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From |
Steven Samuels <[email protected]> |

To |
[email protected] |

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 <[email protected]> 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

-----------------------------------------

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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*

* For searches and help try:

* http://www.stata.com/help.cgi?search

* http://www.stata.com/support/statalist/faq

* http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Multicollinearity and Orthogonalization***From:*SR Millis <[email protected]>

**References**:**Re: st: Multicollinearity and Orthogonalization***From:*Maarten buis <[email protected]>

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