Dynamic Measurement Invariance Cutoffs for Two-Group Fit Index Differences

Measurement invariance is investigated to ensure that a measurement scale functions similarly across different demographic groups or timepoints. A prevailing approach is to fit a series of multiple-group confirmatory factor models and then compare differences in fit indices of constrained and unconstrained models. Common recommendations are that ΔCFI above −.01 or ΔRMSEA less than .01 suggests evidence of invariance. In this paper, we review the methodological literature that highlights that these widely used cutoffs do not generalize well. Specifically, distributions of fit index differences expand or contract based on model and data characteristics, making any single cutoff unlikely to maintain desirable performance across a wide range of conditions. To address this, we propose a method called dynamic measurement invariance (DMI) cutoffs, which is an extension of dynamic fit index (DFI) cutoffs originally devised to accommodate related issues in single-group models. DMI generalizes and executes a simulation based on the researcher’s specific model and data characteristics to derive custom fit index difference cutoffs with optimal performance for the model being evaluated. The paper explains the method and provides simulations and empirical examples to demonstrate its potential contribution, as well as ways in which it could be extended to expand its scope and utility. Open-source software is also provided to improve accessibility of the method.