A tutorial on the Bayesian approach for analyzing structural equation models

A tutorial exposition on the Bayesian approach in analyzing structural equation models (SEMs), which can be regarded as regression models with observed and latent variables, which would encounter serious difficulties when dealing with complicated models and/or data structures.

Abstract

In this paper, we provide a tutorial exposition on the Bayesian approach in analyzing structural equation models (SEMs). SEMs, which can be regarded as regression models with observed and latent variables, have been widely applied to substantive research. However, the classical methods and most commercial software in this area are based on the covariance structure approach, which would encounter serious difficulties when dealing with complicated models and/or data structures. In contrast, the Bayesian approach has much more flexibility in handling complex situations. We give a brief introduction to SEMs and a detailed description of how to apply the Bayesian approach to this kind of model. Advantages of the Bayesian approach are discussed, and results obtained from a simulation study are provided for illustration. The intended audience is statisticians/methodologists who either know about SEMs or simple Bayesian statistics, and Ph.D. students in statistics, psychometrics, or mathematical psychology.