Hierarchical Generalized Linear Models - theory and practice Seminar

Hierarchical generalized linear models (HGLMs) extend the familiar generalized linear models (GLMs) by allowing you to include additional random terms in the linear predictor. However, they do not constrain these terms to follow a Normal distribution nor to have an identity link, as e.g. in generalized linear mixed models. So they provide a richer of class of models that may be more intuitively appealing. The methodology provides improved estimation methods that reduce bias, by the use of the exact likelihood or extended Laplace approximations. In particular, the Laplace approximations seem to avoid the biases that are often found when binary data are analysed by generalized linear mixed models.

The algorithm involves fitting two (or more) interlinked GLMs, firstly to estimate the fixed and random effects in the model that describes the mean, and secondly to model the dispersion of the random terms. So all the familiar model checking techniques are available. We can also exploit other GLM extensions such as prediction and the inclusion of nonlinear parameters in the linear predictor.

The theory will be explained, with examples from GenStat to illustrate its usefulness in practical data analysis.