Date:         Wed, 30 Nov 2011 15:14:31 -0500
Reply-To:     Andrew Cox <wacox@MIZZOU.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Andrew Cox <wacox@MIZZOU.EDU>
Subject:      Re: Underdispersion in Poisson/negative binomial regression (PROC
              GENMOD)

Many thanks to the three people who replied with a suggestion similar to Robin's. SAS actually
offers advice on truncated Poisson and negative binomial distributions at the link below.  I am not
quite sure how to determine whether I have adequate fit, however, as NL mixed output does not
include goodness of fit criteria (deviance, chi-square).


http://support.sas.com/kb/43/522.html



On Wed, 30 Nov 2011 13:32:02 -0600, Robin R High <rhigh@UNMC.EDU> wrote:

>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.