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Model Comparison of Nonlinear Structural Equation Models with Fixed Covariates

Published online by Cambridge University Press:  01 January 2025

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

Recently, it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory. A new nonlinear structural equation model with fixed covariates is proposed in this article. A procedure, which utilizes the powerful path sampling for computing the Bayes factor, is developed for model comparison. In the implementation, the required random observations are simulated via a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. It is shown that the proposed procedure is efficient and flexible; and it produces Bayesian estimates of the parameters, latent variables, and their highest posterior density intervals as by-products. Empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example.

Keywords

nonlinear structural equation modelmodel comparisonBayes factorpath samplingGibbs samplerMetropolis-Hastings algorithmsensitivity
Type
Articles
Information
Psychometrika , Volume 68 , Issue 1 , March 2003 , pp. 27 - 47
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

This research is fully supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. CUHK 4346/01H). The authors are thankful to the Editor, the Associate Editor, and anonymous reviewers for valuable comments which improve the paper significantly, and grateful to ICPSR and the relevant funding agency for allowing use of the data in the example. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.

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