The Performance of Ten Modified Rescaled Statistics as the Number of Variables Increases

Among test statistics for assessing overall model fit in structural equation modeling (SEM), the Satorra–Bentler rescaled statistic T_RML is most widely used when the normality assumption is violated. However, many researchers have found that T_RML tends to overreject correct models when the number of variables (p) is large and/or the sample size (N) is small. Modifications of T_RML have been proposed, but few studies have examined their performance against each other, especially when p is large. This article systematically evaluates 10 corrected versions of T_RML. Results show that the Bartlett correction and a recently proposed rank correction perform better than others in controlling Type I error rates, according to their deviations from the nominal rate. Nevertheless, the performance of both corrections depends heavily on p in addition to N. As p becomes relatively large, none of the corrected versions can properly control Type I errors even when N is rather large.