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A Generalization of the Interpoint Distance Model

Published online by Cambridge University Press:  01 January 2025

John Ross  and
Norman Cliff
John Ross
Affiliation:
University of Western Australia
Norman Cliff
Affiliation:
University of Southern California
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Abstract

Coombs and Kao have conjectured that, given the distances between a set of points representing persons and another representing objects, factor analytic methods can be used to recover the locations of the persons and objects. In the present paper it is proved that the conjecture applies, with some qualifications, to squared distances rather than distances themselves. Possible applications to scaling and to inventory responses are discussed.

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 2 , June 1964 , pp. 167 - 176
Copyright
Copyright © 1964 Psychometric Society

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Footnotes

*

Most of the work that resulted in this paper was done while the authors were affiliated with Educational Testing Service. Portions of this paper were presented at the APA convention, St. Louis, 1962.

References

Coombs, C. H. A theory of psychological scaling, Ann Arbor: Univ. Michigan Press, 1952.CrossRefGoogle Scholar
Coombs, C. H. Inconsistency of preferences in psychological measurement. J. exp. Psychol., 1958, 55, 1–7.CrossRefGoogle ScholarPubMed
Coombs, C. H. A theory of data. Psychol. Rev., 1960, 67, 143–159.CrossRefGoogle ScholarPubMed
Coombs, C. H. and Kao, R. C. On a connection between factor analysis and multidimensional unfolding. Psychometrika, 1960, 25, 219–231.CrossRefGoogle Scholar
Torgerson, W. Theory and methods of scaling, New York: Wiley, 1958.Google Scholar
Tucker, L. R. Intra-individual and inter-individual multidimensionality. In Gulliksen, H. and Messick, S. J. (Eds.), Psychological scaling: Theory and applications. New York: Wiley, 1960, 155–167.Google Scholar
Young, G. and Householder, A. S. Discussion of a set of points in terms of their mutual distances. Psychometrika, 1938, 3, 19–22.CrossRefGoogle Scholar