[R-sig-ME] MCMCglmm: uninformative priors for covariance matrices

[Stott, Iain]

Hi all,

I'm having some trouble specifying priors for a couple of phylogenetic MCMCglmm models, and hoping someone can help!  I posted something similar a while back on the general list, but have progressed since (and think this list is perhaps a better place to be posting to).

I'm trying to run 2 similar MCMCglmm models, both with 2 (correlated) response variables, a single 5-level factorial explanatory, and a phylogeny structuring the error (but no random effects).  For both models, each data point represents a mean response per species.  The first model has response variables of logit-transformed proportion data (range of -3.5 to +10).  The data contains a large number of proportions close to 1, which I think may be complicating things.  The second model has response variables of log-transformed data (range of -3 to 5).  This has quite a positive skew, which I also think may be a causing problems.

Here's my code:
prior<-list(R = list(V = diag(2)*a, n=b),
            G = list(G1=list(V = diag(2)*a, n=b)))

model<-MCMCglmm(cbind(y1,y2) ~ trait:x - 1, 
                random=~us(trait):animal, rcov=~us(trait):units, family=c("gaussian","gaussian"),
                prior=prior, data=data, pedigree=tree, nodes="TIPS",
                thin=100, nitt=150000, burnin=30000, verbose=F)

I've used us(trait) in errors and residuals to deal with the correlated responses.  I'm using default uninformative priors for fixed effects, but I'm having issues choosing priors for errors and residuals: I want to keep these as uninformative as possible, and have been playing around with different parameters by varying a and b in the code above.

The MCMCglmm course notes suggest an uninformative improper prior of V=diag(2)*0, n=-1, but my models won't run with improper priors (I assume due to reducibility).  An alternative of V=diag(2)*0.02, n=3 is suggested.  This runs, but doesn't converge well.  Posterior marginals for animal:trait are very positively skewed (and sometimes bimodal for proportion models), and there is high autocorrelation in chains (which is not remedied by increasing iterations/burnin and/or thinning interval).  Both problems are more marked for proportion models.  The only way I can get normal posteriors is by increasing either the diagonals of V (but this affects variance estimates significantly, and I can't see any obvious justification), or by increasing nu (but again, I can't see any justification). (Note that this doesn't apply to fixed solutions or trait:units, which are much better behaved).

Has anyone got any suggestions for appropriate priors that are as uninformative as possible?  And, am I doing things correctly?  (I'm completely new to MCMCglmm and Bayesian stats as of 2 weeks ago, so please forgive any misinterpretations!)


Thanks,

Iain



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Iain Stott
Centre for Ecology and Conservation
University of Exeter, Cornwall Campus
Tremough
Treliever Road
Penryn
Cornwall
TR10 9EZ
Tel: 01326 371852
http://biosciences.exeter.ac.uk/cec/staff/postgradresearch/iainstott/
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