On the Comparison of Multinomial and Poisson Log-Linear Models

Abstract

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