Bayes Estimation in the Hierarchical Multinomial Probit Model

Abstract

We consider a complete hierarchical multinomial probit (HMNP) model in which both the regression-coefficient vector and the covariance matrix are assumed to have hierarchical structure and propose an MCMC algorithm for numerically computing the Bayes estimates of the parameters. We show by simulation studies that the covariance matrix is estimated with higher accuracy using the method proposed in this paper than that using an HMNP model in which the covariance matrix is not assumed to have hierarchical structure.