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


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Extremely High Correlation between Interaction Term and Each of Its Component Linear Terms
Date   Wed, 12 Dec 2012 10:51:37 -0500

At 04:01 AM 12/12/2012, Johan Hellström wrote:
Lloyd,

Yes, you can save yourself from the trouble of worrying about collinearity caused by interacting terms. Interaction terms and its components are usually correlated and are so correctly. There is no magical trick to reduce the collinearity and although centring variables could be helpful sometimes to ease interpretation, it does not alter anything statistically or substantively.

Best wishes,
Johan Hellstrom

Yes, I don't worry too much about multicollinearity in such instances, unless maybe the model won't converge. For example, if you have x and x^2 in the model, you might need to rescale x if x^2 produces monstrous numbers. So, for example, it may be better to measure income in thousands of dollars rather than in dollars.

The handout that Lloyd mentioned earlier,

http://www.nd.edu/~rwilliam/stats2/l11.pdf

does include some tips for dealing with multicollinarity. For example, avoid doing something stupid like including a scale that was computed from other variables in your model. Or, consider creating a scale if, say, x1-x10 are really just 10 different ways of measuring the same concept.

Other than that, always collecting samples of at least 10 million cases is probably a good idea. Assuming you have unlimited resources for your research.


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Richard Williams, Notre Dame Dept of Sociology
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