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An Analysis and Synthesis of Multiple Correspondence Analysis, Optimal Scaling, Dual Scaling, Homogeneity Analysis and Other Methods for Quantifying Categorical Multivariate Data

Published online by Cambridge University Press:  01 January 2025

Michel Tenenhaus  and
Forrest W. Young
Michel Tenenhaus*
Affiliation:
Centre d'Enseignement Supérieur des Affaires, Jouy-en-Josas, France
Forrest W. Young
Affiliation:
University of North Carolina at Chapel Hill
*
Requests for reprints should be sent to Michel Tenenhaus, Department S.I.A.D., Centre d'Enseignement Superieur des Affaires, 78350 Jouy-en-Josas, Paris, France.
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Abstract

We discuss a variety of methods for quantifying categorical multivariate data. These methods have been proposed in many different countries, by many different authors, under many different names. In the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same data. In the second major section of the paper we introduce the notion of a duality diagram, and use this diagram to synthesize the many superficially different methods into a single method.

Keywords

multiple correspondence analysisoptimal scalingdual scalinghomogeneity analysiscategorical multivariate data
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 1 , March 1985 , pp. 91 - 119
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

The ideas in this paper were worked out by the first author, with some suggestions provided by the second. The current version of this paper has evolved from three previous versions, the first two written by the first author.

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