Bayesian Structural Equation Modeling

Abstract

Structural equation modeling (SEM) is frequently used in social sciences to analyze relations among observed and latent variables and test theoretical propositions regarding relations among these latent variables. Frequentist SEM relies on Maximum Likelihood Estimation, and although this method works well for many simple situations, its performance is unsatisfactory when dealing with complex models or small sample sizes. In search of a method that resolves those problems, Bayesian SEM has been developed recently. These models produce more accurate parameter estimates. The Bayesian approach to SEM offers the possibility of incorporating prior knowledge into SEM, allowing for model extension and improvement. In this research, the theory of both frequentist and Bayesian SEM is described. Subsequently, Bayesian SEM is illustrated with an application in educational sciences. A method is proposed to specify prior distributions that use correlation estimates found in previous research to reflect prior information and our confidence in that information. The results obtained by an informative prior model are analyzed and compared to the results of a noninformative, weakly informative, and frequentist model. It was found that the informative prior model produces more accurate estimates than the noninformative and weakly informative prior models, indicating the correctness of the specified priors.