, Volume 35, Issue 4, pp 475–491 | Cite as

Multidimensional analysis of complex structure: Mixtures of class and quantitative variation

  • Richard Degerman


For certain kinds of structure consisting of quantitative dimensions superimposed on a discrete class structure, spatial representations can be viewed as being composed of two subspaces, the first of which reveals the discrete classes as isolated clusters and the second of which contains variation along the quantitative attributes. A numerical method is presented for rotating a multi-dimensional configuration or factor solution so that the first few axes span the space of classes and the remaining axes span the space of quantitative variation. The use of this method is then illustrated in the analysis of some experimental data.


Experimental Data Public Policy Statistical Theory Quantitative Variation Class Structure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cooley, W. W., & Lohnes, P. R.Multivariate procedures for the behavioral sciences. New York: Wiley, 1962.Google Scholar
  2. Forgy, E. W. Evaluation of several methods for detecting mixtures from different N-dimensional populations. Paper presented at the meeting of the American Psychological Association, 1964.Google Scholar
  3. Fox, B. L., & Landi, D. M. An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix. Rand Corporation Memorandum RM-5269-PR, March 1967.Google Scholar
  4. Garner, W. R.Uncertainty and structure as psychological concepts. New York: Wiley, 1962.Google Scholar
  5. Guttman, L. A new approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.)Mathematical thinking in the social sciences. Glencoe: Free Press, 1954. Pp. 258–345.Google Scholar
  6. Guttman, L. The nonmetric breakthrough for the behavioral sciences.Proceedings, Second National Conference on Data Processing, Rehovoth, January 1966.Google Scholar
  7. Guttman, L. A general nonmetric technique for finding the smallest coordinate space for a configuration of points.Psychometrika, 1968,33, 469–506.Google Scholar
  8. Hadley, G.Linear algebra. Reading, Mass.: Addison-Wesley, 1961.Google Scholar
  9. Halmos, P. E.Finite dimensional vector spaces. Princeton: Van Nostrand, 1958.Google Scholar
  10. Johnson, S. C. Hierarchical clustering schemes.Psychometrika, 1967,32, 241–254.Google Scholar
  11. Kruskal, J. B., & Hart, R. E. A geometric interpretation of diagnostic data for a digital machine: Based on a study of the Morris, Illinois Electronic Central Office.Bell System Technical Journal, 1966,45, 1299–1338.Google Scholar
  12. McQuitty, L. L. A novel application of the coefficient of correlation in the isolation of both typal and dimensional constructs.Educational and Psychological Measurement, 1967,27, 591–599.Google Scholar
  13. Miller, G. A., & Nicely, P. E. An analysis of perceptual confusions among some English consonants.Journal of the Acoustical Society of America, 1955,27, 338–352.Google Scholar
  14. Morton, A. S. Similarity as a determinant of friendship: A multi-dimensional study. (Doctoral dissertation, Princeton University) Ann Arbor, Mich.: University Microfilms, 1959. No. 59-5204.Google Scholar
  15. Rubin, J. Optimal classification into groups: An approach for solving the taxonomy problem. IBM New York Scientific Center Report No. 320-2915, November 1967.Google Scholar
  16. Sawrey, W. L., Keller, L., & Conger, J. J. An objective method of grouping profiles by distance functions and its relation to factor analysis.Educational and Psychological Measurement, 1960,20, 651–673.Google Scholar
  17. Shepard, R. N. Psychological representation of speech sounds. In E. E. David & P. B. Denes (Eds.)Human communication: A unified view. New York: McGraw-Hill, in press.Google Scholar
  18. Torgerson, W. S. Multidimensional representation of similarity structures. In M. M. Katz, J. O. Cole, & W. E. Barton (Eds.)The role and methodology of classification in psychiatry and psychopathology. Washington, D. C.: U. S. Government Printing Office, 1968. Pp. 212–220.Google Scholar
  19. Wickelgren, W. Distinctive features and errors in short term memory for English consonants.Journal of the Acoustical Society of America. 1966,39, 388–398.Google Scholar
  20. Young, F. W., & Torgerson, W. S. TORSCA, A FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis.Behavioral Science, 1967,12, 498.Google Scholar
  21. Young, G., & Householder, A. S. Discussion of a set of points in terms of their mutual distances.Psychometrika, 1938,3, 19–22.Google Scholar

Copyright information

© Psychometric Society 1970

Authors and Affiliations

  • Richard Degerman
    • 1
  1. 1.University of CaliforniaIrvine

Personalised recommendations