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subset selection for logistic regression

7 messages · Wittner, Ben, Frank E Harrell Jr, dr mike +2 more

Wittner, Ben
# 
R-packages leaps and subselect implement various methods of selecting best or
good subsets of predictor variables for linear regression models, but they do
not seem to be applicable to logistic regression models.
 
Does anyone know of software for finding good subsets of predictor variables for
linear regression models?
 
Thanks.
 
-Ben
 
p.s., The leaps package references "Subset Selection in Regression" by Alan
Miller. On page 2 of the
2nd edition of that text it states the following:
 
  "All of the models which will be considered in this monograph will be linear;
that is they
   will be linear in the regression coefficients.Though most of the ideas and
problems carry
   over to the fitting of nonlinear models and generalized linear models
(particularly the fitting
   of logistic relationships), the complexity is greatly increased."
Frank E Harrell Jr
#
Wittner, Ben wrote:
Why are these procedures still being used?  The performance is known to 
be bad in almost every sense (see r-help archives).

Frank Harrell

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      dr mike
    

    

      
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The LASSO method and the Least Angle Regression method are two such that
have both been implemented (efficiently IMHO - only one least squares for
all levels of shrinkage IIRC) in the lars package for R of Hastie and Efron.
There is a paper by Madigan and Ridgeway that discusses the use of the Least
Angle Regresson approach in the context of logistic regression - available
for download from Madigan's space at Ruttgers: 
www.stat.rutgers.edu/~madigan/PAPERS/lars3.pdf 

HTH

Mike

  
  


  


      

    

    

      
      

        


  

        

      Frank E Harrell Jr
    

    

      
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dr mike wrote:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        
Yes things like lasso can help a lot.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Bert Gunter
    

    

      
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To clarify Frank's remark ...

A prominent theme in statistical research over at least the last 25 years
(with roots that go back 50 or more, probably) has been the superiority of
"shrinkage" methods over variable selection. I also find it distressing that
these ideas have apparently not penetrated much (at all?) into the wider
scientific community (but I suppose I shouldn't be surprised -- most
scientists still do one factor at a time experiments 80 years after Fisher).
Specific incarnations can be found in anything Bayesian, mixed effects
models for repeated measures, ridge regression, and the R packages lars and
lasso, among others.

I would speculate that aside from the usual statistics/science cultural
issues, part of the reason for this is that the estimators don't generally
come with neat, classical inference procedures: like it or not, many
scientists have been conditioned by their Stat 101 courses to expect P
values, so in some sense, we are hoisted by our own petard.

Just my $.02 -- contrary(and more knowledgeable) opinions welcome.

-- Bert Gunter

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Christian Hennig
    

    

      
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Perhaps I should not write it because I will discredit myself with this
but...

Suppose I have a setup with 100 variables and some 1000 cases and I want to
boil down the number of variables to a maximum of 10 for practical reasons
even if I lose 10% prediction quality by this (for example because it is
expensive to measure all variables on new cases).  

Is it really so wrong to use a stepwise method?
Let's say I divide the sample into three parts and do variable selction on
the first part, estimation on the second and test on the third part (this
solves almost all problems Frank is talking about on p. 56/57 in his
excellent book). Is there always a tractable alternative? 

Of course it is wrong to interpret the selected variables as "the true
influences" and all others as "unrelated", but if I don't do that?

If it should really be a taboo to do stepwise variable selection, why are p.
58/59 of "Regression Modeling Strategies" devoted to "how to do it of you
must"?

Please forget my name;-)

Christian

        
On Wed, 2 Mar 2005, Berton Gunter wrote:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        
***********************************************************************
Christian Hennig
Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/

            

      
      
      
    

        
#######################################################################
ich empfehle www.boag-online.de

  
  


  


      

    

    

      
      

        


  

        

      Frank E Harrell Jr
    

    

      
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Christian Hennig wrote:

            

      
      
      
    

        
Yes.  Read about model uncertainty and bias in models developed using 
stepwise methods.  One exception: if there is a large number of 
variables with truly zero regression coefficients, and the rest are not 
very weak, stepwise can sort things out fairly well.  But you never know 
this in advance.

            

      
      
      
    

        
That's a good way to find out how bad the method is, not to fix the 
problems inherent in it.

            

      
      
      
    

        
Stress on "if".  And note that if you ask what is the optimum alpha for 
variables to be kept in the model when doing backwards stepdown, it's 
alpha=1.0.  A good compromise is alpha=0.5.  See

@Article{ste01pro,
   author = 		 {Steyerberg, Ewout W. and Eijkemans, Marinus
   J. C. and Harrell, Frank E. and Habbema, J. Dik F.},
   title = 		 {Prognostic modeling with logistic regression
   analysis: {In} search of a sensible strategy in small data sets},
   journal = 	 Medical Decision Making,
   year = 		 2001,
   volume =		 21,
   pages =		 {45-56},
   annote =		 {shrinkage; variable selection; dichotomization of
   continuous varibles; sign of regression coefficient; calibration; 
validation}
}

And on Bert's excellent question about why shrinkage is not used more 
often, here is our attempt at a remedy:

@Article{moo04pen,
   author = 		 {Moons, K. G. M. and Donders, A. Rogier T. and
Steyerberg, E. W. and Harrell, F. E.},
   title = 		 {Penalized maximum likelihood estimation to directly
adjust diagnostic and prognostic prediction models for overoptimism: a
clinical example},
   journal = 	 J Clinical Epidemiology,
   year = 		 2004,
   volume =		 57,
   pages =		 {1262-1270},
   annote =		 {prediction 
research;overoptimism;overfitting;penalization;bootstrapping;shrinkage}
}

Frank