Comparing RMSEA-Based Indices for Assessing Measurement Invariance in Confirmatory Factor Models

Fit indices are descriptive measures that can help evaluate how well a confirmatory factor analysis (CFA) model fits a researcher's data. In multigroup models, before between-group comparisons are made, fit indices may be used to evaluate measurement invariance by assessing the degree to which multiple groups' data are consistent with increasingly constrained nested models. One such fit index is an adaptation of the root mean square error of approximation (RMSEA) called RMSEA_D. This index embeds the chi-square and degree-of-freedom differences into a modified RMSEA formula. The present study comprehensively compared RMSEA_D to ΔRMSEA, the difference between two RMSEA values associated with a comparison of nested models. The comparison consisted of both derivations as well as a population analysis using one-factor CFA models with features common to those found in practical research. The findings demonstrated that for the same model, RMSEA_D will always have increased sensitivity relative to ΔRMSEA with an increasing number of indicator variables. The study also indicated that RMSEA_D had increased ability to detect noninvariance relative to ΔRMSEA in one-factor models. For these reasons, when evaluating measurement invariance, RMSEA_D is recommended instead of ΔRMSEA.