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st: RE: RE: RE: PCA and rotation


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: PCA and rotation
Date   Tue, 22 Dec 2009 12:55:54 -0500

Nick Cox wrote:

>Jay's perspective here ("scale development") is that of a psychometrics
person. <<

Yes, correct. 


>Not all uses of PCA share that objective, or what I understand
that term to mean. <

Agreed. (I'm not sure I do either, if you push me at 4 AM.)


>>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. <

The main problem as I see it is that PCA's most attractive aspect when compared to the common factor model, namely that it uniquely maximizes variance of successively orthogonal linear combinations, is totally undermined by rotation. Reification (i.e., "naming" them) of components is a very dangerous game, because it tends to invite a superficial analysis of the inter-relationships found in the data and also is subject to substantial confirmation bias. The excellent book by JC Gower and DJ Hand (Biplots, CRC Press, 1995) discusses the issues quite nicely. As largely the entire reason to do rotation in the first place is to enable reification, I'd say it's generally a bad idea. 

So it depends on why you're using PCA. If you're using it as a data reduction device to discard variables from consideration in subsequent analysis because they never have high component weights, rotation won't matter. 

(Aside: Gower is quite a character. I finally met him at a conference at Cambridge this summer.) 



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