Generalized linear models

The class of generalized linear models (GLMs) extends the classical linear model for continuous, normal responses to describe the relationship between one or more predictor variables x(1), . . . , x(p) and a wide variety of nonnormally distributed responses Y including binary, count, and positive-valued variates. GLMs expand the class of response densities from the normal to an exponential family that contains the normal, Poisson, binomial, and other popular distributions as special cases. The models produce estimated expected values that conform to response constraints and allow nonlinear relationships between predictors and expected values. It is straightforward to construct the likelihood for a set of data so that maximum likelihood and related likelihood-based methods are popular techniques for parameter estimation and inference. A key point with GLMs is that many of the considerations in model construction are the same as for standard linear regression models as the models have many common features. (C) 2011 John Wiley & Sons, Inc.