Families

The class of generalized linear models handled by facilities supplied in . includes gaussian, binomial, poisson, inverse gaussian and gamma response distributions and also quasi-likelihood models where the response distribution is not explicitly specified. In the latter case the variance function must be specified as a function of the mean, but in other cases this function is implied by the response distribution.

Each response distribution admits a variety of link functions to connect the mean with the linear predictor. Those automatically available are as in Table .

 

Table:   Families and the link functions available to them

$$\begin{tabular} {@{\protect\strutt}\vert c\vert*{6}{c\vert}}... ...tt sqrt & & & & & $\star$\space & $\star$\\ \hline\end{tabular}$$

The combination of a response distribution, a link function and various other pieces of information that are needed to carry out the modelling exercise is called the family of the generalized linear model.