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RE: st: RE: Quadratic term validity


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Quadratic term validity
Date   Wed, 10 Nov 2004 21:57:02 -0000

I'll bow to knowledge here, naturally, 

but 

I still want to know if the quadratic follows 
_deductively_ from plausible postulates, 
or whether it just happens to be a convenient 
functional form for theorists to play with. 

To caricature the point, I could tell you 
that I have a theory that conscience is 
a quadratic in political power, but you'd 
be prudent to want to know where that quadratic
came from and whether it's just decoration for 
a notion I have that something goes up and 
then down. 

Otherwise, I think our concerns are pointing
in the same direction. 

Nick 
n.j.cox@durham.ac.uk 

SamL
 
> Well, um, actually, there is an economic theoretic reason for the
> quadratic term in age, drawn from (among other sources) human capital
> theory--declining returns to _________________ (experience, prior
> training, fill in the blank with what you mean age to 
> signify).  So, I'm
> not sure I'd drop the linear term, as the theory does not imply only
> curving returns.
> 
> There may be other economic theories that justify the 
> quadratic and the
> linear term.
> 
> Finally, statistically, removng the linear term implies no 
> main effect.
> Does that make sense?  It might help to graph the results.  I think no
> linear term would be a major problem, but maybe not.
> 
> HTH.
> Sam
> 
> On Wed, 10 Nov 2004, Nick Cox wrote:
> 
> > Are you really dealing with age or ln age?
> >
> > "Valid" or not depends on your criteria of
> > validity, which are not explicit. From what
> > I gather people like using quadratics in income
> > versus age because they often fit fairly well,
> > and there isn't a economic theory reason
> > for the functional form. So you could make
> > a case for dropping the linear term
> > if it doesn't to seem to help with the fit.
> >
> > On the other hand, there are several grounds
> > for being more circumspect:
> >
> > 1. Just because the linear term looks
> > insignificant does not mean that the
> > model with quadratic term alone is necessarly
> > better, all things considered.
> >
> > 2. The P-value is just one indicator. You
> > don't say anything about the change in R^2
> > or RMS error or (probably most important of
> > all) where there is clear structure
> > if you plot
> >
> > 	residuals from model with quadratic
> > 		term alone
> >
> > 	versus
> >
> > 	age.
> >
> > 3. Inferences are surely complicated by
> > the correlation between age and age^2.
> >
> > 4. There are good discussions of related
> > issues in McCullagh and Nelder's book
> > on generalised linear models and in
> > Nelder's paper in American Statistician
> > November 1998. Loosely, there are
> > grounds for treating polynomial terms
> > as yoked together like a team, although Nelder
> > puts it better than that.
> >
> > Nick
> > n.j.cox@durham.ac.uk
> >
> > Rozilee Asid
> >
> > > My wage model consists of several variables and model. 
> One of my model
> > > consists of quadratic term of age, example
> > > Ln-wage = alpha0 + alpha1.ln_age + alpha2.ln_exp (model 1)
> > > Ln_wage = alpha0 + alpha1.ln_age + alpha2.ln_exp +
> > > alpha3.ln_age^2 (model 2)
> > >
> > > My main attention is to identified whether age play its
> > > significant role in
> > > the model. When I regress the model I found that alpha1 
> coefficient is
> > > negative and insignificant and alpha3 is positive and 
> significant. My
> > > question is before I include the quadratic term of age
> > > variable (model 1),
> > > the alpha1 coefficient is positive and significant.
> > >
> > > Is it valid for me to report the finding from model 2
> > > equations, especially
> > > when alpha1 is negative in the model.

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