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# Re: st: ZIP with Sample Selection

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: ZIP with Sample Selection Date Wed, 1 Dec 2010 08:46:52 +0000 (GMT)

--- On Wed, 1/12/10, James McJoseph wrote:
> 2. Is it appropriate to apply a count model to a data where
> the only count present in the data are: 0, 1, 2.  Counts above
> 2 are possible but very extremely rare. Another consideration, the
> occurance of counts are not equally probable. 0 is more probable
> than 1. 1 is more probable than 2, Hence 3 and above are much less
> probably to even unlikely.

Sounds consistent with a Poisson distribution with a extrememly low
mean. One problem I can imagine is that in your subject line you
refer to a zero inflated poisson. A regular Poisson with such an
extremely low mean will have a huge amount of zeros. I can imagine
that Stata will have trouble distinguishing between a zero inflated
Poisson distribution and such an extreme Poisson. Add a selection
equation to that, and I doubt whether you'll ever get convergence.
Think of it this way: what we do when we do a statistical analysis
is to compare people (or whatever your unit of analysis may be). If
everybody where the same, such a comparsion would be very boring.
In other words it is the differences between people that contains
the information we use in our analysis. If you have such an extreme
Poisson distribution, then your variance is likely to be very low,
which means there is very little information present in your data.
A consequence of that is that even if the dataset is large, you can
still only estimate relatively simple models and certainly not a ZIP
with sample selection, as both the ZIP part and the sample selection
part require lots of information on their own, let alone in
combination.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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