Bivariate animal models with both "ill-conditioned G/R structure" and "Mixed model equations singular" errors

Dear all,

I am using MCMCglmm function to construct bivariate animal models of  
bustard sperm production according to age-classes.

The problem is that the models can stochastically crash before the  
end of the run  (at 2000 iterations or 120000 or other) or can  
finish. For the model which does not finish, R returns different  
errors as:
-Mixed model equations singular: use a (stronger) prior
-ill-conditioned G/R structure: use proper priors if you haven't or  
rescale data if you have

For the models which reach the end, the estimations of genetic  
additive variance appear quite good (nice bell shaped posterior  
disctribution).

The problem still remains when I remove the animal term.
When I run univariate models, it works fine and the posteriors  
distributions look very good.

Strangely, the more data I have, the more models crash (the largest  
amount of data I have is 65000 data for 2400 individuals for one  
model).

The model looks like:

priorExp<-list(G=list(G1=list(V=diag(2), nu=2,  
alpha.mu=rep(0,2),alpha.V=diag(2)*100000),
G2=list(V=diag(2), nu=2, alpha.mu=rep(0,2),alpha.V=diag(2)*100000),
G3=list(V=diag(2), nu=2, alpha.mu=rep(0,2),alpha.V=diag(2)*100000)),
R=list(V=diag(2), nu=2))

spz<-MCMCglmm(cbind(age1_2,age5_6)~trait-1 + trait:tse+  
trait:I(tse^2)+ trait:joe + trait:I(joe^2),
   random=~us(trait):animal+us(trait):ID+us(trait):annee ,
   rcov=~us(trait):units,nitt=150000, thin=1000, burnin=100000,  
prior=priorExp, verbose=TRUE, pedigree=ped,
   family=c("gaussian","gaussian"), data=dat)

For the fixed effects : I use 4 continuous parameters as correction  
for each trait
For the random effects: I use, individuals, years and animal parameters

I have also tried more informative prior (as described in WAMWIKI)  
but the problem was the same.


To give you an example :

Because of computing limitation, I use multi-chain process. I run  
several times the same model (as above) and concatenate results  
(same prior,same burning, same thin and random seed) to obtain at  
least 1000 estimates (50 estimates by model). In this context, I ran  
50 bivariable models with the age-class age1_2 and the age-class  
age5_6 but only 9 models of the 50 models reached the end.

When we look fixed parameters estimates (estimate are binded for the  
nine models : http://ubuntuone.com/3Gi8GwjcRk3P01MxJp2qLe ), we can  
see that the estimates are really close to 0. Could it be the problem?
When we look ramdom parameters estimates (estimate are binded for  
the nine models : http://ubuntuone.com/42oaP9euG1m2LNipMawcHX ), the  
residual estimates do not look very good. Could it be the problem?

Last thing, if I try to add a cubic effect, all the models crash  
(same error than before or memory mapped error).

I really do not know where the problem comes from. Do you have an idea?

Thanks

--
Stephane Chantepie
CNRS Phd  candidate
Mus?um national d'Histoire naturelle
55 rue Buffon
75005 paris
E-mail : chantepie_at_mnhn.fr
--