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Multidimensional Scaling: Combining Observations when Individuals have Different Perceptual Structures

Published online by Cambridge University Press:  01 January 2025

C. B. Horan
C. B. Horan*
Affiliation:
University of Western Australia
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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.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 2 , June 1969 , pp. 139 - 165
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

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.

References

Attneave, F. Dimensions of similarity. American Journal of Psychology, 1950, 63, 516–556CrossRefGoogle ScholarPubMed
Bennett, J. F., & Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data. Psychometrika, 1960, 25, 27–44.CrossRefGoogle Scholar
Coombs, C. H. A theory of data, 1964, New York: Wiley.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.CrossRefGoogle Scholar
Hays, W. L., & Bennett, J. F. Multidimensional unfolding: Determining configuration from complete rank order preference data. Psychometrika, 1961, 26, 221–238.CrossRefGoogle Scholar
Helm, C. E. A multidimensional ratio scaling analysis of color relations. O. N. R. Technical Report, Princeton University, 1959.Google Scholar
Helm, C. E. A succesive intervals analysis of color differences. O. N. R. Technical Report, Princeton University, 1960.Google Scholar
Helm, C. E., & Tucker, L. R. Individual differences in the structure of color-perception. American Journal of Psychology, 1962, 75, 437–444.Google ScholarPubMed
Indow, T., & Kanazawa, K. Multidimensional mapping of Munsell colors varying in hue, chroma, and value. Journal of Experimental Psychology, 1960, 59, 330–336.CrossRefGoogle ScholarPubMed
Indow, T., & Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma. Journal of Experimental Psychology, 1960, 59, 321–329.CrossRefGoogle ScholarPubMed
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 1964, 29, 1–28.CrossRefGoogle Scholar
Messick, S. An empirical evaluation of multidimensional successive intervals. Psychometrika, 1956, 21, 367–375.CrossRefGoogle Scholar
Messick, S. The perceived structure of political relationships. Sociometry, 1961, 24, 270–278.CrossRefGoogle 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.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika, 1962, 27, 125–140.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. II. Psychometrika, 1962, 27, 219–246.CrossRefGoogle Scholar
Shepard, R. N. Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology, 1964, 1, 54–87.CrossRefGoogle Scholar
Torgerson, W. S. Multidimensional scaling I: Theory and method. Psychometrika, 1952, 17, 401–419.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, 1958, N. Y.: Wiley.Google Scholar
Tucker, L. R., & Messick, S. An individual differences model for multidimensional scaling. Psychometrika, 1963, 28, 333–367.CrossRefGoogle 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