The class of generalized linear models handled by facilities supplied in S-PLUS 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 3
Table 3: Families and the link functions available to them
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.