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

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

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書誌事項

公開日: 1970-09

権利情報

https://www.cambridge.org/core/terms

DOI

10.1007/bf02310791

公開者: Cambridge University Press (CUP)

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説明

<jats:p>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.</jats:p>