```Date: Thu, 24 Jun 2004 09:27:03 -0700 Reply-To: Dale McLerran Sender: "SAS(r) Discussion" From: Dale McLerran Subject: Re: Poisson: adding variation Comments: To: Jeffrey Stratford In-Reply-To: Content-Type: text/plain; charset=us-ascii Jeffrey, Extra dispersion can be added to your model in a number of ways. Peter Flom and David Cassell have both mentioned zero-inflation distributions (zero-inflated Poisson and negative binomial). These would, presumably, be good candidate models. Extra dispersion can also be obtained employing a model in which each observation is drawn from a Poisson distribution, but each observation has its own expectation. Now, such a model needs some sort of additional structure in order to be of any value. If we impose the condition that the expectations are drawn from a gamma distribution, then we obtain the negative binomial distribution. So, there are three candidate models to consider: 1) a negative binomial distribution (gamma mixture of Poisson responses), 2) a zero-inflated Poisson (mixture of Poisson responses and a set of observations which have zero value following some other process), and 3) a zero-inflated negative binomial distribution (mixture of gamma mixture of Poissons with a set of observations having zero value following some other process). The GENMOD procedure will fit the negative binomial distribution. I have written on SAS-L about fitting zero-inflated Poisson and zero- inflated negative binomial models. From the presentation of your problem, I would think that all of these models would perform better than a simple Poisson. There is one other point to consider. This is that you may have left some important variables out of your model. Presumably, you have already considered the variables which should be important, and you are still left with more dispersion than would be expected. But it is always worth repeating that lack of fit may be due to some important variables which have been left out of the model. Dale > >>> Jeffrey Stratford 6/23/2004 1:16:21 PM >>> > SAS-users, > > I'm modeling the number of birds seen per site. I have estimated > densities (from the program DISTANCE) and I would like to fit a > Poisson > distribution to the data. The variation of predicted densities from > my > top model, however, is much smaller than the estimated (observed) > densities. The problem might be that the data are "zero heavy" with > most sites having no birds but the range is from 0 - 15 birds (per > hectare). Is there a way to force extra variation into the predicted > range based on the covariates? I'm familiar with adding dscale and > pscale statements but these don't "stretch" the data out enough. > > Thanks, > > Jeff > > > > **************************************** > Jeff Stratford > 331 Funchess Hall > Department of Biological Sciences > Auburn University > Auburn, AL 36849 > FAX 334-844-9234 > http://www.auburn.edu/~stratja > **************************************** > ===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@fhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- __________________________________ Do you Yahoo!? New and Improved Yahoo! Mail - Send 10MB messages! http://promotions.yahoo.com/new_mail ```

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