Generalized linear models with clustered data: fixed and random effects models 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.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Li, Haocheng; Shu, Di; Zhang, Yukun; Yi, Grace Y.: Simultaneous variable selection and estimation for multivariate multilevel longitudinal data with both continuous and binary responses (2018)
- Groll, Andreas; Tutz, Gerhard: Variable selection in discrete survival models including heterogeneity (2017)
- Huang, Lu; Tang, Li; Zhang, Bo; Zhang, Zhiwei; Zhang, Hui: Comparison of different computational implementations on fitting generalized linear mixed-effects models for repeated count measures (2016)
- Tutz, Gerhard; Schmid, Matthias: Modeling discrete time-to-event data (2016)
- Casals, Martí; Langohr, Klaus; Carrasco, Josep Lluís; Rönnegård, Lars: Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles: a simulation study (2015)
- Groll, Andreas; Tutz, Gerhard: Variable selection for generalized linear mixed models by (L_1)-penalized estimation (2014)
- Broström, Göran; Holmberg, Henrik: Generalized linear models with clustered data: fixed and random effects models (2011)
- Zhao, Y.; Staudenmayer, J.; Coull, B. A.; Wand, M. P.: General design Bayesian generalized linear mixed models (2006)