Analysis of multivariate probit models

This paper provides a practical simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the EM algorithm. A practical approach for the computation of Bayes factors from the simulation output is also developed. The methods are applied to a dataset with a bivariate binary response, to a four-year longitudinal dataset from the Six Cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the Panel Survey of Income Dynamics. Bayes factor; Correlated binary data; Gibbs sampling; Marginal likelihood; Markov chain Monte Carlo; Metropolis-Hastings algorithm.