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st: Extremely High Correlation between Interaction Term and Each of Its Component Linear Terms


From   Lloyd Dumont <lloyddumont@yahoo.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Extremely High Correlation between Interaction Term and Each of Its Component Linear Terms
Date   Mon, 10 Dec 2012 04:43:28 -0800 (PST)

Hello, Statalist.
 
I have read up on collinearity again, enough to re-familiarize myself with its potential consequences for my estimates.  (Richard Williams, among others has a nice write-up on this at http://www.nd.edu/~rwilliam/stats2/l11.pdf.)  I understand that one way to think about it is that it essentially makes it more difficult to find statistically significant results.  Thus, if your estimates emerge relatively unscathed, then you can accept the collinearity for what it is, and perhaps, consider your estimates to be conservative at that.

Here is where the plot may thicken, and Williams only touches on this (pp. 10-11): does anything change if you are talking about IVs X1, X2, and X1*X2, where let’s say X1 and X1*X2 are very highly-correlated, say .95 or so?
 
William’s suggestion that I center the variables before creating the interaction helped a bit.  It brought the correlation between X1 and X1*X2 down to .65 (from .97), though it did raise the correlation between X2 and X1*X2 to about .83 (from .38).

This matters, because I am interested in the fact that X1 and X2 are insignificant predictors of Y when entered on the RHS individually or even together.  Yet, when entered alongside their interaction term, X1 and X2 are both statistically significant positive predictors of Y while X1*X2 is a statistically significant negative predictor of Y.  This comports with the theory, making the result quite informative, to the extent I can believe it!

So, can I believe this, or are there even more issues at play when the collinearity is between an interaction term and its components?  And, is there anything else I can do to mitigate the collinearity or its effects?

Thank you for your help.

Lloyd Dumont 

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