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Maximum Likelihood Estimation of Nonlinear Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
Hong-Tu Zhu
Sik-Yum Lee*
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Hong-Tu Zhu
Affiliation:
Department of Mathematics and Statistics, University of Victoria
*
Requests for reprints should be sent to S. Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T. HONG KONG. E-Mail: sylee@sparc2.sta.cuhk.edu.hk
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Abstract

The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlinear relationships are often encountered in social and behavioral sciences. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model. To avoid computation of the complicated multiple integrals involved, the E-step is completed by a Metropolis-Hastings algorithm. It is shown that the M-step can be completed efficiently by simple conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis's formula. The methodology is illustrated with results from a simulation study and two real examples.

Keywords

nonlinear structural equation modelsmissing dataMCECM algorithmMetropolis-Hastings algorithmstandard errors estimates
Type
Articles
Information
Psychometrika , Volume 67 , Issue 2 , June 2002 , pp. 189 - 210
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The order of the authorship is alphabetical. This research is fully supported by a Hong Kong UGC Earmarked grant CUHK 4088/99H. The authors are indebted to the Editor, Associate Editor and anonymous reviewers for valuable comments for improving the paper; and also to ICPSR and the relevant funding agency for allowing use of the data. We thank Xin-Yuan Song, N.H. Tang and Liang Xu for helpful discussions. Assistance of Xin-Yuan Song and Michael K. H. Leung in analyzing the real examples and Esther L.S. Tam in preparing the manuscript is also acknowledged.

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