Generalized linear model (GLM)

A model for linear and non-linear effects of continuous and categorical predictor variables on a discrete or continuous but not necessarily normally distributed dependent (outcome) variable. (Note that in the general linear model, the dependent (outcome) variable should be normally distributed). Normal, binary (or linear logistic; when the outcome variable is a proportion), binomial or Poisson (when the outcome variable is a count), exponential and gamma (when the outcome variable is continuous and non-negative) models are different versions of generalized linear models. Particular types of models arise by specifying an appropriate link function, variance and distribution. For example, normal linear regression corresponds to an identity link function, constant variance and a normal distribution. Logistic regression arises from a logit link function and a binomial distribution (the variance of the response (npq) is related to its mean (np): variance = mean (1 - (mean/n)). Loglinear models are used for binomial or Poisson counts. Standard techniques for analysing censored survival data, such as the Cox regression, can also be handled within the GLM framework.