Computation and application of generalized linear mixed model derivatives using lme4

Ting Wang, Benjamin Graves, Yves Rosseel and Edgar C. Merkle ()
Additional contact information
Ting Wang: American Board of Family Medicine
Benjamin Graves: University of Missouri
Yves Rosseel: Ghent University
Edgar C. Merkle: University of Missouri

Psychometrika, 2022, vol. 87, issue 3, No 17, 1173-1193

Abstract: 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 model; score test; lme4; derivatives; merDeriv (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11336-022-09840-2

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