This paper provides a practical simulation-based Bayesian and non-Baye
sian analysis of correlated binary data using the multivariate probit
model. The posterior distribution is simulated by Markov chain Monte C
arlo methods and maximum likelihood estimates are obtained by a Monte
Carlo version of the EM algorithm. A practical approach for the comput
ation of Bayes factors from the simulation output is also developed. T
he methods are applied to a dataset with a bivariate binary response,
to a four-year longitudinal dataset from the Six Cities study of the h
ealth effects of air pollution and to a seven-variate binary response
dataset on the labour supply of married women from the Panel Survey of
Income Dynamics.