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Correspondence Analysis and Association Models Constrained by a Conditional Independence Graph

Published online by Cambridge University Press:  01 January 2025

Antoine de Falguerolles ,
Said Jmel  and
Joe Whittaker
Antoine de Falguerolles
Affiliation:
Universitë Paul Sabatier, Toulouse
Said Jmel
Affiliation:
Université Nancy II, Nancy
Joe Whittaker*
Affiliation:
Lancaster University
*
Requests for reprints should be sent to Joe Whittaker, Mathematics and Statistics Department, Lancaster University, LAI 4YF UNITED KINGDOM. E-Mail: joe.whittaker@lancaster.ac.uk
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Abstract

The manner in which the conditional independence graph of a multiway contingency table effects the fitting and interpretation of the Goodman association model (RC) and of correspondence analysis (CA) is considered.

Estimation of the row and column scores is presented in this context by developing a unified framework that includes both models. Incorporation of the conditional independence constraints inherent in the graph may lead to equal or additive scores for the corresponding marginal tables, depending on the topology of the graph. An example of doubly additive scores in the analysis of a Burt subtable is given.

Keywords

RC-association modelcollapsibilityconditional independencecorrespondence analysisgraphical modelindependence graphlog-linear modelmultiway contingency tablescore additivity
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 2 , June 1995 , pp. 161 - 180
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

Thanks are due to anonymous referees who substantially improved the original draft of this paper.

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