β Scribed by Richman, Michaf. L. B.
No coin nor oath required. For personal study only.
Jolliffe's comments raise some intcresting and important points concerning both unrotated principal component analysis and rotated principal component analysis that deserve further consideration. These are examined herein, with particular attention to my original review of rotation.
Oblique rotation Factor analysis Monte Carlo analysis
I would like to thank Dr Jolliffe for his generous and insightful comments concerning my article on the rotation of principal components (Richman, 1986; henceforth termed R 86). He presented several valid points, ones that have never been fully addressed in the literature.
My paper had two aims: (i) to provide a thorough review of the theory and application of rotated principal component analysis (RPCA) and (ii) to attempt to provide a guide to the selection of the most appropriate rotation solution from the multitude of available options (i.e. unrotated, Varimax, Promax . . .). Section 2 in R 86 (pp. 295-304) was written to convey my concern about the typical fashion unrotated solutions were being used to interpret individual modes of variation, rather than to comment 'on what principal component analysis can and cannot do' (Jolliffe 1987, p. 507). The term 'individual' is emphasized strongly here, as was the case (R 86, p. 295) when the four motivations for rotation were initially examined. Additionally, both that section and the conclusions (R 86, p. 332) highlighted several potential strengths of unrotated solutions (e.g. economy, ability to extract maximal variance) and potential weaknesses of rotated solutions (e.g. pattern sensitivity to the number of PCs retained, more complex nature and terminology) in an attempt to provide a more balanced examination of the various solutions efficacy (e.g. 'no one solution (unrotated, rotated) or specific criterion will always yield the most accurate results.. . .').
Jolliffe's comments provide an excellent supplement to points I may not have stressed sufficiently. We do disagree on several issues, however, and I now wish to consider those in some depth.
The majority of Jolliffe's comments address definition of PCs and EOFs, interpretation of individual PCs, and the application of the Monte Carlo results for analysis. These will be considered individually.
Jolliffe seems to feel that the distinction between EOFs and PCs is not particularly useful and may be confusing. The need for this distinction arises from two points: (i) many meteorologists rely solely on empirical
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