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Re: st: RE: Quadratic term validity


From   SamL <saml@demog.berkeley.edu>
To   Stata Listserve <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE: Quadratic term validity
Date   Wed, 10 Nov 2004 13:37:04 -0800 (PST)

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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