Darroch, J. N.; Speed, T. P. Additive and multiplicative models and interactions. (English) Zbl 0556.62032 Ann. Stat. 11, 724-738 (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 characterized 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. Cited in 25 Documents MSC: 62H17 Contingency tables 62K15 Factorial statistical designs 62E10 Characterization and structure theory of statistical distributions Keywords:linear models; log-linear models; unified treatment; multiplicative models; Lancaster-additive models; multi-dimensional contingency tables; averaging operators; generalised interaction PDFBibTeX XMLCite \textit{J. N. Darroch} and \textit{T. P. Speed}, Ann. Stat. 11, 724--738 (1983; Zbl 0556.62032) Full Text: DOI