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A Bayesian Approach to Nonlinear Latent Variable Models using the Gibbs Sampler and the Metropolis-Hastings Algorithm

Published online by Cambridge University Press:  01 January 2025

Gerhard Arminger  and
Bengt O. Muthén
Gerhard Arminger*
Affiliation:
Bergische Universität Wuppertal, Department of Economics
Bengt O. Muthén
Affiliation:
University of California, Los Angeles Graduate School of Education & Information Studies
*
Requests for reprints should be sent to Gerhard Arminger, Department of Economics, FB6, Bergische Universität—GH Wuppertal, D-42097 Wuppertal, GERMANY.
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Abstract

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis-Hastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a non-linear model for the dependence of performance on task complexity and goal specificity using empirical data.

Keywords

Gibbs SamplerLISREL modelMetropolis-Hastings algorithmNon-linear functions of latent regressors
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 3 , September 1998 , pp. 271 - 300
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

The first author is indebted to the Graduate School of Education and Information Studies at UCLA for providing a visiting professorship during the winter quarter 1994. The work of the first author was supported by a grant from the Deutsche Forschungsgemeinschaft. The work of the second author was supported by grant 1K02AA00230-01 from NIAAA and by grant 40859 from NIMH to C. Hendricks Brown's Prevention Science Methodology Group. The authors thank Donald Rubin and C. Hendricks Brown for a critical reading of the first draft of the paper. They are especially grateful for the technical assistance of Jörg Wittenberg of the Bergische Universität Wuppertal who designed the program BALAM (Bayesian Analysis of Latent Variable Models). The data for the empirical example have been generously provided by Heinz Holling of the University of Münster, Germany. The authors are indebted to an associate editor and to three anonymous reviewers of Psychometrika whose criticisms, comments and suggestions have been very helpful.

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