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Structural Equation Modeling with Heavy Tailed Distributions

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan ,
Peter M. Bentler  and
Wai Chan
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Peter M. Bentler
Affiliation:
University of California, Los Angeles
Wai Chan
Affiliation:
The Chinese University of Hong Kong
*
Correspondence concerning this article should be addressed to Ke-Hal Yuan, Department of Psychology, University of Notre Dame, Notre Dame, IN 46556, USA. Email: kyuan@nd.edu.
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Abstract

Data in social and behavioral sciences typically possess heavy tails. Structural equation modeling is commonly used in analyzing interrelations among variables of such data. Classical methods for structural equation modeling fit a proposed model to the sample covariance matrix, which can lead to very inefficient parameter estimates. By fitting a structural model to a robust covariance matrix for data with heavy tails, one generally gets more efficient parameter estimates. Because many robust procedures are available, we propose using the empirical efficiency of a set of invariant parameter estimates in identifying an optimal robust procedure. Within the class of elliptical distributions, analytical results show that the robust procedure leading to the most efficient parameter estimates also yields a most powerful test statistic. Examples illustrate the merit of the proposed procedure. The relevance of this procedure to data analysis in a broader context is noted.

Keywords

structural modelkurtosisrobust methodsefficiencypower
Type
Theory and Methods
Information
Psychometrika , Volume 69 , Issue 3 , September 2004 , pp. 421 - 436
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The authors thank the editor, an associate editor and four referees for their constructive comments, which led to an improved version of the paper.

This project was supported by Grant DA01070 from the National Institute on Drug Abuse and a Direct Grant for Research from The Chinese University of Hong Kong.

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