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Re: st: Multicollinearity and Orthogonalization


From   Steven Samuels <sjhsamuels@earthlink.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Multicollinearity and Orthogonalization
Date   Sat, 16 Aug 2008 17:23:54 -0400

-orthog- will orthogonalize x1*x2 to x1 & x2. But I agree with Maarten--why would one want to? The orthogonalized version of x1*x2 would be a complicated function of the original variables and so lose any interpretability.

-Steve


On Aug 16, 2008, at 1:11 PM, Maarten buis wrote:


I would consider multicollinearity a bit of a fake problem: Statistical
techniques will give you correct representation of what is present in
you data, the `problem' is that you don't like what is present in your
data: You cannot distinguish separte effects of two variables that are
perfectly correlated, and you will have a hard time distinguishing
effects of two variables when they are highly correlated. The fact that
interaction terms cost power should not surprise you: the main effects
compare means, while the interaction terms compare the comparisons. So
the interaction terms are one step further removed from your data, so
you should have difficulty in finding those. The only thing that might
worry me about multicolinearity would be numerical problems that it
might cause, but Stata is pretty good at dealing with those.

-- Maarten

--- Erasmo Giambona <e.giambona@gmail.com> wrote:


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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-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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