Dear Hormuzd,
A few of quick thoughts:
1. If you spend a lot of effort in optimizing the knot locations, it becomes
difficult to get the correct confidence bands for the functional form.
Model
uncertainty adds to variance.
2. Durleman and Simon showed that if you fix the number of knots in a restricted
cubic spline (natural spline), allowing the knot locations to be estimated
via
maximum likelihood estimation results in very little improvement in the log
likelihood,
i.e., the shapes are not that sensitive to the locations. Shape is
sensitive to # knots.
3. AIC is a pretty good and quick method for determining # knots, given you fix
the knot locations for each # of knots (I use a set of default percentiles
for this).
But refer back to 1. The approach I've been taking lately is to use
subject
matter or rank correlation measures to decide how many d.f. to spend on
each
predictor, then to spend that. This results in confidence intervals with
the claimed
coverage probability.
-Frank Harrell
-----Original Message-----
From: Katki, Hormuzd (NCI) <katkih@mail.nih.gov>
To: 's-news' <s-news@wubios.wustl.edu>
Cc: Rosenberg, Philip (NCI) <rosenbep@epndce.nci.nih.gov>
Date: Wednesday, April 07, 1999 1:55 PM
Subject: [S] Logistic Regression Model Selection in S-Plus
>
>Dear S-Plus users,
>
>The issue is how to select the optimal # of knots for covariates represented as
>cubic splines in a logistic regression. The goal is to determine the
>relationship between probability of outcome and the covariates, rather than use
>the model to predict outcome of individual observations.
>
>1. What is the state-of-the-art method for this? We are thinking
>cross-validation, but posts on the S-news mailing list between Roy Pardee,
>Frank
>Harrell and Brian Ripley last year suggest to me that the bootstrap may be
>better:
>http://www.biostat.wustl.edu/hyperlists/s-news/199803/msg00135.html
>http://www.biostat.wustl.edu/hyperlists/s-news/199803/msg00140.html
>http://www.biostat.wustl.edu/hyperlists/s-news/199803/msg00156.html
>http://www.biostat.wustl.edu/hyperlists/s-news/199803/msg00163.html
>
>2. Are there any S-Plus functions that implement the state-of-the-art method?
>For example, I have experimented with Frank Harrell's libraries, but his
>concern
>is validating models for the purpose of prediction and it's not clear to me how
>I can use his libraries to select the optimal # of knots (if it is clear,
>please
>inform me).
>
>Any help is greatly appreciated! Thank you for your time,
>
>Hormuzd Katki
>Biostatistics Branch, Division of Cancer Epidemiology and Genetics
>National Cancer Institute
>6120 Executive Blvd. Room 8044 MSC 7244
>Bethesda MD 20892-7244
>301-594-7818 (voice)
>301-402-0081 (fax)
>katkih@mail.nih.gov
>
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