm") # creates post
projpred::get_refmodel(post) # fails

But I wanted to make sure I am clear as to what would need to happen for clogit models to become supported by the projpred package, so that @jgabry and I can help. At help(clogit, package = "survival"), it is pointed out that the likelihood for a clogit model is a special case of that for a Cox model, if that makes things easier. The best documentation of a clogit model is actually in Stata. I would guess that the form of the likelihood is sufficiently nice that projpred should work eventually, but the model (and its submodels) lack an intercept because it is not identified under the likelihood alone, so that is different from what projpred is accustomed to. Also, the prediction task is essentially leave-one-stratum-out rather than leaving one individual out of some stratum.

Reproduce the failure with example(stan_clogit, package = "rstanarm") and projpred::get_refmodel(post). Read help(clogit, package = "survival") and the linked Stata documentation to understand the likelihood and prediction setup; done means projpred supports stan_clogit models, including their no-intercept and leave-one-stratum-out prediction behavior.