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Simple Structure in Component Analysis Techniques for Mixtures of Qualitative and Quantitative Variables

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers
Henk A. L. Kiers*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Henk A. L. Kiers, Department of Psychology, Grote Kruisstr. 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

Several methods have been developed for the analysis of a mixture of qualitative and quantitative variables, and one, called PCAMIX, includes ordinary principal component analysis (PCA) and multiple correspondence analysis (MCA) as special cases. The present paper proposes several techniques for simple structure rotation of a PCAMIX solution based on the rotation of component scores and indicates how these can be viewed as generalizations of the simple structure methods for PCA. In addition, a recently developed technique for the analysis of mixtures of qualitative and quantitative variables, called INDOMIX, is shown to construct component scores (without rotational freedom) maximizing the quartimax criterion over all possible sets of component scores. A numerical example is used to illustrate the implication that when used for qualitative variables, INDOMIX provides axes that discriminate between the observation units better than do those generated from MCA.

Keywords

multiple correspondence analysisINDSCALvarimaxquartimaxorthomaxdiscrimination between objects
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 2 , June 1991 , pp. 197 - 212
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The Netherlands organization for scientific research (NWO) is gratefully acknowledged for funding this project. This research was conducted while the author was supported by a PSYCHON-grant (560-267-011) from this organization. The author is obliged to Jos ten Berge for his comments on an earlier version.

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