Date: Thu, 24 Jun 2004 09:27:03 -0700
Reply-To: Dale McLerran <stringplayer_2@YAHOO.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <stringplayer_2@YAHOO.COM>
Subject: Re: Poisson: adding variation
Content-Type: text/plain; charset=us-ascii
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.
> >>> Jeffrey Stratford <stratja@AUBURN.EDU> 6/23/2004 1:16:21 PM >>>
> 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
> distribution to the data. The variation of predicted densities from
> 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.
> Jeff Stratford
> 331 Funchess Hall
> Department of Biological Sciences
> Auburn University
> Auburn, AL 36849
> FAX 334-844-9234
Fred Hutchinson Cancer Research Center
Ph: (206) 667-2926
Fax: (206) 667-5977
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