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Re: st: Binomial regression


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Binomial regression
Date   Tue, 7 Aug 2007 10:34:39 +0100 (BST)

--- Garry Anderson <g.anderson@unimelb.edu.au> wrote:
> It is interesting that when the poisson regression is used with the
> auto data (see below under Roger Harbord wrote:)  and the
> -predict predn, n- command is used to predict the number of events,
> the predicted number of events for line 71 of the data is 1.789.
> Although the poisson regression can make predictions greater than
> one, does this imply that when using poisson regression to estimate
> relative risks that it should not be used  for estimating the
> probability of the event?
> 
> If so, how would the probability of an event be estimated?

Constant risk differences (identity link) imply that the effects the
explanatory variables on the probability can be represented by straight
lines. This is problematic because this implies that the predicted
probabilities will eventually become less than 0 and more than one.
This is just another way of saying that the risk difference cannot
remain constant. 

Constant risk ratios (log link) imply that the effects the explanatory
variables on the probability can be represented by log functions. This
is problematic because this implies that the predicted probabilities
will eventually become more than one. This is just another way of
saying that the risk ratio cannot remain constant.

In other words constant risk differences and constant risk ratios imply
a model that cannot be true. They may provide a reasonable describtion
of your data, but they can just as well fail to do even that. Good
signs for such failures would be if the model has difficulties
converging, or if it produces (lots of) predictions outside the
allowable range. 

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


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