Dynamic measurement invariance cutoffs for two-group fit index differences.

Abstract

Measurement invariance is investigated to ensure that a measurement scale functions similarly across different groups. 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 a difference in comparative fit index ΔCFI above -.01 or a difference in the root-mean-square error of approximation ΔRMSEA less than .01 suggests evidence of invariance. In this article, we review the methodological literature that highlights that these widely used cutoffs do not generalize well. Specifically, the 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 cutoffs originally devised to accommodate related issues in single-group models. DMI generalizes the procedure used in the seminal Cheung and Rensvold (2002) study by executing a simulation based on the researcher's specific model and data characteristics. DMI derives custom fit index difference cutoffs with optimal performance for the model being evaluated. The article 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 the accessibility of the method. (PsycInfo Database Record (c) 2025 APA, all rights reserved).