A note on the cutoff values of alternative fit indices to evaluate measurement invariance for ESEM models

Abstract

This research examines the performance of the previously proposed cutoff values of alternative fit indices (i.e., change in comparative fit index [ $\text{ΔCFI}$ ], change in Tucker–Lewis index [ $\text{ΔTLI}$ ], and change in root mean squared error of approximation [ $\Delta \text{RMSEA}$ ]) to evaluate measurement invariance for exploratory structural equation modeling (ESEM) models with simulated data. It is important to revisit these cutoff values because they were used widely in validity studies utilizing ESEM models to evaluate measurement invariance for ordinal indicators, but in fact, these cutoff values were developed under confirmatory factor analysis models with continuous indicators. Results of this study show that different cutoff values of $\text{ΔCFI}$ , $\text{ΔTLI}$ , and $\Delta \text{RMSEA}$ should be used for ESEM models with ordinal indicators. Evaluation of partial invariance for ESEM models is also discussed.