Generalized linear mixed model

In statistics, a generalized linear mixed model (GLMM) is a particular type of mixed model (multilevel model). It is an extension to the generalized linear model in which the linear predictor contains random effects as well as the usual fixed effects. These random effects are nearly always assumed to have a normal distribution.

Fitting such models requires integrating over these random effects. In general, these integrals cannot be expressed in analytical form — they require either some form of approximation or numerical quadrature. 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 MCMC have increased in use as increasing computing power and advances in methods have made them more practical.

References

• Breslow, NE (1993). "Approximate Inference in Generalized Linear Mixed Models". Journal of the American Statistical Association. 88 (421): 9–25. {{cite journal}}: Unknown parameter |coauthor= ignored (|author= suggested) (help)

• Fitzmaurice, Garrett M. (2004). Applied longitudinal analysis. Hoboken, NJ: Wiley-Interscience. ISBN 0-471-21487-6. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)