Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-08T11:55:32.504Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Identifiability of Parameters in Thurstone's Multiple Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Olav Reiersøl
Olav Reiersøl*
Affiliation:
Purdue University
Get access Rights & Permissions [Opens in a new window]

Abstract

In econometric literature a parameter in a theoretical model has been called identifiable if it can be uniquely determined in terms of the joint probability distribution of the observed variables. In this paper the identifiability of parameters in four different factor analysis models is considered. The last of these four models corresponds to Thurstone's factor analysis. In Sections 7 and 11, the possibility of a statistical testing of the models is discussed. Section 10 deals with the problem of actually determining the parameter r (the number of common factors) in terms of the probability distribution of the observed variables.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 2 , June 1950 , pp. 121 - 149
Copyright
Copyright © 1950 Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This article will be included in Cowles Commission Paper, New Series, No. 39.

References

Albert, A. A. The matrices of factor analysis. Proc. nat. Acad. Sci., Wash., 1944, 30, 90–95.CrossRefGoogle ScholarPubMed
Albert, A. A. The minimum rank of a correlation matrix. Proc. nat. Acad. Sci., Wash., 1944, 30, 144–146.CrossRefGoogle ScholarPubMed
Haavelmo, T. The probability approach in econometrics. Supplement to Econometrica, 1944, 12.CrossRefGoogle Scholar
Hurwicz, L. Generalization of the concept of identification. Cowles Commission Monograph No. 10. Statistical inference in dynamic economic models, New York: John Wiley and Sons, 1949.Google Scholar
Kelley, T. L. Crossroads in the mind of man, Calif.: Stanford Univ. Press, 1928.Google Scholar
Koopmans, T. C., Rubin, H., and Leipnik, R. B. Measuring the equation systems of dynamic economics. Cowles Commission Monograph No. 10, New York: John Wiley and Sons, 1949.Google Scholar
Koopmans, T. C., and Reiersøl, O.The identification of structural characteristics. To be published.Google Scholar
Ledermann, W. On the rank of the reduced correlational matrix in multiple factor analysis. Psychometrika, 1937, 2, 85–93.CrossRefGoogle Scholar
Reiersøl, O. Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica, 1941, 9, 1–24.CrossRefGoogle Scholar
Thomson, G. H. The proof or disproof of the existence of general ability. Brit. J. Psychol., 1919, 9, 323–336.Google Scholar
Thurstone, L. L. The vectors of mind, Chicago: Univ. Chicago Press, 1935.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Wilson, E. B., and Worcester, J. The resolution of four tests. Proc. nat. Acad. Sci., Wash., 1934, 20, 189–192.CrossRefGoogle ScholarPubMed
Wilson, E. B., and Worcester, J. The resolution of tests into two general factors. Proc. nat. Acad. Sci., Wash., 1938, 25, 20–25.CrossRefGoogle Scholar
Wilson, E. B., and Worcester, J. The resolution of six tests into three general factors. Proc. nat. Acad. Sci., Wash., 1939, 25, 73–77.CrossRefGoogle ScholarPubMed