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Variational Approximations for Categorical Causal Modeling With Latent Variables

Published online by Cambridge University Press:  01 January 2025

K. Humphreys  and
D. M. Titterington
K. Humphreys*
Affiliation:
Department of Medical Epidemiology and Biostatistics, Karolinska Institutet
D. M. Titterington
Affiliation:
Department of Statistics, University of Glasgow
*
Requests for reprints should be sent to Keith Humphreys, Department of Medical Epidemiology and Biostatistics, P.O. Box 281, Karolinska Institutet, 171 77 Stockholm, SWEDEN. E-Mail: [email protected]
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Abstract

Latent class models in the social and behavioral sciences have remained structurally simple. One reason for this is that inference in statistical models can be computationally difficult. Methods for approximate inference, known as variational approximations, which have been developed in the machine learning, graphical modeling and statistical physics literatures, can be used to alleviate the computational difficulties of inference for latent variable models. The aim of the present article is to set these methods alongside some social and behavioral science literature to which they are relevant, and in particular to consider their potential for “categorical causal modeling”, using latent class analysis. We have collated a number of popular categorical-data models with latent variables and causal structure, typically incorporating a Markovian structure. The efficacy of the approximation methods has been demonstrated through simulations related to an important behavioral science model.

Keywords

EM algorithmcausal modellatent classvariational approximation
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 391 - 412
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

Research was supported by a grant from the UK Engineering and Physical Sciences Research Council. The authors would like to thank anonymous reviewers and the Associate Editor for their very helpful comments on earlier versions of the manuscript.

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