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st: RE: Negative Binomial: Exposure vs. Offset


From   "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Negative Binomial: Exposure vs. Offset
Date   Tue, 4 May 2010 09:39:43 -0700

There basically is no difference.  For exposure, you generally don't need to do anything. For offset, you usually take the log.  This comes from modeling a Poisson regression in which you have a model
Expectation=log(mu/exposure)=log(mu)-log(exposure)=X*beta
Transposing you get log(mu)=log(exposure)+X*beta

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Downey, Patrick
Sent: Tuesday, May 04, 2010 9:35 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Negative Binomial: Exposure vs. Offset

Hello,

I'm using a negative binomial regression through the nbreg command in Stata
to estimate crimes committed by a certain population. Different
observations were "on the street" different lengths of time, so I want to
account for that.

I'm confused about the difference between the exposure option and the
offset option. They appear to be doing the same thing. In the online
documentation, it says:

    offset(varname) specifies that varname be included in the model with
the
        coefficient constrained to be 1.

    exposure(varname) specifies a variable that reflects the amount of
        exposure over which the depvar events were observed for each
        observation; ln(varname) with coefficient constrained to be 1 is
        entered into the log-link function.

Could someone please explain the difference between the two or send some
documentation which formalizes the difference mathematically.

Thanks,
Mitch

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