ABSTRACT
Major developments in the methodology of rotation have occurred since 1965. First, the paper of Jennrich and Sampson (1966) showed that it was not necessary or desirable to rotate rst to a reference-structure matrix and then convert that to a factor-pattern matrix. One could apply the rotational criteria directly to the determination of a factor-pattern matrix, and this would more easily avoid a collapse of the factor space into fewer dimensions. Second, while planar rotations in two dimensions continued to dominate the approach to rotation through to the 1990s, since 2000, a number of papers by Jennrich (2001, 2002, 2004, 2006) have demonstrated a uni ed approach to all rotational methods using simultaneous rotations of all factors via r × r transformation matrices T. Furthermore, Jennrich has shown, through a compact but easily mastered notation, that these approaches can be quite easy to program and implement. Thus I regard Jennrich’s contributions to be the wave of the future, and in this chapter I will not dwell on rotations to reference-structure matrices, and will illustrate the planar rotation approach with only the method of direct oblimin. I will describe the criteria of the various popular methods of rotation and then show how they may be applied to obtain factor-pattern matrices by Jennrich’s general approach using gradient-projection algorithms (GPAs).
