How Does Prior Distribution Affect Model Fit Indices of Bayesian Structural Equation Model?

Bayesian structural equation model (BSEM) integrates the advantages of the Bayesian methods into the framework of structural equation modeling and ensures the identification by assigning priors with small variances. Previous studies have shown that prior specifications in BSEM influence model parameter estimation, but the impact on model fit indices is yet unknown and requires more research. As a result, two simulation studies were carried out. Normal distribution priors were specified for factor loadings, while inverse Wishart distribution priors and separation strategy priors were applied for the variance-covariance matrix of latent factors. Conditions included five sample sizes and 24 prior distribution settings. Simulation Study 1 examined the model-fitting performance of BCFI, BTLI, and BRMSEA proposed by Garnier-Villarreal and Jorgensen (Psychol Method 25(1):46-70, 2020) and the PPp value. Simulation Study 2 compared the performance of BCFI, BTLI, BRMSEA, and DIC in model selection between three data generation models and three fitting models. The findings demonstrated that prior settings would affect Bayesian model fit indices in evaluating model fitting and selecting models, especially in small sample sizes. Even under a large sample size, the highly improper factor loading priors resulted in poor performance of the Bayesian model fit indices. BCFI and BTLI were less likely to reject the correct model than BRMSEA and PPp value under different prior specifications. For model selection, different prior settings would affect DIC on selecting the wrong model, and BRMSEA preferred the parsimonious model. Our results indicate that the Bayesian approximate fit indices perform better when evaluating model fitting and choosing models under the BSEM framework.