A Biometrics Invited Paper. Factor Analysis: An Introduction to Essentials II. The Role of Factor Analysis in Research

摘要: If, as the extensive findings with simple structure, supported by few presently available confactor rotations, suggest, oblique factors are rule in nature, orthogonality a special, rather rare, case, it behoves us to outline more fully implications of model, for has certain important new properties. Two main consequences appear, both unknown orthogonal case: (1) The correlations factor its variables, on one hand, and loadings them other, which fuse into same values factors, here become recognizably importantly different; (2) From factoring among can derive second higher order systems do not exist case. differentiation correlation loading be shown geometrically Figure 3, also brings out distinction between reference vectors factors. vector is perpendicular hyperplane, examination projections formed that we perform rotations structure. corresponding line intersection hyperplanes all other than hyperplane. Corresponding whence sees where former positively correlated latter inversely correlated. In same. As 3 shows, lines projection variables axes, nmathematical representation, must run parallel, getting factor, axis. Thus, easily seen,