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Re: st: Polynomial OLS


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Polynomial OLS
Date   Thu, 25 Dec 2008 16:06:48 +0000 (GMT)

--- Claude Francoeur <claude.francoeur@hec.ca> wrote:
> We are doing a polynomial OLS. An explanatory term is squared and
> cubed to account for non linearity of the association with the
> dependent variable. We also took the natural log of these variables
> to mitigate multicolinearity. We are getting significant 
> coefficients. <snip> Is our approach valid?

It is unusual. If you care about multicollinearity of polynomial terms
you are better of using -orthpoly- (see -help orthpoly-). This results
in a model that is equivalent to a regular polynomial regression
whereas your model is not equivalent to a polynomial regression. 

If you primarily care about whether or not the effect is non-linear
rather than polynomial, then you are probably better of with other more
flexible parameterizations. I am much more a fan of splines to
represent non-linear relationships (see: -help mkspline-), while others
like fractional polynomials (see: -help fracpoly- and -help mfp-)

Hope this helps,
Maarten

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

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

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


      
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