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Working paper

Sensitivity of Goodness-of-Fit Indices to Lack of Measurement Invariance with Categorical Indicators and Many Groups

Using Monte Carlo simulation experiments, this paper examines the performance of popular SEM goodness-of-fit indices, namely CFI, TLI, RMSEA, and SRMR, with respect to a specific task of measurement invariance testing with categorical data and many groups (10-50 groups). Study factors include the number of groups, the level of non-invariance in the data, and the absence/presence of model misspecifications other than non-invariance. In sum, the study design yields a total of 81 conditions. All simulated data sets are analyzed using two popular SEM estimators, MLR and WLSMV. The main contribution of this paper to the methodological literature on cross-cultural survey research is that it produces revised guidelines for evaluating the goodness of fit of invariance MGCFA models with many groups.