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

[Suzy <scott_788@wowway.com>]

Nick - Not to beat a dead horse, but I just thought I'd share this with 
you - from:<>

Vincenzo Bagnardi, Antonella Zambon, Piero Quatto and Giovanni Corrao. 
Flexible Meta-Regression Functions for Modeling Aggregate Dose-Response 
Data, with an Application to Alcohol and Mortality. Am J Epidemiol 2004; 
159:1077-1086.

"Although it is rather simple, the family of second-order fractional 
polynomial models offers considerably flexibility. In particular, by 
choosing p1 and p2 from a predefined set P = {–2, –1, –0.5, 0, 0.5, 1, 
2, 3}, a very rich set of possible functions, including some so-called 
U-shaped and J-shaped relations, may be accommodated. The powers are 
expressed according to the Box-Tidwell transformation (12 
<http://aje.oxfordjournals.org/cgi/content/full/159/11/1077#KWH142C12>), 
in which denotes if pi != 0 and log x if pi = 0. When p1 = p2 = p, the 
model becomes log(RR½x) = ß1xp + ß2(xp log x)."

I thought that a second order polynomial = "degree of 2" (M=2) = 
quadratic as shown in my output from fracpoly below (M=2). I had also 
e-mailed the fracplot to show the quadratic curve, but for some reason, 
it was deleted via transport. In any case, the age variable 
transformations (age_1 and age_2) from the fracgen command were 
calculated using the the formulas above - ß1age3 + ß2(age3 log age).

Thus, I still respectfully do not understand why the fracpoly and boxtid 
results are not consistent with this variable. As far as a theoretical 
justification of the functional form of age and the response variable - 
it does make sense for these data.

Nick Cox wrote:


> Sorry, but this to me is just a restatement of 
> your previous posting, and addresses none of 
> the points I raised. 
> That aside, 
> I don't understand how a quadratic function can 
> have powers 3 3. Cubics in my experience are never 
> appropriate for global fits unless there are clear 
> dimensional grounds for using them, which seems unlikely 
> here. 
> Nick 
> n.j.cox@durham.ac.uk 
> Suzy
>
>  
>
> > 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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