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st: RE: RE: PCA and rotation


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: PCA and rotation
Date   Tue, 22 Dec 2009 11:05:41 -0000

Jay's perspective here ("scale development") is that of a psychometrics
person. Not all uses of PCA share that objective, or what I understand
that term to mean. 

I.T. Jolliffe. 2002. Principal component analysis. New York: Springer is
not quite so negative about rotation of PCs, but does list lots of
drawbacks. 

Nick 
n.j.cox@durham.ac.uk 

Verkuilen, Jay

Michael I. Lichter wrote:

>>What's odd is that I've seen a number of articles that use varimax 
rotations  (with Kaiser normalization) of principal components in scale 
development. The authors only use the PCA to guide scale development; 
they perform further analysis with Cronbach's alpha and create summative

scales rather than using factor scores. Still, their interpretation of 
the components are based on rotated component loadings that, at least 
from Rencher's perspective, are "questionable".<<

Rencher is right to be skeptical. Varimax rotation of principal
components in the context of scale is nonsense. Nothing in the math of
principal components suggests that rotation makes any sense at all
(rotation destroys the entire PCA structure's logic!) and similarly
nothing in the context of scale development suggests that scales should
be orthogonal. If you want a nice article laying this out, look at:

K. J. Preacher & R. C. MacCallum. 2003. "Repairing Tom Swift's Electric
Factor Analysis Machine." Understanding Statistics, 2, 13-32. This is
available at http://kuscholarworks.ku.edu/dspace/handle/1808/1492


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