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Constrained Least Squares Estimators of Oblique Common Factors

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald
Roderick P. McDonald*
Affiliation:
Macquarie University
*
Requests for reprints should be addressed to Roderick P. McDonald, School of Education, Macquarie University, North Ryde, N.S.W., 2113, Australia.
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Abstract

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.

Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 337 - 341
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

The research reported in this paper was partly supported by Natural Sciences and Engineering Research Council Grant No. A6346.

References

Anderson, T. W. & Rubin, H. Statistical inference in factor analysis. Proceedings of the third Berkeley Symposium on mathematical statistics and probability, 1956, V, 111–150.Google Scholar
Harris, C. W. On factors and factor scores. Psychometrika, 1967, 32, 363–379.CrossRefGoogle Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, 1971, London: Butterworths.Google Scholar
McDonald, R. P. Descriptive axioms for common factor theory, image theory and component theory. Psychometrika, 1975, 40, 137–152.CrossRefGoogle Scholar
McDonald, R. P. The indeterminacy of components and the definition of common factors. British Journal of mathematical and statistical Psychology, 1977, 30, 165–176.CrossRefGoogle Scholar
McDonald, R. P. & Burr, E. J. A comparison of four methods of constructing factor scores. Psychometrika, 1967, 32, 381–401.CrossRefGoogle Scholar
McDonald, R. P. & Mulaik, S. A. Determinacy of common factors: A nontechnical review. Psychological Bulletin, 1979, 86, 297–306.CrossRefGoogle Scholar
Mulaik, S. A. & McDonald, R. P. The effect of additional variables on factor indeterminacy in models with a single common factor. Psychometrika, 1978, 43, 177–192.CrossRefGoogle Scholar
Schönemann, P. H. & Steiger, J. H. Regression component analysis. British Journal of mathematical and statistical Psychology, 1976, 29, 175–189.CrossRefGoogle Scholar
Steiger, J. H. On the empirical equivalence of regression components and common factors. British Journal of mathematical and statistical Psychology, 1980, 33, 200–204.CrossRefGoogle Scholar
Tucker, L. R. Relations of factor score estimates to their use. Psychometrika, 1971, 36, 427–436.CrossRefGoogle Scholar