Multinomial Probit in Stan

Hi all,

I am interested in modeling ranked preference data (including both partial and complete rankings) using a probit model (I currently believe this is the best kind of model for what I need, no IIA assumptions) in Stan and am looking for advice. My ultimate goal is to be able to fit a model and then generate sets of rankings (both partial and complete) based on that model.

The closest thing I have found so far that resembles what I am aiming to do is the rank ordered probit (ROP) model described in the “Ranking Models” section of this paper ON THE USE OF PROBIT BASED MODELS FOR RANKING DATA ANALYSIS. I understand the likelihood for the model relies on the cumulative distribution function for a multivariate normal, which is not implemented in Stan. However, the Stan user guide contains a section on using multivariate probit models and the data augmentation steps needed to implement them in Stan.

My two specific questions are:

  1. Are there any resources that further breakdown the concepts of the data augmentation procedure needed for multivariate probit models in Stan? I looked at the paper cited in the user guide, but still don’t have a complete grasp on how or why the procedure works.
  2. Maybe the more important question, will the data augmentation procedure described in the user guide allow me to fit a probit model on rank ordered data?

Thanks to anyone who shares any knowledge on this topic!

@avehtari thinks this paper

can be done in Stan.