Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-10T03:50:49.885Z Has data issue: false hasContentIssue false
  • English
  • Français

The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function. II

Published online by Cambridge University Press:  01 January 2025

Roger N. Shepard
Roger N. Shepard*
Affiliation:
Bell Telephone Laboratories
Get access Rights & Permissions [Opens in a new window]

Abstract

The first in the present series of two papers described a computer program for multidimensional scaling on the basis of essentially nonmetric data. This second paper reports the results of two kinds of test applications of that program. The first application is to artificial data generated by monotonically transforming the interpoint distances in a known spatial configuration. The purpose is to show that the recovery of the original metric configuration does not depend upon the particular transformation used. The second application is to measures of interstimulus similarity and confusability obtained from some actual psychological experiments.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 3 , September 1962 , pp. 219 - 246
Copyright
Copyright © 1962 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.)

References

Abelson, R. P. A technique and a model for multidimensional attitude scaling. Public Opinion Quart., 1954, 18, 405–418CrossRefGoogle Scholar
Abelson, R. P. and Sermat, V. Multidimensional scaling of facial expressions. J. exp. Psychol, in press.Google Scholar
Abelson, R. P. and Tukey, J. W. Efficient conversion of nonmetric information into metric information. Proc. Amer. Statist. Assoc. Meetings, Social Statistics Section, 1959, 226–230.Google Scholar
Attneave, F. Dimensions of similarity. Amer. J. Psychol, 1950, 63, 516–556.CrossRefGoogle ScholarPubMed
Coombs, C. H. Psychological scaling without a unit of measurement. Psychol. Rev., 1950, 57, 145–158.CrossRefGoogle ScholarPubMed
Coombs, C. H. An application of a nonmetric model for multidimensional analysis of similarities. Psychol. Rep., 1958, 4, 511–518.CrossRefGoogle Scholar
Coombs, C. H. Theory of data (mimeographed manuscript for forthcoming book).Google Scholar
Coombs, C. H. and Kao, R. C. On a connection between factor analysis and multidimensional unfolding. Psychometrika, 1960, 25, 219–231.CrossRefGoogle Scholar
Deese, J. On the structure of associative meaning. Psychol. Rev., 1961, in press.Google Scholar
Ekman, G. Dimensions of color vision. J. Psychol., 1954, 38, 467–474.CrossRefGoogle Scholar
Ekman, G. Dimensions of emotion. Acta Psychologica, 1955, 11, 279–288.CrossRefGoogle Scholar
Engen, T., Levy, N., and Schlosberg, H. A new series of facial expressions. Amer. Psychologist, 1957, 12, 264–266.CrossRefGoogle Scholar
Fagot, R. F. A method for ordered metric scaling by comparison of intervals. Psychometrika, 1959, 24, 157–168.CrossRefGoogle Scholar
Hays, W. L. and Bennett, J. F. Multidimensional unfolding: Determining configurration from complete rank order preference data. Psychometrika, 1961, 26, 221–238.CrossRefGoogle Scholar
Helm, C., Messick, S. J., and Tucker, L. R. Psychophysical models for relating discrimination and magnitude estimation scales. Psychol. Rev., 1961, 68, 167–177.CrossRefGoogle Scholar
Householder, A. S. and Landahl, H. D. Mathematical biophysics of the central nervous system, Bloomington, Indiana: Principia Press, 1945.CrossRefGoogle Scholar
Indow, T. and Kanazawa, K. Multidimensional mapping of Munsell colors varying in hue, chroma, and value. J. exp. Psychol., 1960, 59, 330–336.CrossRefGoogle ScholarPubMed
Indow, T. and Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma. J. exp. Psychol., 1960, 59, 321–329.CrossRefGoogle ScholarPubMed
Klingberg, F. L. Studies in measurement of the relations between sovereign states. Psychometrika, 1941, 6, 335–352.CrossRefGoogle Scholar
Landahl, H. D. Neural mechanisms for the concepts of difference and similarity. Bull. math. Biophysics, 1945, 7, 83–88.CrossRefGoogle Scholar
McGuire, W. J. A multiprocess model for paired-associate learning. J. exp. Psychol., 1961, 62, 335–347.CrossRefGoogle Scholar
Messick, S. J. An empirical evaluation of multidimensional successive intervals. Psychometrika, 1956, 21, 367–375.CrossRefGoogle Scholar
Restle, F. A metric and an ordering on sets. Psychometrika, 1959, 24, 207–220.CrossRefGoogle Scholar
Richardson, M. W. Multidimensional psychophysics. Psychol. Bull., 1938, 35, 659–660.Google Scholar
Shepard, R. N. Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 1957, 22, 325–345.CrossRefGoogle Scholar
Shepard, R. N. Stimulus and response generalization: Tests of a model relating generalization to distance in psychological space. J. exp. Psychol., 1958, 55, 509–523.CrossRefGoogle Scholar
Shepard, R. N. Stimulus and response generalization: Deduction of the generalization gradient from a trace model. Psychol. Rev., 1958, 65, 242–256.CrossRefGoogle ScholarPubMed
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika, 1962, 27, 125–140.CrossRefGoogle Scholar
Siegel, S. A method for obtaining an ordered metric scale. Psychometrika, 1956, 21, 207–216.CrossRefGoogle Scholar
Stevens, S. S. Mathematics, measurement, and psychophysics. In Stevens, S. S. (Eds.), Handbook of experimental psychology. New York: Wiley, 1951, 1–49.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google 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, New York: Wiley, 1958.Google Scholar