Efficient data augmentation for multivariate probit models with panel data: An application to general practitioner decision-making about contraceptives

TL;DR

This paper introduces an efficient Bayesian data augmentation method for multivariate probit models with panel data, improving sampling of high-dimensional correlation matrices and applying it to analyze Australian general practitioners' contraceptive decision-making.

Contribution

It proposes a novel reparameterization of the correlation matrix and an antithetic variable method, enhancing computational efficiency in Bayesian inference for complex models.

Findings

Identified variation in general practitioners' willingness to discuss contraceptives.

Demonstrated significant efficiency gains with the proposed sampling methods.

Applied methodology to real data, revealing practice patterns and resistance.

Abstract

This article 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 reparameterise the correlation matrix in a principled way and then carry out efficient Bayesian inference using Hamiltonian Monte Carlo. 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 to even discuss these products, let alone recommend them.