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

Miao Yang, Ge Jiang, Ke-hai Yuan

Research output: Contribution to journalArticlepeer-review


Among test statistics for assessing overall model fit in structural equation modeling (SEM), the Satorra–Bentler rescaled statistic TRML is most widely used when the normality assumption is violated. However, many researchers have found that TRML tends to overreject correct models when the number of variables (p) is large and/or the sample size (N) is small. Modifications of TRML 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 TRML. 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.
Original languageEnglish (US)
Pages (from-to)414-438
Number of pages25
JournalStructural Equation Modeling
Issue number3
StatePublished - May 4 2018
Externally publishedYes


  • large number of variables
  • nonnormality
  • rescaled statistic
  • small sample size

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Modeling and Simulation
  • Sociology and Political Science
  • Economics, Econometrics and Finance(all)


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