Re: Principle Component Analysis
- From: Paige Miller <pmiller5NOSPAM@xxxxxxxxxxxxxxxx>
- Date: Sat, 20 Aug 2005 12:09:32 GMT
On 8/20/2005 4:42 AM, RL wrote:
Can anybody tell me how I could use the result of Principle Component Analysis in regression. I read a book about clearing multicollinearity of the independent variables by PCA. I did the PCA already and showed 23 Principle Components. The result could be in the form of latent roots or latent vector but the problem is how do i use this PCA in regression? Do I just regard each Principle Component as the independent variables and regress against the dependent variables or what? I really need help. Thanks
First of all, I think you mean PRINCIPAL components analysis.
Secondly, are these variables with multicollinearity the independent or dependent variables? You didn't say.
If you have multicollinearity among the X variables ... then you COULD use the individual principal components as predictors of your Y variables. HOWEVER -- there is a serious problem here -- some (or perhaps all) of the principal components may not be predictive of the Y variables. On the other hand, they may be very predictive of the Y variables. You just won't know until you try it. The problem is that PCA finds combinations of the X variables that have maximum variance in a dimension (such that the dimensions are perpendicular to the previous dimensions), and that does not imply that the dimensions found are predictive of Y.
Much better is Partial Least Squares (PLS) Regression. This finds orthogonal directions among the X variables that are highly predictive of the Y variables -- if such a direction(s) exists. This handles the problem of multicollinearity in a more useful fashion that PCA does.
-- Paige Miller pmiller5@xxxxxxxxxxxxxxxx http://paiges-page.net
It's nothing until I call it -- Bill Klem, NL Umpire If you get the choice to sit it out or dance, I hope you dance -- Lee Ann Womack .
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