Structural fit indices (SFIs) have been advanced due to the influence of the measurement model on the global fit indices (GFIs). First, GFIs are overly weighted by the measurement model. Second, GFI cut-offs were not determined in the context of varying magnitudes of the factor loadings; as a result, model fit seems to improve as the magnitude decreases, known as the reliability paradox. The focus of this study was to examine the relative performance of the recently proposed SFIs in their ability to detect a misspecified mean structure or covariance structure. This study was executed in the context of multiple group models where the misspecifications were in the form of true differences between populations. Of key interest was the impact construct reliability had on power rates for these SFIs, as well as how they performed relative to GFIs. Findings show that structural measures of fit outperformed the global measures of fit regardless of the type of misfit (e.g., mean or covariance). Measures of fit were more sensitive to the magnitude of the factor loadings when the covariance structure was misspecified, relative to when the mean structure was misspecified.
