Sensitivity of Fit Indices to Model Complexity and Misspecification in Exploratory Structural Equation Modeling

Exploratory structural equation modeling (ESEM) allows items to cross-load on nontarget factors and provides flexibility in modeling multidimensional survey data. However, this flexibility comes at the cost of increased model complexity due to the estimation of a significantly greater number of parameters than conventional SEM. This study systematically evaluated the model fit indices in ESEM through a Monte Carlo simulation. Design factors included model complexity,atent factor correlations, magnitudes and percentages of major cross-loadings, and sample sizes. Results showed that both the number ofatent factors m and the item–factor ratio p/m had distinct impacts on rejection rates, particularly in underspecified models. Among the fit measures, χ2 tests and Mc demonstrated high power for detecting misspecification while, in general, elevating false positives. CFI and TLI provided a more balanced trade-off between false- and true-positive rates. When evaluating ESEM, it is important to consider multiple fit indices and justify the cutoff criteria across models with different factor structures.