### Abstract

Among test statistics for assessing overall model fit in structural equation modeling (SEM), the Satorra–Bentler rescaled statistic

*T*is most widely used when the normality assumption is violated. However, many researchers have found that_{RML}*T*tends to overreject correct models when the number of variables (p) is large and/or the sample size (N) is small. Modifications of_{RML }*T*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_{RML }*T*. 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._{RML}Original language | English (US) |
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Pages (from-to) | 414-438 |

Journal | Structural Equation Modeling |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - May 4 2018 |

Externally published | Yes |

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### Keywords

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

### Cite this

Yang, M., Jiang, G., & Yuan, K. (2018). The Performance of Ten Modified Rescaled Statistics as the Number of Variables Increases.

*Structural Equation Modeling*,*25*(3), 414-438. https://doi.org/10.1080/10705511.2017.1389612