Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-08T12:05:47.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Transformation of a Three-Mode Multidimensional Scaling Solution to Indscal Form

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 Dr. Robert C. MacCallum, Department of Psychology, The Ohio State University, 404C West. 17th Ave., Columbus, Ohio 43210.
Get access Rights & Permissions [Opens in a new window]

Abstract

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. The possibility is raised that it may be profitable to attempt to transform a three-mode solution to the general form of an INDSCAL solution. Operationally, this involves transforming the three-mode core matrix so that each section is, as nearly as possible, a diagonal matrix. A technique is developed for accomplishing such a transformation, and is applied to two sets of data from the literature. Results indicate that the process is both feasible and valuable, providing useful information on the relative appropriateness of the two models.

Keywords

individual differences modelsthree-way scaling models
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 3 , September 1976 , pp. 385 - 400
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.)

References

Reference Notes

Cohen, H. S. Three-mode rotation to approximate INDSCAL structure. Paper presented at the annual meeting of the Psychometric Society, Palo Alto, California, March, 1974.Google Scholar
Cohen, H. S. Further thoughts on three-mode rotation to INDSCAL structure, with jackknifed confidence regions for points. Paper presented at the U.S.—Japan Seminar on Theory, Methods and Applications of Multidimensional Scaling and Related Techniques, University of California at San Diego, August, 1975.Google Scholar
deLeeuw, J. & Pruzansky, S. A new computational method to fit the weighted Euclidean distance model. Unpublished manuscript, Bell Laboratories, 1975.Google Scholar
MacCallum, R. C. A comparison of two individual differences models for multidimensional scaling: Carroll and Chang's INDSCAL and Tucker's three-mode factor analysis. Unpublished doctoral dissertation, University of Illinois, 1974.Google Scholar
Tucker, L. R. Personal communication, 1975.CrossRefGoogle Scholar

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, 283–319.CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, 1967, Chicago: The University of Chicago Press.Google Scholar
Jones, L. E., & Young, F. W. Structure of a social environment: Longitudinal individual differences scaling of an intact group. Journal of Personality and Social Psychology, 1972, 24, 108–121.CrossRefGoogle Scholar
MacCallum, R. C. Effects on INDSCAL of non-orthogonal perceptions of object space dimensions. Psychometrika, 1976, 41, 177–188.CrossRefGoogle Scholar
Meredith, W. Rotation to achieve factorial invariance. Psychometrika, 1964, 29, 187–206.CrossRefGoogle Scholar
Schönemann, P. H. An algebraic solution for a class of subjective metrics models. Psychometrika, 1972, 37, 441–451.CrossRefGoogle Scholar
Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 1972, 37, 3–27.CrossRefGoogle Scholar
Wish, M., & Carroll, J. D. Applications of individual differences scaling to studies of human perception and judgment. In Carterette, E. C. and Friedman, M. P.(Eds.), Handbook of perception. Vol. II. Psychophysical judgment and measurement, 1974, New York: Academic Press.Google Scholar