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This note serves as a reminder that incremental fit indices are a form of standardized effect sizes and hence, all reservations with respect to interpretations of standardized effect sizes also transfer to their interpretation. Such a realization has major implications for the interpretation and use of incremental fit indices, for the theoretical (im)possibility of default universal rules of thumb in their application, and for simulation studies mapping incremental fit indices as if their value is comparable in an absolute sense across any and all conditions. A small but illustrative working example centered around the alleged impact of model type will drive these points home. [ABSTRACT FROM AUTHOR]

As a prerequisite for meaningful comparison of latent variables across multiple populations, measurement invariance or specifically factorial invariance has often been evaluated in social science research. Alongside with the changes in the model chi-square values, the comparative fit index (CFI; Bentler, 1990) is a widely used fit index for evaluating different stages of factorial invariance, including metric invariance (equal factor loadings), scalar invariance (equal intercepts), and strict invariance (equal unique factor variances). Although previous literature generally showed that the CFI performed well for single-group structural equation modeling analyses, its applicability to multiple group analyses such as factorial invariance studies has not been examined. In this study we argue that the commonly used default baseline model for the CFI might not be suitable for factorial invariance studies because (a) it is not nested within the scalar invariance model, and thus (b) the resulting CFI values might not be sensitive to the group differences in the measurement model. We therefore proposed a modified version of the CFI with an alternative (and less restrictive) baseline model that allows observed variables to be correlated. Monte Carlo simulation studies were conducted to evaluate the utility of this modified CFI across various conditions including varying degree of noninvariance and different factorial invariance models. Results showed that the modified CFI outperformed both the conventional CFI and the ΔCFI (Cheung & Rensvold, 2002) in terms of sensitivity to small and medium noninvariance. [ABSTRACT FROM AUTHOR]