[R-sig-ME] MCMC model selection reference

[Steven J. Pierce]

Here are a couple references on DIC that I happen to have handy:

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A.
(2002). Bayesian measures of model complexity and fit. Journal of the Royal
Statistical Society: Series B (Statistical Methodology), 64(4), 583-639.
doi: 10.1111/1467-9868.00353  http://www.jstor.org/stable/3088806 

Barnett, A. G., Koper, N., Dobson, A. J., Schmiegelow, F., & Manseau, M.
(2010). Using information criteria to select the correct variance-covariance
structure for longitudinal data in ecology. Methods in Ecology and
Evolution, 1(1), 15-24. doi: 10.1111/j.2041-210X.2009.00009.x
http://dx.doi.org/10.1111/j.2041-210X.2009.00009.x 


Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Ray Danner [mailto:danner.ray at gmail.com] 
Sent: Saturday, March 31, 2012 2:24 PM
To: r-sig-mixed-models at 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.