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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.
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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

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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.

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