# Re: st: Rescale using covariance matrix for weighted PCA?

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Rescale using covariance matrix for weighted PCA? Date Wed, 21 May 2008 22:42:39 +0100 (BST)

```-pca- allows aweights and fweights, see: -help weights-

hope this helps,
Maarten

> Hello--I would like to do weighted principal-components analysis
> (weighted PCA / WPCA; initialisms added for accessibility in future
> searches); however I am not sure how to do so.  I have variables,
> which may be organized into sets if need be.  I know how to get
> covariance matrices from factor analysis or PCA and I know how to do
> simple rescaling such as dividing an original score by a variable's
> standard deviation.
>
> Is it possible to rescale a variable by manipulating its covariance
> matrix?  References say to weight variables from a particular set by
> dividing by the-reciprocal-of-the square-roo-
> of-the-eigenvalue-of-the-set's-first-principal-component (W)...  and
> also dividing by the standard deviation of the variable.
>
> The exact formula they give is:
> Rescale score=(orig score)/(st dev*W).
>
> So the general method involves doing PCA on sets of variables and
> using the weighitng factor in order to confer proper weight to each
> set.  THen you do facotr analysis on the rescaled scores.
> Can somebody help please?  Thank you.
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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*
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```