Sensitivity of Fit Measures to Lack of Measurement Invariance in Exploratory Structural Equation Modeling

Exploratory structural equation modeling (ESEM) allows for the estimation of all cross-loadings, which leads to the number of parameters estimated substantially greater than that in conventional SEM. This study examined the sensitivity of fit measures (CFI, RMSEA, AIC, BIC, SaBIC, LRT) to measurement noninvariance in ESEM. Results suggested that the sensitivity of the fit measures depended on the magnitude of noninvariance, model complexity, and sample size. The sensitivity of LRT to both metric and scalar noninvariance was high. Comparative fit index tended to filter out small noninvariance with large sample sizes. Root mean squared error of approximation failed to detect even a large measurement noninvariance when the model was complex and sample size was below 300 per group. Information criteria were more sensitive to scalar noninvariance than to metric noninvariance. Implications and recommendations based on the findings were discussed.