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Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition

Published online by Cambridge University Press:  01 January 2025

J. Douglas Carroll  and
Jih-Jie Chang
J. Douglas Carroll
Affiliation:
Bell Telephone Laboratories, Murray Hill, New Jersey
Jih-Jie Chang
Affiliation:
Bell Telephone Laboratories, Murray Hill, New Jersey
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Abstract

An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychological space”. A corresponding method of analyzing similarities data is proposed, involving a generalization of “Eckart-Young analysis” to decomposition of three-way (or higher-way) tables. In the present case this decomposition is applied to a derived three-way table of scalar products between stimuli for individuals. This analysis yields a stimulus by dimensions coordinate matrix and a subjects by dimensions matrix of weights. This method is illustrated with data on auditory stimuli and on perception of nations.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 3 , September 1970 , pp. 283 - 319
Copyright
Copyright © 1970 The Psychometric Society

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