Hello--thank you for the pointer, Maarten. I hadn't known about
different weights and it seems like a useful lesson.
I still wonder, though, about actual 'workflow' for weighting? To
repeat: I want to do weighted PCA, which seems like a two-step PCA in
which vars are first reduced to components and are then weighted by a
factor of teh eigenvalue of teh first component. My reference (de
Silva 2000 - about construction of a poverty index) says:
"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?!
Thanks for reading!
On Wed, May 21, 2008 at 10:25 PM, J Jones <[email protected]> wrote:
> 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.
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