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Date:   Wed, 30 Nov 2011 13:32:02 -0600
Reply-To:   Robin R High <rhigh@UNMC.EDU>
Sender:   "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:   Robin R High <rhigh@UNMC.EDU>
Subject:   Re: Underdispersion in Poisson/negative binomial regression (PROC GENMOD)
Comments:   To: Andrew Cox <wacox@MIZZOU.EDU>
In-Reply-To:   <>
Content-Type:   text/plain; charset="US-ASCII"

You could try a 0 truncated poisson [divide likelihood of poisson by 1-prob(y)=0] with NLMIXED:

proc nlmixed DATA=vt ; parms intrc -.1 _r -.5 _b -.5 _e -.5; eta = intrc + _r*x1 + _b*x2 + _e*x3; mean = exp(eta); loglike= y*LOG(mean) -mean - lgamma(y+1) - log(1 - EXP(-mean)); model y ~ general(loglike); run;

Could do the same for negative binomial, though If # of offspring not much larger than indicated, may not offer an improvement.

Robin High UNMC

From: Andrew Cox <wacox@MIZZOU.EDU> To: SAS-L@LISTSERV.UGA.EDU Date: 11/30/2011 10:22 AM Subject: Underdispersion in Poisson/negative binomial regression (PROC GENMOD) Sent by: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>

Hi, I am working on a project where we are assessing the number of offspring produced as a function of a number of covariates. We are only doing this for adults who produced >=1 young, as the question of failing to produce any young is distinct from how many young are produced per successful reproduction attempt. As such, a histogram of our data looks something like:

* * * * * * * * * * * * * * * * 1 2 3 4 5

That is the general shape, not a reflection of our actual sample size. Anyway, when I run the following code:

proc genmod data=test2; model numyoung=explanvariable / dist=poisson link=log; run;

I get very low deviance (0.2) and Pearson Chi-square (0.18) scores, which indicate either model misspecification or underdispersion. Frankly, I am not sure what I can do to address this. I have tried a negative binomial model with similar results. I see that you can adjust the scale parameter using either Scale=Pearson or Scale=deviance, which adjusts the calculated standard errors, but I am not statistically knowledgable enough to know whether this would adequately address my problem, and if so, why.

Any help is much appreciated.

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