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Multidimensional Unfolding: Determining the Dimensionality of Ranked Preference Data

Published online by Cambridge University Press:  01 January 2025

Joseph F. Bennett  and
William L. Hays
Joseph F. Bennett
Affiliation:
Lincoln Laboratories, Massachusetts Institute of Technology
William L. Hays
Affiliation:
University of Michigan
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Abstract

A model is proposed which treats rankings given by a group of judges as representing regions in an isotonic space of dimensionality r. Three possible criteria for estimating lower bound dimensionality are discussed: mutual boundary, cardinality, and the occurrence of transposition groups. Problems associated with each criterion are mentioned.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 1 , March 1960 , pp. 27 - 43
Copyright
Copyright © 1960 The Psychometric Society

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Footnotes

*

Deceased.

References

Bennett, J. F. Determination of the number of independent parameters of a score matrix from the examination of rank orders. Psychometrika, 1956, 21, 383–393.CrossRefGoogle Scholar
Coombs, C. H. Psychological scaling without a unit of measurement. Psychol. Rev., 1950, 57, 145–158.CrossRefGoogle ScholarPubMed
Coombs, C. H. A theory of psychological scaling, Ann Arbor: Univ. Michigan Press, 1952.Google Scholar
Errara, A. Du coloriage des cartes et de quelques questions d'analysis situs, Paris: Gauthier-Villars, 1921.Google Scholar
Guttman, L. A basis for scaling qualitative data. Amer. sociol. Rev., 1944, 9, 139–150.CrossRefGoogle Scholar
Jordan, K. The calculus of finite differences, New York: Chelsea, 1947.Google Scholar
Thurstone, L. L. Rank order as a psychophysical method. J. exp. Psychol., 1931, 14, 187–201.CrossRefGoogle Scholar