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A Reliability Coefficient for Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker  and
Charles Lewis
Ledyard R Tucker
Affiliation:
University of Illinois
Charles Lewis
Affiliation:
University of Illinois
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Abstract

Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed to indicate quality of representation of interrelations among attributes in a battery by a maximum likelihood factor analysis. Usually, for a large sample of individuals or objects, the likelihood ratio statistic could indicate that an otherwise acceptable factor model does not exactly represent the interrelations among the attributes for a population. The reliability coefficient could indicate a very close representation in this case and be a better indication as to whether to accept or reject the factor solution.

Keywords

Common FactorFactor ModelReliability CoefficientFactor SolutionLikelihood Ratio Statistic

Information

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 1 , March 1973 , pp. 1 - 10
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

This research was supported by the Personnel and Training Research Programs Office of the Office of Naval Research under contract US NAVY/00014-67-A-0305-0003. Critical review of the development and suggestions by Richard Montanelli were most helpful.

References

Browne, M. W. Fitting the factor analysis model. Psychometrika, 1969, 34, 375–39410.1007/BF02289365CrossRefGoogle Scholar
Gulliksen, H., and Tukey, J. W. Reliability for the law of comparative judgment. Psychometrika, 1958, 23, 95–11010.1007/BF02289008CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, 2nd edition, Chicago: University of Chicago Press, 1967Google Scholar
Holzinger, K. J., and Swineford, F. A study in factor analysis: the stability of a bi-factor solution, 1939, Chicago: Dept. of Education, University of ChicagoGoogle Scholar
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–48210.1007/BF02289658CrossRefGoogle Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, 1940, 60, 64–8210.1017/S037016460002006XCrossRefGoogle Scholar
Lord, F. M. A study of speed factors in tests and academic grades. Psychometrika, 1956, 21, 31–5010.1007/BF02289085CrossRefGoogle Scholar
Mosteller, F. Remarks on the method of paired comparisons, III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 1951, 16, 207–21810.1007/BF02289116CrossRefGoogle Scholar
Mullen, F. Factors in the growth of girls seven to seventeen years of age. Unpublished Ph.D. Thesis, Dept. of Education, University of Chicago, 1939.Google Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–11110.1007/BF02288983CrossRefGoogle Scholar
Thurstone, L. L., and Thurstone, T. G. Factorial studies of intelligence, 1941, Chicago: University of Chicago PressGoogle Scholar
Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–13610.1007/BF02289009CrossRefGoogle Scholar
Tucker, L. R, Koopman, R. F., and Linn, R. L. Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 1969, 34, 421–45910.1007/BF02290601CrossRefGoogle Scholar