
> Date: Thu, 26 Jan 2012 13:16:12 -0600
> From: Shawn McCracken <smccracken@tadpoleorg.org>
> To: r-sig-mixed-models@r-project.org
> Subject: [R-sig-ME] GLMM distribution family model comparison using
> 	Poisson w/observation level random effect
> Message-ID:
> 	<CAE+9gVGEtv6coOG1Un=pWVKWyd2s=cZQGZv3SeCgMvvENVjbWA@mail.gmail.com>
> Content-Type: text/plain
> 
> Dear R mixed model users,
> 
> I have been using package glmmADMB to run a full model and then reduced
> model versions with the following distribution families: poisson,
> zero-inflated poisson, poisson w/observation level random effect, negative
> binomial, zero-inflated negative binomial, negative binomial type 1, and
> zero-inflated negative binomial type 1. The models using poisson
> w/observation level random effect give the best fit according to AIC values
> but I am wondering if this is a fair comparison since it has an additional
> random variable (observation)?

Since no one has responded yet, I'll take a stab at this. 

You are correct that it's not quite fair, but it's not straightforward. I'm guessing that negative binomial is the 2nd runner up because it also is based on a Poisson distribution with a mean that comes from a right skewed distribution (Gamma distribution). The difference is that by including an observation level random effect, you have somewhere between 1 and nobs-1 parameters. I believe this gives more flexibility than the 1 extra parameter of the negative binomial model and ideally the model would be penalized for this, but estimating degrees of freedom in mixed models is not straightforward (see Box 3 of Bolker et al 2009 doi:10.1016/j.tree.2008.10.008). By running a glmmadmb example I see that the df only counts 1 parameter for the random effect (it's standard deviation). Approximations of df are controversial.

Mollie
> 
> Thanks,
> 
> Shawn
> 
> 
> -- 
> 
> 
> Shawn F. McCracken
> Ph.D. Candidate - Aquatic Resources
> Department of Biology
> Texas State University
> 601 University Drive
> San Marcos, Texas 78666
> 
> smccracken@txstate.edu
> http://uweb.txstate.edu/~sm1216/
> 
Mollie Brooks
Ph.D. Candidate
NSF IGERT Fellow
Biology Department
University of Florida
mbrooks@ufl.edu
http://people.biology.ufl.edu/mbrooks



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