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


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Model for Poisson-shaped distribution but with non-count data
Date   Tue, 6 Dec 2011 09:32:14 -0500

I wonder if Owen's data are showing both severe skewness and multimodality (I believe he mentioned observing that conditionally). In that case it might be worthwhile to consider a mixture of gammas... not sure if that can be done in Stata:

Wiper, M., Insua, D.R., & Ruggeri, F. (2001). Mixtures of Gamma Distributions with Applications. Journal of Computational and Graphical Statistics, 10(3), 440-454. 

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