The Monte Carlo EM method for estimating multinomial probit latent variable models

Authors:
Xingcai Zhou;Xinsheng Liu
Affiliations:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016 and College of Tongling, Tongling, China 244000;College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016 and Institute of Nanoscience, Nanjing University of Aeronautics and Astronautics, Nanjing, China 21001 ...
Venue:
Computational Statistics
Year:
2008

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Abstract

We propose a multinomial probit (MNP) model that is defined by a factor analysis model with covariates for analyzing unordered categorical data, and discuss its identification. Some useful MNP models are special cases of the proposed model. To obtain maximum likelihood estimates, we use the EM algorithm with its M-step greatly simplified under Conditional Maximization and its E-step made feasible by Monte Carlo simulation. Standard errors are calculated by inverting a Monte Carlo approximation of the information matrix using Louis's method. The methodology is illustrated with a simulated data.