ON THE COMPARISON OF MULTINOMIAL AND POISSON LOG-LINEAR MODELS

We introduce a method for comparing multinomial and Poisson log-linear models which affords an explicit description of their equivalences an d differences. The method involves specifying the model in terms of co nstraint equations, rather than the more common freedom equations. The Poisson and multinomial large sample distributions of log-linear mode l parameter estimators are derived and compared within this constraint equation context; reparameterizations are thereby avoided. As a by-pr oduct, the method provides the practitioner with the adjustment that i s necessary to make valid inferences about all multinomial log-linear parameters when, as a matter of convenience, the Poisson log-linear mo del is fitted. This implies that valid large sample inferences about t he multinomial cell probabilities can be made directly by using the Po isson log-linear model. To illustrate the utility of this approach, se veral examples are considered.