What is a Generalized Linear Model? A traditional linear model is of the form
where Yi is the response variable for the ith observation, xi is a column vector of explanatory variables for the ith response. Note that the p-dimensional vector xi is usually considered to be ?xed, or nonrandom. The p-dimensional vector β of unknown coe?cients is to be estimated on the basis of n observations. The errors i are assumed to be independent normally distributed zero-mean random variables with a constant variance. Hence, holds, that is, the expected value of the output random variable is a linear transformation of the input. All these assumptions are limitations and may not hold in some cases. In particular:
These limitations are dealt with in the setting of the generalized linear model (GLM) or their generalization, the generalized additive model (GAM). GLM have been introduced in Statistics by Nelder and Wedderburn (1972).