ABSTRACT
Generalized linear models (GLMs), originally formulated by J. A. Nelder and R. J. Baker, provide a unifying family of linear models that is widely used in practical regression analysis. The GLMs generalize ordinary linear regression by allowing the models to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Thus, these models allow for describing response variables that have an error distribution other than normal. The exponential families include many of the common distributions, including the normal inverse Gaussian, exponential gamma, Bernoulli, binomial, multinomial Poisson, chi-squared, Wishart, Inverse Wishart and many others. A GLM provides a unified modeling framework for many commonly used statis- tical models. In many applications, the response variable takes one of only two possible values representing success and failure, or more generally the presence or absence of an attribute of interest.
