Log Linear Models for Contingency Tables: A Generalization of Classical Least Squares

Abstract

SUMMARY Log linear models for contingency tables of counts are formulated as a special case of generalized linear models with an additive systematic component Y, Poisson errors for the data and an exponential linking function connecting the expected values of the observations with the predicted Y. Dichotomous response variates can be treated by an extension of this model or equivalently as another generalized linear model with binomial errors. A program package is described for fitting these models, and some redundancies in the literature noted.