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Factor Analysis by Generalized Least Squares

Published online by Cambridge University Press:  01 January 2025

Karl G. Jöreskog  and
Arthur S. Goldberger
Karl G. Jöreskog
Affiliation:
University Institute of Statistics, Uppsala, Sweden
Arthur S. Goldberger
Affiliation:
University of Wisconsin
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Abstract

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 scale 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.

Keywords

Public PolicyStatistical TheoryWeight MatrixGeneralize Little SquareFactor Analysis Model

Information

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 3 , September 1972 , pp. 243 - 260
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

The work on this project was done when the first author was Research Statistician at Educational Testing Service, Princeton, N. J. The second author was in part supported by a grant from the Research Committee of the University of Wisconsin Graduate School. The authors wish to thank Michael Browne for many helpful comments and Marielle van Thillo for valuable assistance in the numerical computations.

References

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