Abstract
This paper demonstrates the feasibility of using a Newton-Raphson algorithm to solve the likelihood equations which arise in maximum likelihood factor analysis. The algorithm leads to clean easily identifiable convergence and provides a means of verifying that the solution obtained is at least a local maximum of the likelihood function. It is shown that a popular iteration algorithm is numerically unstable under conditions which are encountered in practice and that, as a result, inaccurate solutions have been presented in the literature. The key result is a computationally feasible formula for the second differential of a partially maximized form of the likelihood function. In addition to implementing the Newton-Raphson algorithm, this formula provides a means for estimating the asymptotic variances and covariances of the maximum likelihood estimators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anderson, T. W., & Rubin, H. Statistical inference in factor analysis.Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Univ. of Califfornia Press, 1956,5, 111–149.
Fletcher, R., & Powell, M. J. D. A rapidly convergent descent method for minimization.Computer Journal, 1963,6, 163–168.
Harman, H. H.Modern factor analysis. Univ. of Chicago Press, 1960.
Henrici, P.Elements of numerical analysis. Wiley, New York, 1964.
Jennrich, R. I., & Sampson, P. F. Application of stepwise regression to non-linear estimation.Technometrics, 1968,10, 63–72.
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis.Psychometrika, 1967,32, 443–482.
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood.Proceedings of the Royal Society of Edinburgh, 1940,60, 64–82.
Rao, C. R. Estimation and tests of significance in factor analysis.Psychometrika, 1955,20, 93–111.
Author information
Authors and Affiliations
Additional information
This research was supported by the Air Force Office of Scientific Research, Grant No. AF-AFOSR-4.59-66 and by National Institutes of Health, Grant No. FR-3.
Rights and permissions
About this article
Cite this article
Jennrich, R.I., Robinson, S.M. A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika 34, 111–123 (1969). https://doi.org/10.1007/BF02290176
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02290176