Hi Ray,

It looks like Steven provided some good references for DIC. I'm not a  
statistician, so am not as familiar with this subject as others, but I  
have not found a completely satisfactory solution. For those of us  
coming from a maximum likelihood background with a good foundation in  
AIC, the Bayesian framework requires a bit of a shift in philosophy  
and methods. In a non-Bayesian analysis, parameters are thought of as  
fixed at their true but unknown value. Often in a Bayesian framework,  
each parameter is consider random with an associated distribution.  
Therefore, in a Bayesian GLMM-like analysis it is common to select a  
set of predictor variables for inclusion in the model. Then all  
parameters are estimated (posterior probabilities). Based on knowledge  
of the system, all variables included in the model are assumed to be  
potentially important and have real effects even if the posterior  
estimates suggest effectively zero effect (95% credibility intervals  
overlap 0). Therefore, no model selection is done balancing fit and  
complexity. Future researchers may choose to not include those  
variables that were essentially 0 from your analysis.

I hope that makes sense and that my poor vocabulary specific to the  
field didn't detract from the idea. This is not to say that DIC cannot  
be used, I just thought I would point out the potentially different  
philosophical approaches. Someone on the list more familiar with this  
might correct errors I made, elaborate, or provide counter arguments.

Best of luck with whichever approach you take,
Dan
------------------------------------------------------------------------------------
Daniel J. Hocking
114 James  Hall
Department of Natural Resources & the Environment
University of New Hampshire
Durham, NH 03824

dhocking@unh.edu
http://sites.google.com/site/danieljhocking/
http://quantitativeecology.blogspot.com/
http://richnessoflife.blogspot.com/

"All truths are easy once they are discovered; the point is to  
discover them." - Galileo Galilei
-------------------------------------------------------------------------------------



On Apr 1, 2012, at 1:30 PM, <r-sig-mixed-models-request@r-project.org>  
<r-sig-mixed-models-request@r-project.org> wrote:

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> -----Original Message-----
> From: Ray Danner [mailto:danner.ray@gmail.com]
> Sent: Saturday, March 31, 2012 2:24 PM
> To: r-sig-mixed-models@r-project.org
> Subject: [R-sig-ME] MCMC model selection reference
>
> Dear list,
>
> I'm looking for guidance on model selection using DIC values.  I'm
> particularly interested in comparing mixed models created with the
> package MCMCglmm.  I currently use AIC for my models built with lme
> and (g)lmer and like the ability to calculate evidence ratios and
> model average predictions, which are very easy for readers to
> conceptualize.  AICcmodavg is great for these things.
>
> Can anyone recommend a resource that describes the appropriate use of
> DIC for model selection (and its limitations)?  I'm mainly an
> ecologist, so a less-technical treatment would be ideal.
>
> My main questions are:
> 1. Can DIC be used to select among mixed models?
> Kery and Schaub (2012 p. 42) raise concerns about counting the correct
> number of parameters and state that WinBUGS does not calculate them
> appropriately, though Millar (2009) provides a method that is
> appropriate for hierarchical models.  On the other hand, Saveliev et
> al. (2009) use DIC to compare models with random effects built with
> the BRugs package.  Hadfield's MCMCglmm Tutorial says that lower DIC
> is better, but doesn't give details about use.
>
> 2. Any rules of thumb on what constitutes sufficiently large deltaDIC
> values?  Are evidence ratios acceptable?
>
> 3. Can DIC be used to calculate model average predictions?
>
> Thanks in advance and please forgive me if I missed your publication.
> Ray
>
>
> Refs
> Kery and Schaub. 2012. Bayesian Population Analysis Using WinBUGS: A
> Hierarchical Perspective.
> Millar. 2009. Comparison of hierarchical Bayesian models for
> overdispersed count data using DIC and Bayes' Factors. Biometrics
> 65:962-969.
> Saveliev et al. 2009. Ch. 23 in Zuur, Mixed Effects Models and
> Extensions in Ecology with R.
>
>
>
>


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