[R-sig-ME] MCMCglmm prior choice for random intercept model

[Joe King]

Hello MCMCglmm experts !

I have a random intercept model for which I am using MCMCglmm with the following type of call

MC1<-MCMCglmm(bly~x1+x2,random=~school,data=dt,family="categorical" ,prior=list(R=list(V=1,fix=1), G=list(G1=list(V=1, nu=0)))
        , slice=T, nitt=iter, ,burnin=burn )

I was told that this prior specification: ....G=list(G1=list(V=1, nu=0))) is non-informative for the random effect variance. Is this correct ?

One problem I am having with my models is, when I run a null model (with no covariates, only bly~,random=~school) then the posterior mean for random intercept ( the G-structure : ~school) is lower than when I add covariates, although the 95% credible intervals overlap. This happens with several batches of similar data. Is this a cause for concern and could it be related to the prior specification ? 

Thank you !
JK