Re: st: RE: transformation of a continuous variable for a logisticregression model

[Suzy <scott_788@wowway.com>]

Thanks for your response Nick. In a nutshell, age is not linear in the 
logit. I'm using the fracpoly command to identify the best functional 
form for age in  the full model. The result returned from Fracpoly was a 
quadratic function with powers 3 3 (which also looks good with 
fracplot). However, when I  further assessed the model using the Boxtid 
command, the results with the new age transformation - the results were 
not favorable (the Ho was rejected). When I transformed another 
continuous variable in the same  full logistic model (quadratic with 
powers 1 2 by Fracpoly),  the Boxtid results were favorable, all graphs 
looked very good, and the diagnostics were good (linktest, etc...).  I'm 
trying to understand why my results aren't consistent (Fracpoly and 
Boxtid) with the age variable, but is with all other continuous variables?

Nick Cox wrote:


> I am not clear what you think Statalist members know
> that can help you here. For example, the field 
> in which you are working, what the response variable 
> -dmcat- means, and what other predictors there may be are all
> hidden from view, so the chance of giving opinions 
> drawing on substantive expertise is zero. Otherwise
> put, you appear to be assuming that the choices
> here can all be made on purely statistical criteria, 
> an attitude which always worries me greatly. 
> What I have observed, as a kind of anthropologist of
> statistical science, is that age plays very different
> roles in different fields. Economists often seem 
> to find that a quadratic in age does very nicely, 
> whereas biostatisticians often seem to need 
> more complicated representations, which seems
> perfectly plausible given the complexities of
> childhood, adolescence, etc. 
> Either way, -fracpoly- like other programs has
> no inbuilt sensor (or censor) selecting theoretically or 
> scientifically sensible functional forms. So, 
> I suggest that you plot the curve implied against
> age and think about it as something that needs justification
> or interpretation independently from the data. 
> Nick 
> n.j.cox@durham.ac.uk 
> Suzy
>
>  
>
> > I am trying to transform one final continuous independent 
> > variable (age) 
> > in a logistic regression model. I've tried what I know that's 
> > available 
> > via Stata. For example, I used the fracpoly command and the best 
> > transformation was a second order polynomial with powers 3 3.
> >
> > Fractional polynomial model comparisons:
> > ---------------------------------------------------------------
> > age              df       Deviance      Gain   P(term) Powers
> > ---------------------------------------------------------------
> > Not in model      0       2098.129        --     --
> > Linear            1       1834.224     0.000    0.000  1
> > m = 1             2       1805.957    28.267    0.000  -1
> > m = 2             4       1791.327    42.897    0.001  3 3
> > m = 3             6       1790.526    43.699    0.670  -2 3 3
> > m = 4             8       1788.431    45.793    0.351  -2 -2 3 3
> > ---------------------------------------------------------------
> >
> >
> > I then used fracgen to generate the new age variables - age_1 
> > and age_2.
> >
> > fracgen age 3 3
> > -> gen double age_1 = X^3 
> > -> gen double age_2 = X^3*ln(X) 
> >   (where: X = (age+1)/10)
> >
> >
> >
> >
> >
> > The coefficients for age_1 and age_2 from the full logistic 
> > regression 
> > model:
> > --------------------------------------------------------------
> > ----------------
> >       Y var | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. 
> > Interval]
> > -------------+------------------------------------------------
> > ----------------
> >       age_1 |   1.087994   .0093302     9.83   0.000      1.06986    
> > 1.106436
> >       age_2 |   .9644247   .0037538    -9.31   0.000     .9570955    
> > .9718101
> >
> >
> > However the boxtid command rejected the null for both age_1 
> > and age_2....
> >
> >  age_1    |   .0100805   .0007172     14.055   Nonlin. dev. 
> > 24.646  (P 
> > = 0.000)
> >        p1 |   .0535714   .2122906      0.252
> > --------------------------------------------------------------
> > ----------------
> >  age_2    |  -.0021756   .0004885     -4.453   Nonlin. dev. 
> > 7.894   (P 
> > = 0.005)
> >        p1 |   3.864227   2.133377      1.811
> >
> >
> > In all other respects, the preliminary diagnostics look good...
> >
> > Linktest:
> > --------------------------------------------------------------
> > ----------------
> >       dmcat |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
> > Interval]
> > -------------+------------------------------------------------
> > ----------------
> >        _hat |   .8900851   .1153855     7.71   0.000     .6639337    
> > 1.116236
> >      _hatsq |  -.0319886   .0307101    -1.04   0.298    -.0921793    
> > .0282022
> >       _cons |  -.0450195   .1069617    -0.42   0.674    -.2546606    
> > .1646215
> > --------------------------------------------------------------
> > ----------------
> > lroc
> >
> > Logistic model for dmcat
> >
> > number of observations =     3354
> > area under ROC curve   =   0.8647
> >
> > etc...etc...etc...
> >
> > My question is should I be concerned with the results of the Boxtid 
> > command? Is there something I've done incorrectly or something else I 
> > can do/should do?
> >    
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>
>
>  

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