Normal Models

Abstract

The classical normal linear models are especially simple mathematically, as compared to other members of the exponential dispersion family, for a number of reasons:

• the canonical link function for the normal distribution is the identity;

• the variance function does not depend on the mean;

• all cumulants after the second are zero;

• all dependence relationships in the multivariate normal distribution are contained in the (second-order) covariance or correlation matrix;

• in a multivariate normal distribution, the conditional distribution of one variable given the others is just the linear multiple regression model.