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Sociological Methods & Research, Vol. 35, No. 3, 352-381 (2007)
DOI: 10.1177/0049124106292357
© 2007 SAGE Publications

A Unified Maximum Likelihood Approach for Analyzing Structural Equation Models With Missing Nonstandard Data

Sik-Yum Lee

The Chinese University of Hong Kong, China

Xin-Yuan Song

The Chinese University of Hong Kong, China

In this article, the authors present a unified approach for maximum likelihood analysis of structural equation models that involve subtle model formulations and nonstandard data structures. Based on the idea of data augmentation, they describe a generic Monte Carlo expectation-maximization algorithm for estimation. They propose path sampling for computing the observed data likelihood functions that usually involve complicated integrals and show how to apply this method for computing the Bayesian information criterion for model comparison. An application of the proposed unified approach to a two-level nonlinear structural equation model with missing continuous and ordered categorical data is presented. An illustrative example with a real data set is given.

Key Words: MCEM algorithm • Gibbs sampler • Bayesian information criterion • path sampling


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