, Volume 35, Issue 3, pp 283–319 | Cite as

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

  • J. Douglas Carroll
  • Jih-Jie Chang


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.


Individual Difference Public Policy Scalar Product Statistical Theory Auditory Stimulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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