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st: Multicollinearity and Orthogonalization


From   "Erasmo Giambona" <e.giambona@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Multicollinearity and Orthogonalization
Date   Sat, 16 Aug 2008 12:43:16 -0400

Dear Statalisters,

I recently came across the following article (An Overview of Remedial
Tools for Collinearity in SAS
Chong Ho Yu, Tempe, AZ), which is accessible on the web by googling
it. One of the topics addressed in the article is how to deal with the
collinearity between an interaction term (e.g. x1*x2) and its
components (e.g., x1 and x2) in a regression model as the following:

y = a + b(x1*x2) + c*x1 + d*x2 + e (1). The remedy is
orthogonalization, which consists of runnig the following regression:
x1*x2 = a1 + b1*x1+b2*x2 + error (2), and use the error of this
regression instead of x1*x2 in (1). I understand that in so doing we
create a variable "error" that is uncorrelated to either x1 and x2.
Now, I am a bit puzzled on whether or to what extent orthogonalization
is a remedy to collinearity.

I would appreacite if someone can provide any hints on the topic.
Regards,
Erasmo
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