Undefined R-structure MCMCglmm

Hi Chris,

Zip models are essentially bivariate in MCMCglmm with the first  
"trait" being the poisson part and the second "trait" the zero- 
inflation part.  An appropriate models would be something of the form:

fit1 <- MCMCglmm(sus ~ trait + trait:ethnic + trait:sped + trait:ell +  
trait:risk + trait:male + trait:grade-1, random=~us(trait):id.f,  
rcov~idh(trait):units, data=enroll.long.m, verbose=TRUE, DIC=TRUE,  
family="zipoisson")

This model is probably the least parsimonious model. Each fixed effect  
can have an effect on the zero-inflation and the poisson process  
(hence the interaction with trait) and there are separate id.f random  
effects for each process with the covariance estimated.  Because there  
is no information to estimate this covariance within a data point I  
usually set it to zero using the idh(...) structure. Moreover, the  
residual variance of the zero-inflation cannot be estimated as in  
standard binary analyses so it should be fixed (I fix at 1 usually).  
The appropriate prior in this case would be something like

prior=list(R=list(V=matrix(V=diag(c(v1, 1)), fix=2, n=2),  
G=list(G1=list(V=V2, n=2)))

where v1 is the prior for the Poisson over-dispersion, and V2 is a 2x2  
matrix specifying the covariance matrix for id.f.

You may also want to consider not having a random effect for the zero  
inflation, but only for the Poisson part, in which case you can set  
this value close to zero.

prior=list(R=list(V=matrix(V=diag(c(v1, 1)), fix=2, n=2),  
G=list(G1=list(V=diag(c(v2, 1e-10)), n=2)))

where v2 is now the id.f variance component  for the Poisson part.   
Note, you cannot do this for the residual variance or the chain will  
not mix.

You can also do the same for the fixed effects by placing strong  
priors around zero for the zero-inflation coefficients.

Typically ZIP and high dimensional multinomial models are the hardest  
to fit, and mixing may be a problem. Specifying pl=TRUE and looking at  
the posterior traces of the latent variables can often be a better  
indicator of problem than looking at the traces of  the fixed effects  
and variance components. I usually see problems with zip mdoels when  
the mean of the Poisson process is so high that zero's are not  
expected from the Poisson process alone.

I'd be interested to know how you get on.

Cheers,

Jarrod

Undefined R-structure MCMCglmm

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