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

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.

[1]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[2]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[3]  L. Tucker,et al.  An individual differences model for multidimensional scaling , 1963 .

[4]  R. Shepard.  Metric structures in ordinal data , 1966 .

[5]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[6]  J. Ross.  A remark on tucker and Messick's “points of view” analysis , 1966 .

[7]  V. Mcgee.  Multidimensional Scaling Of N Sets Of Similarity Measures: A Nonmetric Individual Differences Approach. , 1968, Multivariate behavioral research.

[8]  Bruce Bloxom,et al.  INDIVIDUAL DIFFERENCES IN MULTIDIMENSIONAL SCALING , 1968 .

[9]  Forrest W. Young.  Computer program abstracts , 1968 .

[10]  N Cliff,et al.  The “idealized individual” interpretation of individual differences in multidimensional scaling , 1968, Psychometrika.

[11]  C. Horan.  Multidimensional scaling: Combining observations when individuals have different perceptual structures , 1969 .

[12]  Individual difference models in multidimensional scaling : an empirical comparison , 1970 .

[13]  V. Rao.  The salience of price in the perception and evaluation of product quality : a multidimensional measurement model and experimental test , 1970 .

[14]  Peter D. Bricker,et al.  Comparison of Sorting and Pairwise Similarity Judgment Techniques for Scaling Auditory Stimuli , 1970 .

[15]  Leonard S. Cahen,et al.  Educational Testing Service , 1970 .

[16]  P. D. Bricker,et al.  Individual Differences and Multidimensional Scaling of Speech Perception Data , 1971 .

[17]  Paul E. Green,et al.  Applied multidimensional scaling : a comparison of approaches and algorithms , 1972 .