ABSTRACT
Generalized linear mixed models (GLMM) combine the ideas of generalized linear models with the random effects modeling ideas of the previous two chapters. The response is a random variable, Yi, taking observed values, yi, for i = 1, . . . ,n, and follows an exponential family distribution as defined in Chapter 8:
f (yi|θi,φ) = exp [
yiθi−b(θi) a(φ)
+ c(y,φ) ]
Let EYi = µi and let this be connected to the linear predictor ηi using the link function g by ηi = g(µi). Suppose for simplicity that we use the canonical link for g so that we may make the direct connection that θi = µi.
