Advertisement

Psychometrika

, Volume 35, Issue 3, pp 349–366 | Cite as

On metric multidimensional unfolding

  • Peter H. Schönemann
Article

Abstract

The problem of locating two sets of points in a joint space, given the Euclidean distances between elements from distinct sets, is solved algebraically. For error free data the solution is exact, for fallible data it has least squares properties.

Keywords

Euclidean Distance Public Policy Statistical Theory Joint Space Free Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. Bennett, J. F., & Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data.Psychometrika, 1960,25, 27–43.CrossRefGoogle Scholar
  3. Bloxom, B. Individual differences in multidimensional scaling. ETS Research Bulletin 68-45. Princeton: Educational Testing Service, 1968.Google Scholar
  4. Carroll, J. D., & Chang, Jih-Jie. Relating preference data to multidimensional scaling solutions via a generalization of Coombs' unfolding model. Paper read at the Spring Meeting of the Psychometric Society, Madison, Wisconsin, 1967.Google Scholar
  5. Carroll, J. D., & Chang, Jih-Jie. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 283–319.Google Scholar
  6. Coombs, C. H. Inconsistencies of preferences in psychological measurement.Journal of Experimental Psychology, 1958,55, 1–7.PubMedGoogle Scholar
  7. Coombs, C. H.A theory of data. New York: Wiley, 1964.Google Scholar
  8. Coombs, C. H., & Kao, R. C. Nonmetric factor analysis. Department of Engineering Research Bulletin No. 38. Ann Arbor: University of Michigan, 1955.Google Scholar
  9. Eckart, C., & Young, G. The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.CrossRefGoogle Scholar
  10. Goode, F. M. Interval scale representation of ordered metric scales. Dittoed manuscript, University of Michigan, 1957.Google Scholar
  11. Hays, W. L., & Bennett, J. F. Multidimensional unfolding: Determining configuration from complete rank order preference data.Psychometrika, 1961,26, 221–238.CrossRefGoogle Scholar
  12. Krantz, D. H. Rational distances functions for multidimensional scaling.Journal of Mathematical Psychology, 1967,4, 226–244.CrossRefGoogle Scholar
  13. Kruskal, J. B. How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Unpublished report, Bell Telephone Laboratories, 1968.Google Scholar
  14. Lingoes, J. C. A general nonparametric model for representing objects and attributes in a joint space. In J. C. Gardin (Ed.),Les Comptes-rendus de Colloque International sur L'emploi des Calculateurs en Archeologie: Problèmes Sémiologiques et Mathématiques. Marseilles: Centre Nationale de la Recherche Scientifiques, in press.Google Scholar
  15. Ross, J., & Cliff, N. A generalization of the interpoint distance model.Psychometrika, 1964,29, 167–176.Google Scholar
  16. Schonemann, P. H. Fitting a simplex symmetrically.Psychometrika, 1970,35, 1–21.Google Scholar

Copyright information

© Psychometric Society 1970

Authors and Affiliations

  • Peter H. Schönemann
    • 1
  1. 1.The Ohio State UniversityUSA

Personalised recommendations