# st: RE: RE: Count data regression

 From "Rajesh Tharyan" To Subject st: RE: RE: Count data regression Date Thu, 23 Mar 2006 17:00:56 -0000

Hi scott,

2. For the Poisson MLE, valid inference requires equality of the conditional
mean and variance (equidispersion) - it does not require that the dependent
variable have a Poisson distribution.

I didn't get point two..  my impression was that it is the distribution of
the underlying variable which sort of dictated whether you used a poisson
regression or a nb regression..etc. but of course with a poission
distributed variable you always have mean=variance..

Thanks
rajesh

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Scott Merryman
Sent: 23 March 2006 16:09
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Count data regression

A few points:

1. If you take the log of the number of days then you have a non-count
dependent variable.  How would you interpret the estimated coefficients in a
Poisson or negative binomial model?

2. For the Poisson MLE, valid inference requires equality of the conditional
mean and variance (equidispersion) - it does not require that the dependent
variable have a Poisson distribution.

3. The Poisson is still consistent if the count data are over-dispersed
though the t-stats will tend to be inflated.  (See Cameron and Trivedi
"Regression analysis of count data" p 59-60)

4. -nbreg- provides a likelihood ratio test that alpha = 0.

Scott

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Hugh Colaco
> Sent: Thursday, March 23, 2006 9:12 AM
> To: statalist
> Subject: st: Count data regression
>
> My dependent variable is the number of days, a count variable which is
> censored from below at 2. The summary stats are below (see # 1). As
> you can see, the number of days ranges from 2 to 2426. Since the
> unconditional variance > mean, I assume that I should use a Neg
> binomial reg rather than a Poisson reg.
>
> However, if I take the log of the number of days, then the
> unconditional variance < mean (see # 2), so I could run a Poisson reg.
>
> Any thoughts on the above? Is there any issue if I first take the log
> and then run a poisson or neg binomial regression? Would it defeat the
> very purpose of the count regression? Anything else I need to
> consider?
>

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