Psychometrika

, Volume 25, Issue 2, pp 173–182 | Cite as

An analysis of Guttman's simplex

  • Philip H. DuBois
Article

Abstract

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically inton/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomesn/2 is contradictory to Guttman's contention that the minimal rank isn — 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.

Keywords

Public Policy Factor Loading Statistical Theory Simple Structure Minimal Rank 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ahmavaara, Y. and Markkanen, T.The unified factor model. The Finnish Foundation for Alcohol Studies Publication No. 7. Helsinki: Undenmaan Kirjapaino, 1958. Pp. 66–73.Google Scholar
  2. [2]
    Borgatta, E. F. On analyzing correlation matrices: some new emphases.Publ. Opin. Quart., 1959,22, 516–528.Google Scholar
  3. [3]
    Bonnardel, R. Les diagrammes d'intercorrelations dans le radex de Guttman.Travail hum., 1956,19, 296–313.Google Scholar
  4. [4]
    DuBois, P. H.Multivariate correlational analysis. New York: Harper, 1957.Google Scholar
  5. [5]
    Gabriel, K. R. The simplex structure of the progressive matrices test.Brit. J. statist. Psychol., 1954,7, 9–14.Google Scholar
  6. [6]
    Guttman, L. Image theory for the structure of quantitative variates.Psychometrika, 1953,18, 277–296.Google Scholar
  7. [7]
    Guttman, L. Two new approaches to factor analysis. Project Nonr-713(00), Ann. Tech. Rep., Internat. Publ. Opin. Res., and Israel Inst. Appl. Soc. Res., 1953.Google Scholar
  8. [8]
    Guttman, L. A new approach to factor analysis: the radex. In P. F. Lazarsfeld (Ed.),Mathematical thinking in the social sciences. Glencoe, Ill.: Free Press, 1954. Pp. 258–348.Google Scholar
  9. [9]
    Guttman, L. Some necessary conditions for common-factor analysis.Psychometrika, 1954,19, 149–161.Google Scholar
  10. [10]
    Guttman, L. An outline of some new methodology for social research.Publ. Opin. Quart., 1954–1955,18, 395–404.Google Scholar
  11. [11]
    Guttman, L. A generalized simplex for factor analysis.Psychometrika, 1955,20, 173–182.Google Scholar
  12. [12]
    Guttman, L. La méthode radex d'analyse factorielle. InL'analyse factorielle et ses applications. Paris: Editions du Centre National de la Recherche Scientifique, 1955. Pp. 209–219.Google Scholar
  13. [13]
    Guttman, L. Empirical verification of the radex structure of mental abilities and personality traits.Educ. psychol. Measmt, 1957,17, 391–407.Google Scholar
  14. [14]
    Guttman, L. To what extent can communalities reduce rank?Psychometrika, 1958,23, 297–308.Google Scholar
  15. [15]
    Jones, M. B. The uses of simplex theory in training research.Amer. Psychologist, 1958,13, 398. (Abstract)Google Scholar
  16. [16]
    Thurstone, L. L. Factorial studies of intelligence.Psychometric Monogr. No. 2. Chicago: Univ. Chicago Press, 1941.Google Scholar

Copyright information

© Psychometric Society 1960

Authors and Affiliations

  • Philip H. DuBois
    • 1
  1. 1.Washington UniversityUSA

Personalised recommendations