Bayesian inference for multivariate ordinal data using parameter expansion

Multivariate ordinal data arise in many applications. This article proposes a new, efficient method for Bayesian inference for multivariate probit models using Markov chain Monte Carlo techniques. The key idea is the novel use of parameter expansion to sample correlation matrices. A nice feature of the approach is that inference is performed using straightforward Gibbs sampling. Bayesian methods for model selection are also discussed. Our approach is motivated by a study of how women make decisions on taking medication to reduce the risk of breast cancer. Furthermore, we compare and contrast the performance of our approach with other methods.