The R Book

Generalized Linear Mixed Models

Pseudoreplicated data with non-normal errors lead to a choice of generalized linear mixed-effects models using lmer with a specified error family. These were previously handled by the function glmmPQL which is part of the MASS library (see Venables and Ripley, 2002). That function fitted a generalized linear mixed model with multivariate normal random effects, using penalized quasi-likelihood (hence the ‘PQL’). The default method for a generalized linear model fit with lmer has been switched from PQL to the more reliable Laplace method, as explained in Chapter 14. The lmer function can deal with the same error structures as a generalized linear model, namely Poisson (for count data), binomial (for binary data or proportion data) or gamma (for continuous data where the variance increase with the square of the mean). The model call is just like a mixed-effects model but with the addition of the name of the error family, like this:

lmer(y~fixed+(time | random), family=binomial)

For a worked example, involving patients who were tested for the presence of a bacterial infection on a number of occasions (the number varying somewhat from patient to patient), see pp. 604–609. The response variable is binary: yes for infected patients or no for patients not scoring as infected, so the family is binomial. There is a single categorical explanatory variable (a fixed effect) called treatment, which has three levels: drug, drug plus supplement, and placebo. The ...