Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-11T14:49:11.323Z Has data issue: false hasContentIssue false
  • English
  • Français

A General Approach to Confirmatory Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

K. G. Jöreskog
K. G. Jöreskog*
Affiliation:
Educational Testing Service
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large sample x2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 2 , June 1969 , pp. 183 - 202
Copyright
Copyright © 1969 The 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 work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service.

References

Anderson, T. W. An introduction to multivariate statistical analysis, 1958, New York: Wiley.Google Scholar
Anderson, T. W., & Rubin, H. Statistical inference in factor analysis. In Neyman, J. (Eds.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. V. Berkeley: University of California Press. 1956, 111–150.Google Scholar
Fletcher, R., & Powell, M. J. D. A rapidly convergent descent method for minimization. Computer Journal, 1963, 2, 163–168.CrossRefGoogle Scholar
Holzinger, K. J., & Swineford, F. A study in factor analysis: The stability of a bi-factor solution. University of Chicago: Supplementary Educational Monographs, No. 48, 1939.Google Scholar
Howe, W. G. Some contributions to factor analysis. Report No. ORNL-1919, 1955, Oak Ridge, Tennessee: Oak Ridge National Laboratory.Google Scholar
Jöreskog, K. G. Testing a simple structure hypothesis in factor analysis. Psychometrika, 1966, 31, 165–178.CrossRefGoogle ScholarPubMed
Jöreskog, K. G. UMLFA — A computer program for unrestricted maximum likelihood factor analysis, Revised Edition, Princeton, N. J.: Educational Testing Service, 1967.Google Scholar
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Jöreskog, K. G., & Gruvaeus, G. RMLFA — A computer program for restricted maximum likelihood factor analysis, 1967, Princeton, N. J.: Educational Testing Service.Google Scholar
Jöreskog, K. G., & Lawley, D. N. New methods in maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 1968, 21, in press.CrossRefGoogle Scholar
Kendall, M. G., & Stuart, A. The advanced theory of statistics, vol. 2, 1961, London: Charles Griffin and Co..Google Scholar
Lawley, D. N. Estimation in factor analysis under various initial assumptions. British Journal of Statistical Psychology, 1958, 11, 1–12.CrossRefGoogle Scholar
Lawley, D. N. Some new results in maximum likelihood factor analysis. Proceedings of the Royal Society of Edinburgh, 1967, 67, 256–264.Google Scholar
Lawley, D. N., & Maxwell, A. E. Factor analysis as a statistical method, 1963, London: Butterworth.Google Scholar
Lawley, D. N., & Maxwell, A. E. Factor transformation methods. British Journal of Statistical Psychology, 1964, 17, 97–103.CrossRefGoogle Scholar
Lockhart, R. S. Asymptotic sampling variances for factor analytic models identified by specified zero parameters. Psychometrika, 1967, 32, 265–277.CrossRefGoogle ScholarPubMed
Reiersøl, O. On the identifiability of parameters in Thurstone's multiple factor analysis. Psychometrika, 1950, 15, 121–149.CrossRefGoogle ScholarPubMed
Thurstone, L. L. Multiple-factor analysis, 1947, Chicago: University of Chicago Press.Google Scholar
Thurstone, L. L., & Thurstone, T. G.. Factorial studies of intelligence. Psychometric Monographs No. 2, 1941, Chicago: University of Chicago Press.Google Scholar
Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–136.CrossRefGoogle Scholar
Tucker, L. R., Koopman, R. F., & Linn, R. L. Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 1968, in press.Google Scholar
Vernon, P. E. The structure of human abilities, 1951, London: Methuen.Google Scholar