subset selection for logistic regression
Christian Hennig wrote:
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?
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.
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?
That's a good way to find out how bad the method is, not to fix the problems inherent in it.
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"?
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
Please forget my name;-) Christian On Wed, 2 Mar 2005, Berton Gunter wrote:
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
-----Original Message----- From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Frank E Harrell Jr Sent: Wednesday, March 02, 2005 5:13 AM To: Wittner, Ben Cc: r-help at lists.R-project.org Subject: Re: [R] subset selection for logistic regression Wittner, Ben wrote:
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
Why are these procedures still being used? The performance is known to be bad in almost every sense (see r-help archives). Frank Harrell
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 Professor and Chair School of Medicine
Department of Biostatistics
Vanderbilt University
______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
*********************************************************************** Christian Hennig Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
From 1 April 2005: Department of Statistical Science, UCL, London
####################################################################### ich empfehle www.boag-online.de
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University