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Computation and application of generalized linear mixed model derivatives using lme4

Published online by Cambridge University Press:  01 January 2025

Ting Wang ,
Benjamin Graves ,
Yves Rosseel  and
Edgar C. Merkle Open the ORCID record for Edgar C. Merkle [Opens in a new window]
Ting Wang
Affiliation:
American Board of Family Medicine
Benjamin Graves
Affiliation:
University of Missouri
Yves Rosseel
Affiliation:
Ghent University
Edgar C. Merkle*
Affiliation:
University of Missouri
*
Correspondence should be made to Edgar C. Merkle, University of Missouri, Columbia, MO, USA. Email: merklee@missouri.edu
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Abstract

Maximum likelihood estimation of generalized linear mixed models (GLMMs) is difficult due to marginalization of the random effects. Derivative computations of a fitted GLMM’s likelihood are also difficult, especially because the derivatives are not by-products of popular estimation algorithms. In this paper, we first describe theoretical results related to GLMM derivatives along with a quadrature method to efficiently compute the derivatives, focusing on fitted lme4 models with a single clustering variable. We describe how psychometric results related to item response models are helpful for obtaining the derivatives, as well as for verifying the derivatives’ accuracies. We then provide a tutorial on the many possible uses of these derivatives, including robust standard errors, score tests of fixed effect parameters, and likelihood ratio tests of non-nested models. The derivative computation methods and applications described in the paper are all available in easily obtained R packages.

Keywords

generalized linear mixed modelscore testlme4derivativesmerDeriv
Type
Application Reviews and Case Studies
Information
Psychometrika , Volume 87 , Issue 3 , September 2022 , pp. 1173 - 1193
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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