, Volume 35, Issue 3, pp 283–319

Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition

  • J. Douglas Carroll
  • Jih-Jie Chang

DOI: 10.1007/BF02310791

Cite this article as:
Carroll, J.D. & Chang, JJ. Psychometrika (1970) 35: 283. doi:10.1007/BF02310791


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.

Copyright information

© Psychometric Society 1970

Authors and Affiliations

  • J. Douglas Carroll
    • 1
  • Jih-Jie Chang
    • 1
  1. 1.Bell Telephone LaboratoriesMurray Hill

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