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Computation and application of generalized linear mixed model derivatives using lme4

Author

Listed:
  • Ting Wang

    (American Board of Family Medicine)

  • Benjamin Graves

    (University of Missouri)

  • Yves Rosseel

    (Ghent University)

  • Edgar C. Merkle

    (University of Missouri)

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.

Suggested Citation

  • Ting Wang & Benjamin Graves & Yves Rosseel & Edgar C. Merkle, 2022. "Computation and application of generalized linear mixed model derivatives using lme4," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1173-1193, September.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:3:d:10.1007_s11336-022-09840-2
    DOI: 10.1007/s11336-022-09840-2
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