, Volume 37, Issue 3, pp 243–260 | Cite as

Factor analysis by generalized least squares

  • Karl G. Jöreskog
  • Arthur S. Goldberger


Aitken's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are seale free and asymptotically efficient. The estimates are computed by a rapidly converging Newton-Raphson procedure. A new technique is used to deal with Heywood cases effectively.


Public Policy Statistical Theory Weight Matrix Generalize Little Square Factor Analysis Model 
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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  1. Aitken, A. C. On least squares and the linear combination of observations.Proceedings of the Royal Society of Edinburgh, 1934–35,55, 42–48.Google Scholar
  2. Anderson, T. W. Some scaling models and estimation procedures in the latent class model. In U. Grenander (Ed.),Probability and statistics: The Harald Cramér volume. New York: Wiley, 1959, Pp. 9–38.Google Scholar
  3. Anderson, T. W. & Rubin, H. Statistical inference in factor analysis.Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1956. Pp. 111–149.Google Scholar
  4. Browne, M. W. Analysis of covariance structures. Paper presented at the annual conference of the South African Statistical Association, October 1970.Google Scholar
  5. Clarke, M. R. B. A rapidly convergent method for maximum-likelihood factor analysis.The British Journal of Mathematical and Statistical Psychology, 1970,23, 43–52.Google Scholar
  6. Ferguson, T. S. A method of generating best asymptotically normal estimates with application to the estimation of bacterial densities.Annals of Mathematical Statistics, 1958,29, 1049–1062.Google Scholar
  7. Harman, H. H.Modern factor analysis. (2nd ed.) Chicago: University of Chicago Press, 1967.Google Scholar
  8. Jennrich, R. I. & Robinson, S. M. A Newton-Raphson algorithm for maximum likelihood factor analysis.Psychometrika, 1969,34, 111–123.CrossRefGoogle Scholar
  9. Jöreskog, K. G.Statistical estimation in factor analysis. Stockholm: Almqvist & Wiksell, 1963.Google Scholar
  10. Jöreskog, K. G. Some contributions to maximum likelihood factor analysis.Psychometrika, 1967,32, 443–482.CrossRefGoogle Scholar
  11. Lawley, D. N. A modified method of estimation in factor analysis and some large sample results.Proceedings of the Uppsala Symposium on Psychological Factor Analysis, March 17–19, 1953. Nordisk Psykologi's Monograph Series No. 3. Stockholm: Almqvist & Wiksell, 1953. Pp. 35–42.Google Scholar
  12. Lawley, D. N. Some new results in maximum likelihood factor analysis.Proceedings of the Royal Society of Edinburgh, Section A, 1967,67, 256–264.Google Scholar
  13. Malinvaud, E.Statistical methods of econometrics. Chicago: Rand-McNally. 1966.Google Scholar
  14. Neyman, J. Contribution to the theory of x2 test.Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1949, Pp. 239–273.Google Scholar
  15. Rothenberg, T. Structural restrictions and estimation efficiency in linear econometric models. Cowles Foundation Discussion Paper No. 213. New Haven, Conn.: Yale University, 1966.Google Scholar
  16. Taylor, W. F. Distance functions and regular best asymptotically normal estimates.Annals of Mathematical Statistics, 1953,24, 85–92.Google Scholar
  17. Wilkinson, J. H.The algebraic eigenvalue problem. Oxford: Oxford University Press, 1965.Google Scholar
  18. Zellner, A. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias.Journal of the American Statistical Association, 1962,57, 348–368.Google Scholar

Copyright information

© Psychometric Society 1972

Authors and Affiliations

  • Karl G. Jöreskog
    • 1
  • Arthur S. Goldberger
    • 2
  1. 1.University Institute of StatisticsUppsalaSweden
  2. 2.University of WisconsinUSA

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