Computation and application of generalized linear mixed model derivatives using lme4

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.

Score-based tests for detecting heterogeneity in linear mixed models

“…This allows researchers to apply score-based tests to mixed models and other models where observations are not independent. It extends related work on score-based tests for mixed models (Fokkema et al, 2018;Wang et al, 2021Wang et al, , 2022, allowing us to for heterogeneity with respect to level-1 auxiliary variables. While this chapter provides evidence that self-normalization is promising for score-based tests, it leaves open many issues for future work.…”

“…Because the sum of scores across all cases is by definition zero (e.g., B 1,n = 0), the second term in parentheses disappears in most score-based applications. The only exception here may be situations where the scores involve an integral approximation, as in GLMMs (e.g., Wang, Graves, Rosseel, & Merkle, 2022). In these situations, the scores may not sum to exactly zero due to the approximation.…”

The Effects of Acute Deep Seawater Supplementation on Muscle Function after Triathlon

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“…Since it employs modern, efficient linear algebra methods, such as those implemented in the Eigen package, as well as reference classes to prevent undue copying of large objects, the lme4 package is likely to be faster and more memory-efficient than other programs. Additionally, the software is capable of constructing generalized linear mixed models using the glmer function, so as to maximize the amount of information available when loss patients are included in some of the analyzed conditions [32]. Our post hoc analysis was performed using R program version 3.6 and the emmeans function using the Tukey method.…”

Long-Term Exposure to Fine Particulate Constituents and Vascular Damage in a Population with Metabolic Abnormality in China

“…All statistical analyses were conducted using the SPSS software version 23.0 (IBM Corp., Armonk, NY, USA) and R software version 4.0.5 (R Foundation for Statistical Computing, Vienna, Austria). The "lme4" package was used to evaluate the relationship between PM component exposure and outcome 36) and the "qgcomp" and "knitr" packages to build a multiple PM component model 34) . P＜0.05 on both sides was considered to indicate statistical significance.…”