Skip to main content
SpringerLink
Log in

Multidimensional scaling: Combining observations when individuals have different perceptual structures

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The usual methods of combining observations to give interpoint distance estimates based on interstimulus differences are shown to lead to a distortion of the stimulus configuration unless all individuals in a group perceive the stimuli in perceptual spaces which are essentially the same. The nature of the expected distortion is shown, and a method of combining individual distance estimates which produces only a linear deformation of the stimulus configuration is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Attneave, F. Dimensions of similarity.American Journal of Psychology, 1950,63, 516–556.

    Google Scholar 

  • Bennett, J. F., & Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data.Psychometrika, 1960,25, 27–44.

    Google Scholar 

  • Coombs, C. H.A theory of data. New York: Wiley, 1964.

    Google Scholar 

  • Coombs, C. H., & Kao, R. C. On a connection between factor analysis and multidimensional unfolding.Psychometrika, 1960,25, 219–231.

    Google Scholar 

  • Eckart, C. T., & Young, G. The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.

    Google Scholar 

  • Hays, W. L., & Bennett, J. F. Multidimensional unfolding: Determining configuration from complete rank order preference data.Psychometrika, 1961,26, 221–238.

    Google Scholar 

  • Helm, C. E. A multidimensional ratio scaling analysis of color relations. O. N. R. Technical Report, Princeton University, 1959.

  • Helm, C. E. A succesive intervals analysis of color differences. O. N. R. Technical Report, Princeton University, 1960.

  • Helm, C. E., & Tucker, L. R. Individual differences in the structure of color-perception.American Journal of Psychology, 1962,75, 437–444.

    Google Scholar 

  • Indow, T., & Kanazawa, K. Multidimensional mapping of Munsell colors varying in hue, chroma, and value.Journal of Experimental Psychology, 1960,59, 330–336.

    Google Scholar 

  • Indow, T., & Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma.Journal of Experimental Psychology, 1960,59, 321–329.

    Google Scholar 

  • Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–28.

    Google Scholar 

  • Messick, S. An empirical evaluation of multidimensional successive intervals.Psychometrika, 1956,21, 367–375.

    Google Scholar 

  • Messick, S. The perceived structure of political relationships.Sociometry, 1961,24, 270–278.

    Google Scholar 

  • Messick, S., & Abelson, R. P. The additive constant problem in multidimensional scaling.Psychometrika, 1956,21, 1–17.

    Google Scholar 

  • Moore, D. W., & Ross, J. A fast principal components factor analysis program for the IBM 1620.Educational and Psychological Measurement, 1964,24, 675–676.

    Google Scholar 

  • Shepard, R. N. Stimulus and response generalization: Tests of a model relating generalization to distance in psychological space.Journal of Experimental Psychology, 1958,55, 509–523.

    Google Scholar 

  • Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I.Psychometrika, 1962,27, 125–140. (a)

    Google Scholar 

  • Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. II.Psychometrika, 1962,27, 219–246. (b)

    Google Scholar 

  • Shepard, R. N. Attention and the metric structure of the stimulus space.Journal of Mathematical Psychology, 1964,1, 54–87.

    Google Scholar 

  • Torgerson, W. S. Multidimensional scaling I: Theory and method.Psychometrika, 1952,17, 401–419.

    Google Scholar 

  • Torgerson, W. S.Theory and methods of scaling. N. Y.: Wiley, 1958.

    Google Scholar 

  • Tucker, L. R., & Messick, S. An individual differences model for multidimensional scaling.Psychometrika, 1963,28, 333–367.

    Google Scholar 

  • Young, G., & Housholder, A. S. Discussion of a set of points in terms of their mutual distances.Psychometrika, 1938,3, 19–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Western Australia, Australia

    C. B. Horan

Authors
  1. C. B. Horan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work reported in this paper forms part of that which was undertaken towards a Ph.D. Degree in the University of Western Australia under the supervision of Dr. John Ross. The author was killed in a road accident before the completion of his Ph.D. The final revision of this paper was made by Ross, to whom enquiries and requests for reprints should be addressed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Horan, C.B. Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika 34, 139–165 (1969). https://doi.org/10.1007/BF02289341

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289341

Keywords

Search

Navigation