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Statistical inference in generalized linear mixed models: a review.

Francis Tuerlinckx1, Frank Rijmen, Geert Verbeke

  • 1Department of Psychology, University of Leuven, Belgium. francis.tuerlinckx@psy.kuleuven.be

The British Journal of Mathematical and Statistical Psychology
|October 28, 2006
PubMed
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This review covers statistical inference for generalized linear mixed models (GLMMs), focusing on methods to handle intractable integrals in non-normal, clustered data analysis. It explores numerical and analytical approximations for estimating fixed effects and variance components.

Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Generalized linear mixed models (GLMMs) extend generalized linear models for non-normal, clustered data.
  • GLMMs incorporate fixed effects and random cluster-specific effects, requiring estimation of variance components.

Purpose of the Study:

  • To review statistical inference methods for GLMMs.
  • To discuss approaches for handling intractable integrals in GLMM likelihood estimation.
  • To overview hypothesis testing for GLMM parameters.

Main Methods:

  • Focus on GLMMs with normally distributed cluster-specific parameters.
  • Discusses integration of cluster-specific effects for parameter estimation.
  • Categorizes methods into numerical and analytical approximations for intractable integrals.

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Main Results:

  • The integral over cluster-specific effects is often intractable for normal mixing distributions.
  • Two main classes of methods exist: numerical and analytical approximations.
  • Methods are available for estimating fixed effects, variance components, and testing hypotheses.

Conclusions:

  • Accurate statistical inference in GLMMs relies on effective handling of intractable integrals.
  • The choice between numerical and analytical approximations depends on the specific GLMM.
  • A comprehensive overview of inference methods and hypothesis testing is provided.