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The Analysis of Three-Way Contingency Tables by Three-Mode Association Models

Published online by Cambridge University Press:  01 January 2025

Carolyn J. Anderson
Carolyn J. Anderson*
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Carolyn Anderson, Department of Educational Psychology, University of Illinois, 210 Education Building, 1310 S. Sixth Street, Champaign, IL 61820. Electronic address: [email protected]
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Abstract

The RC(M) association model (Goodman, 1979, 1985, 1986, 1991) is useful for analyzing the relationship between the variables of a 2-way cross-classification. The models presented here are generalizations of the RC(M) association model for 3-way tables. The family of models proposed here, “3-mode association” models, use Tucker's 3-mode components model (Tucker, 1964, 1966; Kroonenberg, 1983) to represent either the three factor interaction or the combined effects of two and three factor interactions. An example from a study in developmental psychology (Kramer & Gottman, 1992) is provided to illustrate the usefulness of the proposed models.

Keywords

loglinear modelsassociation modelsthree-factor interactionsTucker's 3-mode components model
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 3 , September 1996 , pp. 465 - 483
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

I thank Stanley Wasserman, Laurie Kramer, Ulf Böckenholt, Larwence Hubert, Jeffrey Tanaka, and five anonymous reviewers for valuable comments.

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