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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. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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