Bayesian Estimation and Model Selection of Multivariate Linear Model with Polytomous Variables.

This article provides a Bayesian analysis of the multivariate linear model with polytomous variables. The computational burden due to the intractable multiple integrals induced by the polytomous variables and the model is solved by augmenting the underlying latent continuous measurements of the observed polytomous data. A Gibbs sampler algorithm is implemented to produce the Bayesian estimate. A Bayes factor approach is proposed for model selection, and it is approximated by the Bayesian information criterion (BIC) via the bridge sampling. The proposed methodology is illustrated by examples using multivariate linear regression and multivariate two-way analysis of variance with real data.