Bayesian Data-Model Fit Assessment for Structural Equation Modeling

Abstract Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes and illustrates key features of Bayesian approaches to model diagnostics and assessing data–model fit of structural equation models, discussing their merits relative to traditional procedures. Keywords: Bayesian model checkingdata–model fitstructural equation modeling Notes 1In what has frequently been termed empirical Bayes estimation, certain unknown entities (i.e., those at the highest level of a hierarchical specification) are not assigned prior distributions, and instead are estimated using frequentist strategies (see, e.g., CitationGill, 2007, p. 425).