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st: RE: Quadratic term validity


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Quadratic term validity
Date   Wed, 10 Nov 2004 21:23:06 -0000

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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