# st: RE: Quadratic term validity

 From "Nick Cox" To 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

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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