Evaluation and Comparison of SEM, ESEM, and BSEM in Estimating Structural Models with Potentially Unknown Cross-loadings

Cross-loadings are common in multidimensional instruments; however, they cannot be appropriately addressed in conventional structural equation modeling (SEM) owing to the assumption of zero cross-loadings in standard confirmatory factor analysis (CFA). Although it has been proposed that exploratory structural equation modeling (ESEM) and Bayesian structural equation modeling (BSEM) can address this issue more flexibly, their performance in structural parameter estimation has not been adequately compared. This study uses simulated data to evaluate and compare SEM, ESEM, and BSEM in estimating structural models under different manipulation conditions (i.e., sample size, target loading, cross-loading, and path coefficient). The results demonstrated that the performances of these approaches were similar in the case of zero cross-loadings. SEM performed worse as cross-loadings increased, and the performance of BSEM significantly depended on the accuracy of the priors for cross-loadings. ESEM was inferior to BSEM with correctly specified prior means for cross-loadings in most evaluation measures and exhibits unstable performance in conditions with small target loadings. Recommended strategies for selecting an appropriate modeling approach are discussed based on our findings.