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

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.

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Carroll, J.D., Chang, JJ. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition. Psychometrika 35, 283–319 (1970). https://doi.org/10.1007/BF02310791

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Keywords

  • Individual Difference
  • Public Policy
  • Scalar Product
  • Statistical Theory
  • Auditory Stimulus