```Date: Wed, 30 Nov 2011 15:14:31 -0500 Reply-To: Andrew Cox Sender: "SAS(r) Discussion" From: Andrew Cox 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 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 >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" > > > >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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