Re: st: Multicollinearity and Orthogonalization

[Steven Samuels <sjhsamuels@earthlink.net>]

-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
>
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>
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>
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