Bayesian Structural Equation Modeling

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Abstract Structural equation models (SEMs) with latent variables are routinely used in social science research, and are of increasing importance in biomedical applications. Standard practice in implementing SEMs relies on frequentist methods. This chapter provides a simple and concise description of an alternative Bayesian approach. We provide a brief overview of the literature, describe a Bayesian specification of SEMs, and outline a Gibbs sampling strategy for model fitting. Bayesian inferences are illustrated through an industrialization and democratization case study from the literature. The Bayesian approach has some distinct advantages, due to the availability of samples from the joint posterior distribution of the model parameters and latent variables, that we highlight. These posterior samples provide important information not contained in the measurement and structural parameters. As is illustrated using the case study, this information can often provide valuable insight into structural relationships.