A Bayesian multivariate probit for ordinal data with semiparametric random-effects

A heterogeneous thresholds probit for ordered ratings is developed to remove conditional independence among responses and incorporate respondent traits. We propose a semiparametric approach to relaxing normality of random-effects in the probit model that account for differences in response style. Simulation studies provide evidence of the ability for the proposed semiparametric model to better recover an underlying distribution of respondent effects than the parametric one with a normal hierarchical prior. The application to ratings on the value of information sources for automobiles demonstrates significant correlations among responses and irregularity in the shape of unobserved heterogeneity.