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st: RE: PCA and rotation


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: PCA and rotation
Date   Mon, 21 Dec 2009 16:48:45 -0500

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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