Likelihood analysis of multivariate probit models using a parameter expanded MCEM algorithm

Huiping Xu, Bruce A. Craig

Research output: Contribution to journalArticle

6 Scopus citations


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 theMonte 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.

Original languageEnglish (US)
Pages (from-to)340-348
Number of pages9
Issue number3
StatePublished - Aug 1 2010
Externally publishedYes


  • Correlated binary data
  • Gibbs sampler
  • Monte Carlo expectation maximization algorithm
  • Parameter expansion

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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