Re: [R] overdispersion + GAM

From: Gavin Simpson <gavin.simpson_at_ucl.ac.uk>
Date: Tue, 12 Feb 2008 01:19:31 +0000

On Mon, 2008-02-11 at 14:46 -0500, Ravi Varadhan wrote:
> No. Binomial data can indeed be overdispersed. See McCullagh & Nelder
> (1989, section 4.5). Accounting for over(under)dispersion in binomial and
> Poisson distributions is, in fact, one of the original impetus for GEE type
> developments. See also a nice paper by Liang & McCullagh (Biometrics 1993,
> p. 623-630), which discusses numerous examples of overdispersion in binary
> data.
>
> Ravi.

Hi Ravi,

I was very careful to say "Bernoulli" rather than "binomial". I understand that overdispersion can be present in Poisson or binomial (M>1), hence the need for a quasibinomial family function. I was, however, always led to believe that overdispersion in binary data was not possible, and that was how I interpreted the OP's statement about presence/absence data.

This appears to have been discussed recently on the R-help list:

http://finzi.psych.upenn.edu/R/Rhelp02a/archive/91242.html is a reply to a posting by Peter Dalgaard (in response to an original question on R-help - apologies, I can't seem to get to the email archives on tolstoy to find the start of the thread).

My response was in the same vein as Peter's ">> There is no such thing as overdispersion for binary data." (quoted from his response to the OP). To be fair (for those not going to look at the thread), Peter then follows this up later in the thread saying (in reply to John Maindonald's posting) "I don't really disagree, of course. I was mainly being provocative."

The two messages from Peter and John in that thread are very interesting; I'm not sure I fully understand what they are going on about, but I get the gist.

And of course, I would be more than happy to be corrected and pointed in the direction of something not too technical (I'm an ecologist, not a statistician or mathematician) that discusses this. To that end, I'll be hunting out McCullagh & Nelder and the Biometrics paper you cite, Ravi, but if you or anyone can point to other literature, I'd be most grateful.

All the best,

G

>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan_at_jhmi.edu
>
> Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On
> Behalf Of Gavin Simpson
> Sent: Monday, February 11, 2008 12:37 PM
> To: anna banana
> Cc: r-help_at_r-project.org
> Subject: Re: [R] overdispersion + GAM
>
> On Mon, 2008-02-11 at 07:35 -0800, anna banana wrote:
> > Hi,
> >
> > there are a lot of messages dealing with overdispersion, but I couldn't
> find
> > anything about how to test for overdispersion. I applied a GAM with
> binomial
> > distribution on my presence/absence data, and would like to check for
> > overdispersion. Does anyone know the command?
>
> Bernoulli data (presence/absence of single species say) can't be
> overdispersed, so there is no need to test or correct for it.
>
> G
>
> >
> > Many thanks,
> >
> > Anna

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