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Analysis of Structural Equation Model with Ignorable Missing Continuous and Polytomous Data

Published online by Cambridge University Press:  01 January 2025

Xin-Yuan Song  and
Sik-Yum Lee
Xin-Yuan Song
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 Sik-Yum 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

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.

Keywords

structural equation modelpolytomous variablesmissing dataGibbs samplerMetropolis-Hastings algorithmmissing pattern
Type
Articles
Information
Psychometrika , Volume 67 , Issue 2 , June 2002 , pp. 261 - 288
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The work described in this paper was fully supported by a grant from the Research Grants Council of the HKSAR (Project No. CUHK 4088/99H). The authors are greatly indebted to the Editor and anonymous reviewers for valuable comments in improving the paper; and also to D. E. Morisky and J.A. Stein for the use of their AIDS data set.

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