FACTOR ANALYSIS BY MINIMIZING RESIDUALS (MINRES)

摘要

This paper describes a new method of factor analysis, "built on the foundations of the subject laid in the 1930's, but not realizable before the advent of modern-day computing capabilities. Specifically, the new method estimates factor loadings in such a way as to make the sum of squares of off-diagonal residuals a minimum. Communalities consistent with this criterion are produced as a by-product. Several distinct computing procedures were considered in the course of the experimental work before a highly efficient technique was developed. The final procedure is illustrated with a numerical example. Some important properties of a minres solution are emphasized, including its relationship to principal-factor analysis and maximum-likelihood factor estimates. Finally, several unresolved problems are pointed out as a guide to possible future research.