Bayesian Methods for Analyzing Structural Equation Models With Covariates, Interaction, and Quadratic Latent Variables

Abstract

The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a maximum likelihood estimate. Other advantages over the traditional approaches are discussed. More important, we demonstrate through examples how to use the freely available software WinBUGS to obtain Bayesian results for estimation and model comparison. Simulation studies are conducted to assess the empirical performances of the approach for situations with various sample sizes and prior inputs.

ACKNOWLEDGMENTS

This research was fully supported by Grant CUHK 4243/03H from the Research Grants Council of the Hong Kong Special Administration Region. We are thankful to reviewers for valuable comments that improved the article substantially. The assistance of Jing-Heng Cai in producing the revision is gratefully acknowledged.