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From |
"J Jones" <statafan@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Rescale using covariance matrix for weighted PCA? |

Date |
Wed, 21 May 2008 23:19:04 +0100 |

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 <statafan@googlemail.com> 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. > * > * 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/ > * * 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/

**Follow-Ups**:**RE: st: Rescale using covariance matrix for weighted PCA?***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

**References**:**st: Rescale using covariance matrix for weighted PCA?***From:*"J Jones" <statafan@googlemail.com>

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