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RE: st: Rescale using covariance matrix for weighted PCA?


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Rescale using covariance matrix for weighted PCA?
Date   Wed, 21 May 2008 18:32:18 -0400

J Jones: 

>>"Factor analysis method uses the correlation structure of the
variables or the covariance structure <epsilon>. In using the covariance
matrix we can manually rescale variables (XI_i) by dividing with their
respective standard deviations (sigma_i)."

How the heck do they use the covariance matrix to scale the variable?!<<

Well I'm not entirely sure what the text is saying but you can compute a
correlation matrix from a covariance matrix as follows:

Let C be the covariance matrix and D = diag(C)^-1/2. Then R = DCD.

The method for linear transformations of variables works more generally.
If you have a covariance matrix C and want to rescale the original
varibles, replace D with the scaling factors you want. 

This will be explained in a standard multivariate statistics text or
matrix book e.g., Tools for Applied Multivariate Analysis by Paul Green
and J. Douglas Carroll. 

Jay


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