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Global Convergence of the EM Algorithm for Unconstrained Latent Variable Models with Categorical Indicators

Published online by Cambridge University Press:  01 January 2025

Alexander Weissman
Alexander Weissman*
Affiliation:
Psychometric Research, Law School Admission Council
*
Requests for reprints should be sent to Alexander Weissman, Psychometric Research, Law School Admission Council, 662 Penn Street, Box 40, Newtown, PA 18940, USA. E-mail: aweissman@lsac.org
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Abstract

Convergence of the expectation-maximization (EM) algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented. The sufficient conditions under which global convergence of the EM algorithm is attainable are provided in an information-theoretic context by interpreting the EM algorithm as alternating minimization of the Kullback–Leibler divergence between two convex sets. It is shown that these conditions are satisfied by an unconstrained latent class model, yielding an optimal bound against which more highly constrained models may be compared.

Keywords

EM algorithmlatent variable modelslatent class modelsinformation theoryKullback–Leibler divergencerelative entropyvariational calculusconvex optimizationoptimal bounds

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 1 , January 2013 , pp. 134 - 153
Copyright
Copyright © The Psychometric Society

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