I’m trying to fit a model to rank ordered data, with a few complications:

- I have latent classes including some people who reverse the order accidentally or who respond randomly,
- I want to model a few covariances between responses (when response X is ranked high, response X’ is also ranked high)
- Missing items

My full model specification is here: RPubs - Probit ranking

I’ve seen examples of exploded logit models (e.g. A simple way to model rankings with Stan - Bruno Nicenboim) along with summing out discrete parameters (5.3 Summing out the responsibility parameter | Stan User’s Guide), but computing the probabilities of the orderings in the model I’ve specificed seems impossible in stan (in R use `mvtnorm::pmvnorm`

).

Am I overlooking something? Any pointers to similar models would be appreciated; currently my Gibbs sampler takes forever, and I’d like to use stan if I could.