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Cluster Correspondence Analysis

Published online by Cambridge University Press:  01 January 2025

M. van de Velden ,
A. Iodice D’Enza  and
F. Palumbo
M. van de Velden*
Affiliation:
Erasmus University Rotterdam
A. Iodice D’Enza
Affiliation:
Università di Cassino e del Lazio Meridionale
F. Palumbo
Affiliation:
Università degli Studi di Napoli Federico II
*
Correspondence should be made to M. van de Velden, Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands. Email: vandevelden@ese.eur.nl
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Abstract

A method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved. In a unified framework, a brief review of alternative methods is provided and we show that the proposed method is equivalent to GROUPALS applied to categorical data. Performance of the methods is appraised by means of a simulation study. The results of the joint dimension reduction and clustering methods are compared with the so-called tandem approach, a sequential analysis of dimension reduction followed by cluster analysis. The tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure. Our simulation study confirms this conjecture. Moreover, the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods.

Keywords

correspondence analysiscluster analysisdimension reductioncategorical data
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 1 , March 2017 , pp. 158 - 185
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-016-9514-0) contains supplementary material, which is available to authorized users.

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