The Annals of Statistics

Additive and Multiplicative Models and Interactions

J. N. Darroch and T. P. Speed

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 724-738.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346240

Digital Object Identifier
doi:10.1214/aos/1176346240

Mathematical Reviews number (MathSciNet)
MR707924

Zentralblatt MATH identifier
0556.62032

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62E30

Keywords
Generalised interaction Lancaster model linear model log-linear model

Citation

Darroch, J. N.; Speed, T. P. Additive and Multiplicative Models and Interactions. Ann. Statist. 11 (1983), no. 3, 724--738. doi:10.1214/aos/1176346240. https://projecteuclid.org/euclid.aos/1176346240


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