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# Re: st: Poisson and Negbin models

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Poisson and Negbin models Date Mon, 29 Oct 2012 10:17:08 +0100

```> The first indication is it that Y is overdispersed as the mean and the variance is not equal, nor close being equal (mean 4.347222 < var 542.6806). A formal Goodness-of-fit test of Y alone, using estat gof- after -poisson \$y-, indicates Y is significantly different from a Poisson distribution (chi2 = 1726.882, Prob > chi2(71) = 0.0000). Similarly the LR test of alpha related to the output from -nbreg \$y- indicates that the negbin model is preferred over the Poisson (LR=0:  chibar2(01) = 1570.16 Prob>=chibar2 = 0.000).

Those are not appropriate tests as you would not expect the marginal
distribution of y to Poisson or negative binomially distribution,
otherwise you would not have added the explanatory variables later
on... See e.g. <http://www.maartenbuis.nl/presentations/berlin12.html>

> When I run the model Y=X1 X2…Xn, using the -nbreg- command, I end up with some problems. The model outcome indicates some problem with the alpha, and a LR test indicating that the Poission is preferred over the negbin model:
<snip>
> -------------+----------------------------------------------------------------
>     /lnalpha |  -18.90698   558.4214       113.393    1075.579
> -------------+----------------------------------------------------------------
>        alpha |   6.15e-09   3.43e-06                             0           .
> ------------------------------------------------------------------------------
> I would appreciate if someone could explain what seems to be the problem(s) here, and some indication on the problem related to the alpha in the negbin model.

A Poisson model is a negative binomial model with an alpha of 0. In
your case the alpha is 0.000000000615 (if I counted the 0s correctly).
So to all intends and purposes you estimated a Poisson model with
-nbreg-.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

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

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