Factor analysis by minimizing residuals (minres)

This paper is addressed to the classical problem of estimating factor loadings under the condition that the sum of squares of off-diagonal residuals be minimized. Communalities consistent with this criterion are produced as a by-product. The experimental work included several alternative algorithms before a highly efficient method was developed. The final procedure is illustrated with a numerical example. Some relationships of minres to principal-factor analysis and maximum-likelihood factor estimates are discussed, and several unresolved problems are pointed out.The authors wish to thank the Factor Analysis Work Group (supported, in part, by ONR) for valuable criticisms and suggestions made in the course of a discussion of the present work in April, 1965.