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Re: st: Model for Poisson-shaped distribution but with non-count data


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Model for Poisson-shaped distribution but with non-count data
Date   Tue, 6 Dec 2011 07:33:37 -0500

In a quick look at the blog that Nick mentioned, I did not see any
mention of the fact that the Poisson distribution is discrete.  In the
limit (as the mean of the distribution becomes large), that matters
less, but one would need to view the possible data values as discrete.

Some of the equations in the blog are not quite correct.  For example,
since Poisson regression is a form of generalized linear model, the
linear predictor is fitted to log(E(y)), rather than to log(y).  The
random component of the GLM is a Poisson distribution.

David Hoaglin

On Tue, Dec 6, 2011 at 4:00 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> -gammafit- (SSC) has been available for some years, but random
> intercepts are fancier than it does.
>
> However, I am more concerned with two dogmas surfacing here without
> little or no foundation, that
>
> 1. Poisson models are for counts only
>
> 2. You choose models based on the marginal distribution of the
> response or outcome variable.
>
> See http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/
> for an excellent exposition that makes no such assumption on Poisson.
> On the evidence here I would still try out -poisson- or a related
> command.
>
> I don't know where #2 comes from.  Every decent modelling text
> explains that assumptions are about conditional distributions, and not
> that important even then.
>
> Nick

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