Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-07T08:26:43.694Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum Likelihood Estimation and Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Gale Young
Gale Young*
Affiliation:
Olivet College
Get access Rights & Permissions [Opens in a new window]

Abstract

Fisher's method of maximum likelihood is applied to the problem of estimation in factor analysis, as initiated by Lawley, and found to lead to a generalization of the Eckart matrix approximation problem. The solution of this in a special case is applied to show how test fallability enters into factor determination, it being noted that the method of communalities underestimates the number of factors.

Information

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 1 , February 1941 , pp. 49 - 53
Copyright
Copyright © 1941 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.)

Article purchase

Temporarily unavailable

Footnotes

*

Dr. George Brown of Princeton University has independently made the same suggestion in some unpublished work.

*

In particular, if tbe tests have equal reliabilities, factoring the correlation matrix with unity in the diagonals is indicated.

References

Eckart, Car. and Young, Gal. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Fisher, R. A. On the mathematical foundations of theoretical statistics. Phil. Trans. Roy. Soc. A., 1921, 222, 309–368.Google Scholar
Fisher, R. A. Theory of statistical esitmation. Proc. Camb. Phil. Soc., 1925, 22, 700–725.CrossRefGoogle Scholar
Fisher, R. A. Inverse probability. Proc. Camb. Phil. Soc., 1930, 26, 528–535.CrossRefGoogle Scholar
Householder, A. S. and Young, Gal. Matrix approximation and latent roots. Amer. Math. Monthly, 1938, 45, 165–171.CrossRefGoogle Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proc. Roy. Soc. of Edinburgh, 1939, 60, Part 1, No. 6.Google Scholar
Young, Gal. Factor analysis and the index of clustering. Psychometrika, 1939, 4, 201–208.CrossRefGoogle Scholar