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Re: st: pca and predict--confusion about what it does


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: pca and predict--confusion about what it does
Date   Sat, 20 Oct 2012 21:06:16 -0400

On Sat, Oct 20, 2012 at 6:45 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> That's (what shall we say) one point of view. Another is that PCA is a
> multivariate transformation technique. No model, no estimation.

Agreed, you can think of it simply as a re-expression of the data
matrix into a weighted sum of mutually orthogonal rank one "layers".

In many problems I have absolutely no issue with that interpretation,
but choosing the SVD to decompose a matrix is at least an implicit
commitment to a least squares loss function. IMO this is a model,
though of course not a full probability model.



Factor
> analysis is a branch of alchemy, so I'll refrain fom comment.

It certainly doesn't need to be, though I very much agree that the
older literature has a heavy dose of alchemy in it. If you "believe"
in HLM (some days I do and some days I don't ;), factor analysis isn't
really all that different. Factor analysis and PCA essentially being a
bilinear model with different loss functions compared to the linear
model of HLM.
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