<p>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 &amp; 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.</p>

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

  • Chunhua Cao,
  • Xinya Liang

摘要

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.