© 2020 Royal Statistical Society The paper considers the problem of estimating a multivariate probit model in a panel data setting with emphasis on sampling a high dimensional correlation matrix and improving the overall efficiency of the data augmentation approach. We reparameterize the correlation matrix in a principled way and then carry out efficient Bayesian inference by using Hamiltonian Monte Carlo sampling. We also propose a novel antithetic variable method to generate samples from the posterior distribution of the random effects and regression coefficients, resulting in significant gains in efficiency. We apply the methodology by analysing stated preference data obtained from Australian general practitioners evaluating alternative contraceptive products. Our analysis suggests that the joint probability of discussing combinations of contraceptive products with a patient shows medical practice variation among the general practitioners, which indicates some resistance even to discuss these products, let alone to recommend them.