Probing beyond: The impact of model size and prior informativeness on Bayesian SEM fit indices

Abstract Examining how well a hypothesized model fits observed data is pivotal in Bayesian structural equation modeling (SEM). Recent efforts have aimed to formulate Bayesian SEM fit indices akin to those used in frequentist SEM. However, the assessment of these fit indices in Bayesian SEM has been limited in scope. This research entailed two simulation studies to explore the impact of various factors, including prior choices, model misspecification, model size, and sample size, on the sensitivity of fit indices. The first study delved into the prior sensitivity of Bayesian SEM fit indices (BRMSEA [Bayesian root mean square error of approximation], BCFI [Bayesian comparative fit index], BTLI [Bayesian Tucker–Lewis index], and PP p [posterior predictive p -value]) under latent factor and cross-loading misspecifications. The second study explored how alterations in model complexity influenced the prior sensitivity of these fit indices to model misspecifications. The findings indicate a robust performance of Bayesian fit indices under relatively severe model misspecification, suggesting a preference for highly informative priors when prior knowledge is certain. As model size increased, PP p exhibited a balanced performance between true and false positive rates, whereas BRMSEA was less reliable in the presence of latent factor misspecification. Implications for applied research are discussed.