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Decompositions and Biplots in Three-Way Correspondence Analysis

Published online by Cambridge University Press:  01 January 2025

André Carlier  and
Pieter M. Kroonenberg
André Carlier
Affiliation:
Laboratoire de Statistique et Probabilités, Université Paul Sabatier, Toulouse, France
Pieter M. Kroonenberg*
Affiliation:
Department of Education, Leiden University, Leiden, The Netherlands
*
Requests for reprints should be sent to P. M. Kroonenberg, Department of Education, Wassenaarseweg 52, 2333 AK Leiden, THE NETHERLANDS.
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Abstract

In this paper correspondence analysis for three-way contingency tables is presented using three-way generalisations of the singular value decomposition. It is shown that in combination with Lancaster's (1951) additive decomposition of interactions in three-way tables, a detailed analysis is possible of the deviations from independence. Finally, biplots are shown to produce powerful graphical representations of the results from three-way correspondence analyses. An example from child development is used to illustrate the theoretical developments.

Keywords

Additive decomposition of interactionsinertiathree-mode principal component analysisPARAFACmother-child interaction
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 2 , June 1996 , pp. 355 - 373
Copyright
Copyright © 1996 The Psychometric Society

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