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Re: st: parametric vs. nonparametric estimators


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: parametric vs. nonparametric estimators
Date   Wed, 16 Jun 2004 19:23:56 +0100

At 18:52 16/06/2004, Thomas wrote:
Dear Nick and Rich,

maybe I miss something, but my problem is as follows:

suppose I have a data set with 100 objects and two binary variables, X
(sex=male (coded 1) or female (coded 0)) and Y (disease=absent (coded 0) or
present (coded 1)) for example. My goal is to estimate the probability
P(Y=1|X=1). Suppose 50 of the 100 persons are male and of this 10 have a
disease, then my so called "nonparametric" estimate of P(Y=1|X=1) is
10/50=0.200. By nonparametric I mean, that no assumption about the
distribution of Y is made. By using logistic regression, I assume that Y can
be related to a latent variable Y* which has a logistic distribution. Now,
for example, the logistic regression estimate of P(Y=1|X=1) is 0.201. What
does the difference between 0.200 and 0.201 tell me?
Probably not a great deal. A difference of half a percent in fitted value could easily be due to imperfect numerical precision during an iterative fit, which your "parametric" estimate uses and your "nonparametric" model doesn't.

Roger


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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