Generalized linear mixed model

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In statistics, a generalized linear mixed model (GLMM) is a particular type of mixed model with random and fixed effects in the linear predictor.


It is an extension to the generalized linear model in which the linear predictor contains random effects in addition to the usual fixed effects. These random effects are usually assumed to have a normal distribution.


Fitting such models by maximum likelihood involves integrating over these random effects. In general, these integrals cannot be expressed in analytical form. Various approximate methods have been developed, but none has good properties for all possible models and data sets (ungrouped binary data being particularly problematic). For this reason, methods involving numerical quadrature or Markov chain Monte Carlo have increased in use as increasing computing power and advances in methods have made them more practical.

See also[edit]

  • Generalized estimating equation


  • Fitzmaurice, Garrett M.; Laird, Nan M.; Ware, James H. (2004). Applied longitudinal analysis. Hoboken, NJ: Wiley-Interscience. ISBN 0-471-21487-6.