Factor analysis by generalized least squares

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 seale 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.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.