Rotation

This chapter provides an overview of the main components of rotation, from the work of Thurstone to the present. Because it was simpler, early rotation methods used orthogonal rotation, and in particular varimax rotation. At first, every rotation method came with a rotation algorithm designed specifically for the method, or more precisely for the criterion that defined the method. The chapter presents a primarily historical overview of rotation methods in exploratory factor analysis (EFA). A number of EFA use oblique quartimin or oblique geomin as default choices for a rotation method, and presently at least these seem appropriate first choices. The chapter includes a discussion of rotation, rotation criteria, rotation algorithms, choosing a rotation method, producing standard errors for rotated loadings, and some real data applications. It provides explicit formulas for ordinary least squares and maximum likelihood extraction and for arbitrary Crawford-Ferguson (CF) rotation.