Rank order modeling in stan, with some complications

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

  1. I have latent classes including some people who reverse the order accidentally or who respond randomly,
  2. I want to model a few covariances between responses (when response X is ranked high, response X’ is also ranked high)
  3. 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.


not sure if it solves your complications, but have you checked the Thurstonian model? I think it can account for covariances (2), and missing items (3) should be straightforward, not sure about (1) though.

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Yes, the base model is a thurstonian model. But the complication of latent classes (and the need to sum out the categories) seems a challenge, because I can’t compute the lpdf of the rank under the mixture components, I think: it involves a multivariate normal integral. Not sure if there’s a better way to think about it…?

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