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Influence Analysis of Structural Equation Models with Polytomous Variables

Published online by Cambridge University Press:  01 January 2025

Wai-Yin Poon ,
Shu-Jia Wang  and
Sik-Yum Lee
Wai-Yin Poon*
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Shu-Jia Wang
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Sik-Yum Lee
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
*
Requests for reprints should be sent to Dr. Wai-Yin Poon, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. E-mail: [email protected]
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Abstract

The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.

Keywords

Structural equation modelpolytomous variablesensitivitylocal influencecontingency table
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 4 , December 1999 , pp. 461 - 473
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

The work described in this paper was partially supported by a Chinese University of Hong Kong Postdoctoral Fellows Scheme and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Ref. No. CUHK4186/98P). We are indebted to P.M. Bentler and M.D. Newcomb for providing the data set, Michael Leung for his assistance, and the Editor and the referees for some very valuable comments.

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