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Generalized linear models with clustered data: Fixed and random effects models

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  • Broström, Göran
  • Holmberg, Henrik

Abstract

The statistical analysis of mixed effects models for binary and count data is investigated. In the statistical computing environment R, there are a few packages that estimate models of this kind. The package lme4 is a de facto standard for mixed effects models. The package glmmML allows non-normal distributions in the specification of random intercepts. It also allows for the estimation of a fixed effects model, assuming that all cluster intercepts are distinct fixed parameters; moreover, a bootstrapping technique is implemented to replace asymptotic analysis. The random intercepts model is fitted using a maximum likelihood estimator with adaptive Gauss-Hermite and Laplace quadrature approximations of the likelihood function. The fixed effects model is fitted through a profiling approach, which is necessary when the number of clusters is large. In a simulation study, the two approaches are compared. The fixed effects model has severe bias when the mixed effects variance is positive and the number of clusters is large.

Suggested Citation

  • Broström, Göran & Holmberg, Henrik, 2011. "Generalized linear models with clustered data: Fixed and random effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3123-3134, December.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3123-3134
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    References listed on IDEAS

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    1. Emmanuel Lesaffre & Bart Spiessens, 2001. "On the effect of the number of quadrature points in a logistic random effects model: an example," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 325-335.
    2. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    3. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3441-3458, March.
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    3. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    4. Kitano, Shinichi & Mitsunari, Yuka & Yoshino, Akira, 2022. "The impact of information asymmetry on animal welfare-friendly consumption: Evidence from milk market in Japan," Ecological Economics, Elsevier, vol. 191(C).

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