Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-06T08:34:31.393Z Has data issue: false hasContentIssue false
  • English
  • Français

A Monte Carlo Evaluation of Interactive Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Roger A. Girard  and
Norman Cliff
Roger A. Girard*
Affiliation:
University Of Southern California
Norman Cliff
Affiliation:
University Of Southern California
*
Requests for reprints should be sent to Roger A. Girard, University of Southern California, School of Medicine, 2025 Zonal Avenue, Los Angeles, California 90033.
Get access Rights & Permissions [Opens in a new window]

Abstract

Interactive Scaling with Individual Subjects (ISIS) developed by Young & Cliff [1972], is a method involving interaction between subject and computer in real time to determine which judgments made by the subject are critical to the definition of a dimensional structure. The procedure is based on the mathematical fact that it is possible to define a space of R dimensions in terms of only the interpoint distances between all stimuli being scaled and a subset of (R +1) of these stimuli. For errorless judgments, any subset of (R + 1) stimuli is appropriate. However, fallible data require that the subset consist of stimuli that are maximally dissimilar, and the ISIS procedure is designed to obtain such an optimum subset (a “basis”).

This research evaluates a modified version of ISIS with respect to (a) a metric MDS analysis based on all possible pairs of the stimuli, and (b) a metric MDS analysis based on a subset of one-third of the possible pairs, or about the same number as that required by ISIS. Results show that the ISIS method achieves better fit than (b) at low error levels, and may also achieve better fit than (b) at higher error levels if the size of the basis is increased. The more stimuli in the basis the more indices of fit approach those of (a).

A new method of introducing error in MDS studies is used in the evaluation.

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 1 , March 1976 , pp. 43 - 64
Copyright
Copyright © 1976 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.)

Footnotes

This research is based in part on the doctoral dissertation of the first author, and was supported by research grant MH-16474 from the National Institute of Mental Health, Public Health Service.

References

Baker, R. F., and Young, F. W. Interactive scaling with individual subjects II: An improved system, 1974, Chapel Hill: University of North Carolina.Google Scholar
Ekman, G., and Kuennapas, T. Distribution function for similarity estimates. Perceptual & Motor Skills, 1969, 29, 967–983.CrossRefGoogle Scholar
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 1964, 29, 1–27. (a)CrossRefGoogle Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 1964, 29, 115–129. (b)CrossRefGoogle Scholar
Ramsay, J. O. Some statistical considerations in multidimensional scaling. Psychometrika, 1969, 34, 167–182.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I.. Psychometrika, 1962, 27, 125–140. (a)CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. II. Psychometrika, 1962, 27, 219–246. (b)CrossRefGoogle Scholar
Sherman, C. R. Nonmetric multidimensional scaling: A monte carlo study of the basic parameters. Psychometrika, 1972, 37, 323–355.CrossRefGoogle Scholar
Spence, I. A monte carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 1972, 37, 461–486.CrossRefGoogle Scholar
Spence, I. and Domoney, D. W. Incomplete designs for nonmetric multidimensional scaling. Psychometrika, 1974, 39, 469–490.CrossRefGoogle Scholar
Stenson, H. H., and Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure. Psychological Bulletin, 1969, 71, 122–126.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, 1958, New York: John Wiley & Sons.Google Scholar
Wagenaar, W. A., & Padmos, P. Quantitative interpretation of stress in Kruskal's multidimensional scaling technique. British Journal of Mathematical and Statistical Psychology, 1971, 24, 101–110.CrossRefGoogle Scholar
Young, F. W. A Fortran IV program for nonmetric multidimensional scaling, 1968, Chapel Hill: University of North Carolina.Google Scholar
Young, F. W. Nonmetric multidimensional scaling: recovery of metric information. Psychometrika, 1970, 35, 455–473.CrossRefGoogle Scholar
Young, F. W., and Cliff, N. Interactive scaling with individual subjects. Psychometrika, 1972, 37, 385–415.CrossRefGoogle Scholar