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Re: st: Binomial regression


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Binomial regression
Date   Fri, 3 Aug 2007 15:10:52 -0400

Constantine et al. --
I think Constantine is not taking the point of Maarten, Bobby, Vince,
and Marcello, so my input is unlikely to sway him.  Nevertheless, here
goes: your model makes little sense when your predictions make no
sense--you cannot reasonably assume that there is a constant effect of
x on probabilities if predicted probabilities stray outside [0,1].
Hence, convergence failure indicates a failure of your assumptions
that the effect of x on probability is linear, as opposed to logistic
or some other g(xb) that stays in [0,1].  You can always back out a
mean marginal effect of x on predicted probability conditional on the
distribution of other explanatory variables, however, to get your
estimates in terms of risk differences.  Or run a linear probability
model, which avoids convergence issues, and damn the consequences.

Kit wrote: But the link function is not a CDF.
True--but I think Marcello has in mind that g(xb) must have the
properties of a CDF to produce predictions interpretable as
probabilities.  So a linear g=xb must be truncated to
g=min(max(xb,0),1) which looks like the CDF of a uniform X.

On 8/3/07, Marcello Pagano <pagano@hsph.harvard.edu> wrote:
> Anyway, if you have the risks you can, of course, calculate the
> differences of the risks.  The problem, as you point out, is how this
> risk difference is related to other covariates.
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