Likelihood Analysis of Multivariate Probit Models Using a Parameter Expanded MCEM Algorithm

Abstract

Multivariate binary data arise in a variety of settings. In this article we propose a practical and efficient computational framework for maximum likelihood estimation of multivariate probit regression models. This approach uses the Monte Carlo expectation maximization (MCEM) algorithm, with parameter expansion to complete the M-step, to avoid the direct evaluation of the intractable multivariate normal orthant probabilities. The parameter expansion not only enables a closed-form solution in the M-step, but also improves efficiency. Using the simulation studies, we compare the performance of our approach with the MCEM algorithms developed by Chib and Greenberg (1998) and Song and Lee (2005), as well as the iterative approach proposed by Li and Schafer (2008). Our approach is further illustrated using a real-world example.