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The performance of Bayesian fit measures in detecting misspecified multilevel structural equation modeling
1Educational Research, Department of Educational Studies in Psychology, Research Methodology, and Counseling, University of Alabama, 520 Colonial Dr, Tuscaloosa, AL, 35401, USA. ccao6@ua.edu.
Behavior Research Methods
|June 29, 2026
Summary
Bayesian fit measures in multilevel structural equation modeling (MSEM) effectively detect within-level misspecification. However, deviance information criterion (DIC), widely applicable information criterion (WAIC), and leave-one-out cross-validation (LOO) are most sensitive to between-level misspecification.
Area of Science:
- Statistics
- Psychometrics
- Quantitative Psychology
Background:
- Frequentist multilevel structural equation modeling (MSEM) struggles with detecting between-level misspecification.
- Bayesian estimation offers potential advantages in MSEM due to convergence and parameter estimation.
- Prior research has not evaluated Bayesian fit measures for detecting MSEM misspecification.
Purpose of the Study:
- Investigate the performance of Bayesian fit measures in detecting model misspecification in MSEM.
- Compare the sensitivity of various Bayesian fit indices to misspecification at different structural levels.
- Examine the impact of prior specification on Bayesian fit measure performance.
Main Methods:
- Simulation study design.
- Multilevel structural equation modeling (MSEM) with Bayesian estimation.
- Evaluation of multiple Bayesian fit indices (e.g., DIC, WAIC, LOO).
Main Results:
- All Bayesian fit indices detected within-level misspecification.
- Sensitivity to between-level misspecification varied among Bayesian fit indices.
- Deviance information criterion (DIC), widely applicable information criterion (WAIC), and leave-one-out cross-validation (LOO) showed higher sensitivity to between-level misspecification.
Conclusions:
- Bayesian fit measures are valuable for assessing MSEM model fit, particularly for within-level misspecification.
- DIC, WAIC, and LOO are recommended for detecting between-level misspecification in MSEM.
- Researchers should consider prior specification when interpreting Bayesian fit indices in MSEM.
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