The Performance of Ten Modified Rescaled Statistics as the Number of Variables Increases. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Yang, Miao; Jiang, Ge; Yuan, Ke-Hai
• Is Part Of: Structural equation modeling. Volume 25:Issue 3(2018)
• Page Start: 414
• Page End: 438
• Publication Date: 2018-05-04
• Subjects: large number of variables -- nonnormality -- rescaled statistic -- small sample size; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2017.1389612
• Languages: English
• ISSNs: 1070-5511

Abstract

Abstract : Among test statistics for assessing overall model fit in structural equation modeling (SEM), the Satorra–Bentler rescaled statistic is most widely used when the normality assumption is violated. However, many researchers have found that tends to overreject correct models when the number of variables ( p ) is large and/or the sample size ( N ) is small. Modifications of 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 . 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.