ABSTRACT

The generalized linear model (GLM) allows a suitable transform of the mean of the response variable to be modeled as a linear function of the explanatory variables, and to have an error distribution appropriate for the type of response involved. Some important cases of the GLM are logistic regression for the binary response variables and Poisson regression for responses that are counts. Logistic regression is a GLM with a binomial error distribution, and typically used with the logit link function. In GLMs a measure of fit is provided by a quantity known as the deviance which measures how closely the model-based fitted values of the response approximate the observed value. When fitting GLMs with binomial or Poisson error distributions, overdispersion can often be spotted by comparing the residual deviance with its degrees of freedom.