Additive and Multiplicative Models and Interactions
J. N. Darroch, Terence Paul Speed · The Annals of Statistics · 1983
A unified treatment is given of the classical additive models for complete factorial experiments and of multiplicative models and Lancaster-additive models for multi-dimensional contingency tables. The models are characterised by properties of being simplest subject to having a prescribed set of marginals. It is shown that, by using averaging operators and the notion of a generalised interaction, the interaction properties of these models can be derived very simply.