, Volume 35, Issue 1, pp 1–21 | Cite as

Fitting a simplex symmetrically

  • Peter H. Schönemann


A method for fitting a perfect simplex [Guttman, 1954] is suggested which, in contrast to Kaiser's [1962], is independent of the order of the manifest variables. It is based on a procedure for scaling a set of points from their pairwise distances [Torgerson, 1958; Young & Householder, 1938] which is reviewed in compact notation in the Appendix. The method is extended to an iterative algorithm for fitting a quasi-simplex. Some empirical results are included.


Latent Variance Weight Vector Common Part Manifest Variable Common Factor Model 
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. Coombs, C. H.A theory of data. New York: Wiley, 1964.Google Scholar
  2. Fleishman, E. A. A factor analysis of intra-task performance on two psychomotor tests.Psychometrika, 1953,18, 45–55.CrossRefGoogle Scholar
  3. Guttman, L. A new approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.),Mathematical thinking in the social sciences. Glencoe, Illinois: Free Press, 1954.Google Scholar
  4. Humphreys, L. G. Investigations of the simplex.Psychometrika, 1960,25, 313–323.CrossRefGoogle Scholar
  5. Kaiser, H. F. Scaling a simplex.Psychometrika, 1962,27, 155–162.CrossRefGoogle Scholar
  6. Levin, J. A least squares fit to a simplex. Paper read at the meetings of the American Psychological Association, New York, September 1961.Google Scholar
  7. Mukherjee, B. N. Derivation of likelihood-ratio tests for Guttman quasi-simplex covariance structures.Psychometrika, 1966,31, 97–123.CrossRefGoogle Scholar
  8. Rozeboom, W. W.Foundations of the theory of prediction. Homewood, Illinois: Dorsey Press, 1966.Google Scholar
  9. Schönemann, P. H. On the formal differentiation of traces and determinants. Research Memo No. 27. Chapel Hill: University of North Carolina Psychometric Laboratory, 1965.Google Scholar
  10. Torgerson, W. S.Theory and method of scaling. New York: Wiley, 1958.Google Scholar
  11. Young, G. and Householder, A. S. Discussion of a set of points in terms of their mutual distances.Psychometrika, 1938,3, 19–22.CrossRefGoogle Scholar

Copyright information

© Psychometric Society 1970

Authors and Affiliations

  • Peter H. Schönemann
    • 1
  1. 1.Educational Testing ServiceUSA

Personalised recommendations