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Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of “Eckart-Young” decomposition. (English) Zbl 0202.19101
Summary: 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.

MSC:
62H25 Factor analysis and principal components; correspondence analysis
91C15 One- and multidimensional scaling in the social and behavioral sciences
Software:
TORSCA
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References:
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