The performance of Bayesian fit measures in detecting misspecified multilevel structural equation modeling.

Previous research on multilevel structural equation modeling (MSEM) using frequentist estimation showed that approximate fit indices in SEM failed to detect between-level model misspecification. Bayesian estimation is a promising alternative to MSEM because of its high convergence rates and improved parameter estimates with weakly informative priors (Depaoli & Clifton, 2015). However, no previous research has examined the sensitivity of Bayesian fit measures in detecting model misspecification at different levels. This paper used a simulation study to investigate the performance of Bayesian fit measures in detecting model misspecification in MSEM. The results indicated that all Bayesian fit indices were sensitive to within-level model misspecification, but their performance in detecting between-level model misspecification varied. Overall, the deviance information criterion (DIC), widely applicable information criterion (WAIC), and leave-one-out cross-validation (LOO) exhibited higher sensitivity to between-level model misspecification than the other fit indices. The influence of prior specification varied across Bayesian fit measures. Implications for empirical researchers and future research directions are discussed.