Family of generalized linear models

The main models we have considered so far, namely linear models, binary response models (generalizable as ordered response models) and Poisson models, are special cases of the generalized linear model (GLM) or exponential family. It will help us in considering extensions of these models to three levels, and to multivariate responses, if we can start to write each of the models using GLM notation. In GLMs, the explanatory variables xij affect the response (yij) via the linear predictor (θij), where:

θij = γ00 + P∑ p=1

γp0xpij .