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

*(English)*Zbl 0202.19101Summary: 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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\textit{J. D. Carroll} and \textit{J.-J. Chang}, Psychometrika 35, 283--319 (1970; Zbl 0202.19101)

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##### References:

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