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Psychometrika

, Volume 37, Issue 1, pp 3–27 | Cite as

Relations between multidimensional scaling and three-mode factor analysis

  • Ledyard R Tucker
Article

Abstract

A combination is achieved of two lines of psychometric interest: a) multidimensional scaling and b) factor analysis. This is accomplished with the use of three-mode factor analysis of scalar product matrices, one for each subject. Two of the modes are the groups of objects scaled and the third mode is the sample of subjects. Results are an object space, a person space, and a system for changing weights given to dimensions and of angles between dimensions in the object space for individuals located at different places in the person space. The development is illustrated with data from an adjective similarity study.

Keywords

Public Policy Scalar Product Statistical Theory Multidimensional Scaling Object Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bellman, R. R.Introduction to matrix analysis. New York: McGraw-Hill, 1960.Google Scholar
  2. Carroll, J. D., & Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 283–319.Google Scholar
  3. Cliff, N. The “idealized individual” interpretation of individual differences in multidimensional scaling.Psychometrika, 1968,33, 225–232.Google Scholar
  4. Eckart, C., & Young, G. The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.Google Scholar
  5. Helm, C. E., & Tucker, L. R Individual differences in the structure of color-perception.American Journal of Psychology, 1962,75, 437–444.Google Scholar
  6. Horan, C. B. Multidimensional scaling: Combining observations when individuals have different perceptual structures.Psychometrika, 1969,34, 139–165.Google Scholar
  7. Horst, P.Matrix algebra for social scientists. New York: Holt, Rinehart, and Winston, 1963.Google Scholar
  8. Johnson, R. M. On a theorem stated by Eckart and Young.Psychometrika, 1963,28, 259–263.Google Scholar
  9. Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis.Psychometrika, 1958,23, 187–200.Google Scholar
  10. Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964,29, 115–129.Google Scholar
  11. MacDuffee, C. C.The theory of matrices, New York: Chelsea, 1946.Google Scholar
  12. Ross, J. A remark on Tucker and Messick's “points of view” analysis.Psychometrika, 1966,31, 27–31.Google Scholar
  13. Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.Google Scholar
  14. Tucker, L. R. Some mathematical notes on three-mode factor analysis.Psychometrika, 1966,31, 279–311.Google Scholar
  15. Tucker, L. R. and Messick, S. An individual difference model for multidimensional scaling.Psychometrika, 1963,28, 333–367.Google Scholar

Copyright information

© Psychometric Society 1972

Authors and Affiliations

  • Ledyard R Tucker
    • 1
  1. 1.University of IllinoisUSA

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