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Interactive Scaling with Individual Subjects

Published online by Cambridge University Press:  01 January 2025

Forrest W. Young  and
Norman Cliff
Forrest W. Young
Affiliation:
University of North Carolina
Norman Cliff
Affiliation:
University of Southern California
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Abstract

A metric multidimensional scaling (MDS) procedure based on computer-subject interaction is developed, and an experiment designed to validate the procedure is presented. The interactive MDS system allows generalization of current MDS systems in two directions: (a) very large numbers of stimuli may be scaled; and (b) the scaling is performed with individual subjects, facilitating the investigation of individual as well as group processes. The experiment provided positive support for the interactive MDS system. Specifically, (a) individual data are amenable to meaningful interpretation, and they provide a tentative basis for quantitative investigation; and (b) grouped data provide meaningful interpretive and quantitative results which are equivalent to results from standard paired-comparisons methods.

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 4 , December 1972 , pp. 385 - 415
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

This report was supported in part by a PHS research grant, No. M-10006, from the National Institute of Mental Health, in part by a Science Development grant, No. GU-2059, from the National Science Foundation, both granted to the Psychometric Laboratory at the University of North Carolina, and in part by a PHS research grant, No. MH-16474, from the National Institute of Mental Health, Public Health Service, granted to the second author. The major portion of this research was performed while the second author was the L. L. Thurstone Distinguished Fellow at the Psychometric Laboratory of the University of North Carolina while on leave from the University of Southern California. The authors are indebted to Amnon Rapoport and Thomas S. Wallsten for their critical evaluations of an earlier version of this report. While this paper was entirely a cooperative effort on the part of both authors, the first author was primarily responsible for the algorithms, and the second for developing the mathematical model.

References

Carroll, J. D., & Chang, J. J. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition. Psychometrika, 1970, 35, 283–320CrossRefGoogle Scholar
Coombs, C. H. A theory of data, 1964, New York: WileyGoogle Scholar
Fillenbaum, S., & Rapoport, A. Structures in the subjective lexicon, 1971, New York: Academic PressGoogle Scholar
Klahr, David A monte carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure. Psychometrika, 1969, 34, 319–330CrossRefGoogle Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 1964, 29, 115–130CrossRefGoogle Scholar
Miller, R. G. Simultaneous statistical inference, 1966, New York: McGraw-HillGoogle Scholar
Nunnally, J. C. Psychometric theory, 1967, New York: McGraw-HillGoogle Scholar
Rosenberg, S., Nelson, C., & Vivekananthan, P. S. A multidimensional approach to the structure of personality impressions. Journal of Personality and Social Psychology, 1968, 9, 283–294CrossRefGoogle Scholar
Ross, J., & Cliff, N. A generalization of the interpoint distance model. Psychometrika, 1964, 29, 167–176CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function: I & II. Psychometrika, 1962, 27, 125–140CrossRefGoogle Scholar
Shepard, R. N., Romney, K., & Nerlove, S. Multidimensional scaling: Theory and applications in the behavioral sciences, 1972, New York: Seminar PressGoogle Scholar
Sherman, C. R. Nonmetric multidimensional scaling: A monte carlo study of the basic parameters. Psychometrika, 1972, 37, 323–355CrossRefGoogle Scholar
Spence, I. A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 1972, 37, (in press).CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, 1958, New York: WileyGoogle Scholar
Young, F. W. Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 1970, 35, 455–473CrossRefGoogle Scholar