, Volume 35, Issue 3, pp 283-319

First online:

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

  • J. Douglas CarrollAffiliated withBell Telephone Laboratories
  • , Jih-Jie ChangAffiliated withBell Telephone Laboratories

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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.