A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects

A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with... We present a variational maximization–maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss–Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects

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Publisher
Springer US
Copyright
Copyright © 2017 by The Psychometric Society
Subject
Psychology; Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Statistical Theory and Methods
ISSN
0033-3123
eISSN
1860-0980
D.O.I.
10.1007/s11336-017-9555-z
Publisher site
See Article on Publisher Site

Abstract

We present a variational maximization–maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss–Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation.

Journal

PsychometrikaSpringer Journals

Published: Feb 28, 2017

References

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