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A Multidimensional Scaling Model for the Size-Weight Illusion

Published online by Cambridge University Press:  01 January 2025

Terrence R. Dunn and
Richard A. Harshman
Terrence R. Dunn*
Affiliation:
University of Melbourne
Richard A. Harshman
Affiliation:
University of Western Ontario
*
Requests for reprints should be sent to T. R. Dunn, California State University, Division of Information Systems. 5670 Wilshire Blvd., Los Angeles, CA. 90036.
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Abstract

The kinds of individual differences in perceptions permitted by the weighted euclidean model for multidimensional scaling (e.g., INDSCAL) are much more restricted than those allowed by Tucker’s Three-mode Multidimensional Scaling (TMMDS) model or Carroll’s Idiosyncratic Scaling (IDIOSCAL) model. Although, in some situations the more general models would seem desirable, investigators have been reluctant to use them because they are subject to transformational indeterminacies which complicate interpretation. In this article, we show how these indeterminacies can be removed by constructing specific models of the phenomenon under investigation. As an example of this approach, a model of the size-weight illusion is developed and applied to data from two experiments, with highly meaningful results. The same data are also analyzed using INDSCAL. Of the two solutions, only the one obtained by using the size-weight model allows examination of individual differences in the strength of the illusion; INDSCAL can not represent such differences. In this sample, however, individual differences in illusion strength turn out to be minor. Hence the INDSCAL solution, while less informative than the size-weight solution, is nonetheless easily interpretable.

Keywords

individual differencesmultidimensional scalingthree-mode factorINDSCALsize-weight illusions

Information

Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 1 , March 1982, pp. 25 - 45
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

This paper is based on the first author’s doctoral dissertation at the Department of Psychology, University of Illinois at Urbana-Champaign. The aid of Professor Ledyard R Tucker is gratefully acknowledged.

References

Reference Notes

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Carroll, J. D. & Chang, J. J. IDIOSCAL (individual differences in orientation scaling): A generalization of INDSCAL allowing idiosynchratic reference systems as well as an analytic approximation to INDSCAL. Paper presented at meetings of the Psychometric Society, Princeton, N.J. 1972.Google Scholar
Cohen, H. S. Three-mode rotation to approximate INDSCAL structure. Paper presented at the meetings of the Psychometric Society, Stanford, California, 1974.Google Scholar
Harshman, R. A. Oblique coordinate systems in multidimensional scaling: Theory and experimental test. Unpublished manuscript, May 1973.Google Scholar

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