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.
