Evaluating the Selection of Normal-Theory Weight Matrices in the Satorra–Bentler Correction of Chi-Square and Standard Errors

Yan Xia, Yiu Fai Yung, Wei Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

In the application of the Satorra–Bentler scaling correction, the choices of normal-theory weight matrices (i.e., the model-predicted vs. the sample covariance matrix) in the calculation of the correction remains unclear. Different software programs use different matrices by default. This simulation study investigates the discrepancies due to the weight matrices in the robust chi-square statistics, standard errors, and chi-square-based model fit indexes. This study varies the sample sizes at 100, 200, 500, and 1,000; kurtoses at 0, 7, and 21; and degrees of model misspecification, measured by the population root mean square error of approximation (RMSEA), at 0,.03,.05,.08,.10, and.15. The results favor the use of the model-predicted covariance matrix because it results in less false rejection rates under the correctly specified model, as well as more accurate standard errors across all conditions. For the sample-corrected robust RMSEA, comparative fit index (CFI) and Tucker–Lewis index (TLI), 2 matrices result in negligible differences.

Original languageEnglish (US)
Pages (from-to)585-594
Number of pages10
JournalStructural Equation Modeling
Volume23
Issue number4
DOIs
StatePublished - Jul 3 2016
Externally publishedYes

Keywords

  • Satorra–Bentler robust correction
  • model fit
  • nonnormality
  • standard error

ASJC Scopus subject areas

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

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