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multivariate MCMCglmm

2 messages · Ingleby, Fiona, Jarrod Hadfield

Ingleby, Fiona
# 
Dear All,

A beginner's question, I'm afraid. I'm trying to fit a multivariate mixed model using the MCMCglmm function. I have a 22-dimensional response variable which is reduced to 3 dimensions after carrying out a suitable principal components analysis. I fitted the following prior:

prior<-list(R=list(V=diag(3)/2,nu=0.05),G=list(G1=list(V=diag(3)/2,nu=0.05)))

for the model:

model<-MCMCglmm(cbind(pc1,pc2,pc3)~X*Y+Z,random=~us(trait):X,rcov=~us(trait):units,prior=prior,family=c("gaussian","gaussian","gaussian"),data=data,nitt=18000,burnin=3000,verbose=F)

The model ran with no problems and I was happy that I understood the results.

However, I was recently advised that by carrying out my analysis using 3 PCs which explain ~75% of the variation, I could have lost some important variation and should therefore try the model with all 22 original response variables. So I fitted the same model, but with a 22-dimensional response, and also adjusted the 'family' command to suit my response matrix. Then I adjusted the prior as follows:

prior<-list(R=list(V=diag(22)/2,nu=0.05),G=list(G1=list(V=diag(22)/2,nu=0.05)))

and I get an error message saying I have an 'ill-conditioned G/R structure'. 

My question is two-fold: firstly, can anyone offer guidance as to where I'm going wrong with the 22-dimensional dataset analysis; and secondly, if (as I fear) the reason my second model isn't working is because I have fundamentally misunderstood some aspect of prior distribution specification for multivariate models in general, then is my prior for the first model actually a suitable one?

I would greatly appreciate any guidance offered, and apologies if I have missed something really obvious, I'm new to this type of analysis.

Many thanks,

Fiona
1 day later
Jarrod Hadfield
# 
Hi,

For a 22-dimensional response you have 506 (co)variance parameters to  
estimate for the random effects and the residuals. You would need a  
massive data-set replicated at the right level to get precise  
estimates. The prior is improper (it would need to have nu>21 to be  
proper) so the posterior covariance matrix is able to become singular.  
The probability of a singularity becomes very high when the  
dimensionality of the covariance matrix is large and/or there is  
little information in the data (see Hill & Thompson 1974 Biometrics).  
Personally, I would try and focus on a lower-dimensional aspect of the  
data as you had done initially, or try reduced-rank analyses as  
implemented in programs such as WOMBAT and ASReml

Cheers,

Jarrod





Quoting "Ingleby, Fiona" <fci201 at exeter.ac.uk> on Fri, 3 Jun 2011  
19:58:26 +0100: