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A Bayesian Analysis of Finite Mixtures in the LISREL Model

Published online by Cambridge University Press:  01 January 2025

Hong-Tu Zhu  and
Sik-Yum Lee
Hong-Tu Zhu
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 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

In this paper, we propose a Bayesian framework for estimating finite mixtures of the LISREL model. The basic idea in our analysis is to augment the observed data of the manifest variables with the latent variables and the allocation variables. The Gibbs sampler is implemented to obtain the Bayesian solution. Other associated statistical inferences, such as the direct estimation of the latent variables, establishment of a goodness-of-fit assessment for a posited model, Bayesian classification, residual and outlier analyses, are discussed. The methodology is illustrated with a simulation study and a real example.

Keywords

Bayesian analysisfinite mixturesLISREL modelsGibbs samplerconditional distributionsgoodness-of-fit assessmentBayesian classificationresidual and outlier analyses
Type
Articles
Information
Psychometrika , Volume 66 , Issue 1 , March 2001 , pp. 133 - 152
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

This research was supported by a Hong Kong UGC Earmarked grant CUHK 4026/97H. The authors are indebted to the Editor, the Associate Editor, and three anonymous reviewers for constructive comments in improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.

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