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 likelihoodfunctions 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 proposedunified 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