Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T19:07:54.711Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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