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Psychometrika

, Volume 19, Issue 1, pp 27–38 | Cite as

The mathematical theory of factorial invariance under selection

  • Yrjö Ahmavaara
Article

Abstract

It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.

Keywords

Public Policy Factor Loading Statistical Theory Mathematical Theory Linear Transformation 
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. 1.
    Thurstone, L. L. Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.Google Scholar
  2. 2.
    Thomson, G. H. The factorial analysis of human ability. London: Univ. London Press, 1948.Google Scholar
  3. 3.
    Pearson, K. On the influence of natural selection on the variability and correlation of organs.Phil. Trans. roy. Soc. 1902 A,200, 1–66.Google Scholar
  4. 4.
    Aitken, A. C. Note on selection from a multivariate normal population.Proc. Edin. math. Soc., 1934,4, 106–110.Google Scholar
  5. 5.
    Thomson, G. H. The influence of univariate selection on the factorial analysis of ability.Brit. J. Psychol., 1938,28, 451–459.Google Scholar
  6. 6.
    Ledermann, W. Note on Professor Godfrey H. Thomson's article “The influence of univariate selection on factorial analysis of ability.”Brit. J. Psychol., 1938,29, 69–73.Google Scholar
  7. 7.
    Thomson, G. H. and Ledermann, W. The influence of multivariate selection on the factorial analysis of ability.Brit. J. Psychol., 1939,29, 288–305.Google Scholar

Copyright information

© Psychometric Society 1954

Authors and Affiliations

  • Yrjö Ahmavaara
    • 1
  1. 1.Helsinki UniversityUSA

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