THE EFFECT OF DOMAIN SHAPE ON PRINCIPAL COMPONENTS ANALYSES - A REPLY

In a previous paper, I reevaluated the domain shape dependence arguments of Buell and concluded that 'unrotated' principal components do represent, to a very large degree, the underlying structure represented in the dispersion matrix. Richman's comments are largely based as a defence of component rotation-a subject that was not addressed in my original paper. It is my thesis that much of the alleged uninterpretability of 'unrotated' components stems from an attempt to retrieve characteristic scenarios or 'modes of the variation' (which PCA does not purport to do) and not from an overdependence on the shape of the domain. This misapplication often results from a confusion of the goals of principal components analysis and common factor analysis as is evidenced in Richman's comments.