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st: RE: AIC and BIC in Poisson and GLM


From   "Visintainer, Paul" <Paul.Visintainer@baystatehealth.org>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: AIC and BIC in Poisson and GLM
Date   Mon, 25 Apr 2011 14:40:54 -0400

Peter,

If you compute AIC and BIC using -estat ic- after each model, I think they will be the same.  In the -glm- output, the AIC and BIC are given in blue. If you click on them, it describes the differences between the output estimate and the -estat ic- estimate.

-Paul

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Lachenbruch, Peter
Sent: Monday, April 25, 2011 12:21 PM
To: 'statalist@hsphsun2.harvard.edu'
Subject: st: AIC and BIC in Poisson and GLM

I was developing a simple class example for poisson regression using the poisson command and the glm command.  The log likelihood was the same in both regressions; the coefficients were the same.  When I looked at the AIC and BIC reported by glm I got 

                                                   AIC             =  7.920031
Log likelihood   = -33.60015344                    BIC             =  2.922026
For the estat command with poisson I got
. estat ic

-----------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
        full |     10   -495.0676   -33.60015      6     79.20031    81.01582
-----------------------------------------------------------------------------
               Note:  N=Obs used in calculating BIC; see [R] BIC note

I would expect these to be the same, but they ain't.  I suspect there may be a normalizing constant lurking around here somewhere.  
I don't want to fix this unless it's truly a bug; but I would like to be able to explain this to my students.

Tony

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



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