Projections of Three Types of Factor Pattern
In transforming any given correlation matrix, i R, into a primary factor solution, two steps are] commonly taken. The first is to transform the n by n correlation matrix, of rank m, into an arbitrary orthogonal factor matrix of size n by m, such as the centro id matrix, F. The second is to rotate this factor matrix into the desired primary factor pattern. This second step ob viously depends upon a concept of the desired primary factor pattern. An indefinite number of rotations might be made, and consequently one has no notion of when to cease this opera tion unless an exact step-by-step specification of the number and character of the rotations to be made is set up beforehand, or a criterion for recognizing the primary solution is avail able. An attempt is made in this paper to give a geometric formulation of the primary factor solution that provides such a criterion for certain types of desired factor pattern. One approach to the translation of this into an analytic criterion will then be suggested.