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Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
Nian-Sheng Tang
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
Nian-Sheng Tang
Affiliation:
Yunnan University, Kunming
*
Requests for reprints should be sent to Professor 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

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables, parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the newly developed Bayesian methodologies.

Keywords

Bayes factorGibbs samplerMetropolis–Hastings algorithmmodel comparisonnonignorable missing datapath sampling
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 541 - 564
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

This research is fully supported by a grant (CUHK 4243/03H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the editor and reviewers for valuable comments for improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data.

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