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Robust Mean and Covariance Structure Analysis Through Iteratively Reweighted Least Squares

Published online by Cambridge University Press:  02 January 2025

Ke-Hai Yuan  and
Peter M. Bentler
Ke-Hai Yuan*
Affiliation:
University of North Texas
Peter M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Ke-Hai Yuan, Department of Psychology, University of North Texas, PO Box 311280, Denton TX 76203-1280.
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Abstract

Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure.

Keywords

mean and covariance structuresstructural equationsgeneralized least squares
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 1 , March 2000 , pp. 43 - 58
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The authors acknowledge the constructive comments of three referees and the Editor that lead to an improved version of the paper. This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017 and by the University of North Texas Faculty Research Grant Program.

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