Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T10:08:55.936Z Has data issue: false hasContentIssue false
  • English
  • Français

Obtaining Maximum-Likelihood Estimates of Factor Loadings and Communalities Using an Easily Implemented Iterative Computer Procedure

Published online by Cambridge University Press:  01 January 2025

W. J. Hemmerle
W. J. Hemmerle*
Affiliation:
University of Rhode Island
Get accessRights & Permissions [Opens in a new window]

Abstract

This paper considers the problem of computing estimates of factor loadings, specific variances, and communalities for a factor analytic model. The equations for maximum-likelihood estimators are discussed. Iterative formulas are developed to solve the maximum-likelihood equations and a simple and efficient method of implementation on a digital computer is described. Use of the iterative formulas and computing techniques for other estimators of factor loadings and communalities is also considered to provide a very general approach for this aspect of factor analysis.

Information

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 3 , September 1965, pp. 291 - 302
Copyright
Copyright © 1965 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

References

Anderson, T. W. An introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Anderson, T. W. and Rubin, H. Statistical inference in factor analysis. Proc. Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. V. Berkeley and Los Angeles: Univ. Calif. Press, 1956, 111–150..Google Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–263.CrossRefGoogle Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proc. royal Soc. Edinburgh, 1940, 60, 64–82.CrossRefGoogle Scholar
Lawley, D. N. Further investigations in factor estimation. Proc. roy. Soc. Edinburgh, 1942, 61, 176–185.Google Scholar
Ortega, J. M. On Sturm sequences for tri-diagonal matrices. J. Assoc. comput. Mach., 1960, 7, 260–263.CrossRefGoogle Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Share General Program Library. Fortran Subroutine How. Share Distribution Number 1321.Google Scholar
Wilkinson, J. H. The calculation of eigenvectors of codiagonal matrices. Comput. J., 1958, 1, 90–96.CrossRefGoogle Scholar
Wilkinson, J. H. Householder's method for the solution of the algebraic eigenproblem. Comput. J., 1960, 3, 23–27.CrossRefGoogle Scholar