A unified treatment of the weighting problem

A general procedure is described for obtaining weighted linear combinations of variables. This includes as special cases, multiple regression weights, canonical variate analysis, principal components, maximizing composite reliability, canonical factor analysis, and certain other well-known methods. The general procedure is shown to yield certain desirable invariance properties, with respect to transformations of the variables.The author wishes to thank Dr. A. J. Cropley for preparing the necessary computer programs for this study.