Illustrating the Value of Prior Predictive Checking for Bayesian Structural Equation Modeling

Abstract

A unique feature of Bayesian estimation is the inclusion of prior knowledge through prior distributions. These prior distributions can benefit or impair many components of the ensuing analysis. Priors are especially important to assess in the context of structural equation models (SEMs), which often carry data and modeling complexities where priors can be particularly influential. In this article, we illustrate a statistical approach to assess the impact of our prior specifications: the prior predictive checking procedure. We introduce a comprehensive prior predictive checking workflow that organizes the procedure into clear steps, and we relate this workflow to the SEM framework. Through three examples, we demonstrate how the workflow can aid researchers in more fully understanding different aspects of their prior specification within SEM. Code and additional resources are provided in the online Supplemental Materials to facilitate future application of the prior predictive checking procedure within the SEM framework.