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Effects on Indscal of Non-Orthogonal Perceptions of Object Space Dimensions

Published online by Cambridge University Press:  01 January 2025

Robert C. MacCallum
Robert C. MacCallum*
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Robert C. MacCallum, Department of Psychology, The Ohio State University, Columbus, Ohio 43210.
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Abstract

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker’s three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.

Keywords

multidimensional scalingindividual differences models for multidimensional scalingthree-mode factor analysisthree-way scaling models
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 177 - 188
Copyright
Copyright © 1976 The Psychometric Society

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References

Reference Note

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Tucker, L. R and Messick, S. An individual differences model for multidimensional scaling. Psychometrika, 1963, 28, 333–367.CrossRefGoogle Scholar
Carroll, J. D. and Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 1970, 35, 283–319.CrossRefGoogle Scholar
Horan, C. B. Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 1969, 34, 139–165.CrossRefGoogle Scholar
McGee, V. E. Multidimensional scaling of N sets of similarity measures: A nonmetric individual differences approach. Multivariate Behavioral Research, 1968, 3, 233–248.CrossRefGoogle Scholar
Shepard, R. N. Introduction to Volume I. In Shepard, R. N., Romney, A. K., and Nerlove, S. B. (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences. Vol. I: Theory, New York: Seminar Press, 1972.Google Scholar
Torgerson, W. W. Theory and methods of scaling, 1958, New York: Wiley.Google Scholar
Tucker, L. R. Some mathematical notes on three-mode factor analysis. Psychometrika, 1966, 31, 279–311.CrossRefGoogle ScholarPubMed
Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 1972, 37, 3–27.CrossRefGoogle Scholar
Tucker, L. R and Messick, S. An individual differences model for multidimensional scaling. Psychometrika, 1963, 28, 333–367.CrossRefGoogle Scholar