Bayesian nonparametric multivariate ordinal regression

Abstract

Abstract Multivariate ordinal data are modelled as a finite stick‐breaking mixture of multivariate probit models. Parametric multivariate probit models are first developed for ordinal data, then generalized to finite mixtures of multivariate probit models. Specific recommendations for prior settings are found to work well in simulations and data analyses. Interpretation of the model is carried out by examining aspects of the mixture components as well as through averaged effects focusing on the mean responses. A simulation verifies that the fitting technique works, and an analysis of alcohol drinking behaviour data illustrates the usefulness of the proposed model. The Canadian Journal of Statistics 43: 337–357; 2015 © 2015 Statistical Society of Canada