multiple comparisons with MCMCglmm?

If you are using the MCMC results to make comparisons in 
the same manner as for frequentist results, then the sampling 
properties are entirely comparable.  If you want to move from
comparison-wise 5% CIs to overall 5% CIs, then some kind of 
multiple range correction might in principle be used.  But this
usually not the way to go; MCMC gives you sampling statistics
from which you can fairly directly extract overall 5% CIs.  You 
can directly extract the sampling distribution for, e.g., the Tukey 
HSD, if that is what you want.

(If you are in a Bayesian mindset, you might think of the frequentist 
analysis as derived using an unstated Bayesian prior -- typically 
there is a prior that will give you the frequentist results.)

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

Hello,

Is correction for multiple comparisons ever necessary with MCMCglmm, or with any other method deriving the credible intervals from MCMC sampling?

My gut feeling is no, since we are deriving credible intervals for all the effects (or their combinations, if anyone is interested in pairwise comparisons a'la Tukey) jointly from the results of the same MCMC chain. I am, however, not sure at all whether this logic makes any sense.

The only [hopeful] bit that I managed to find on the web is the paper by Gelman et al 2012 ( http://www.stat.columbia.edu/~gelman/research/published/multiple2f.pdf ), but it is really more about multilevel (i.e., mixed) models rather than MCMC-based methods.

I would greatly appreciate any advice.

cheers

Mikhail Matz, University of Texas at Austin

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