Dear all,

I am using the MCMCglmm function for a multinomial model. I have some questions, I hope you could give me some advices :


1)      Firstly, I am using a model like this one (5 levels for M and 3 for AP2, my random effect is ID (individual)) :


k <- length(levels(d$M))
I <- diag(k-1)
J <- matrix(rep(1, (k-1)^2), c(k-1, k-1))

m <- MCMCglmm(M ~ -1 + trait * Sexe - Sexe,
              random = ~ us(trait):ID,
             rcov = ~ us(trait):units,
             prior = list(
                R = list(fix=1, V=0.5 * (I + J), n = 4),
                G = list(
                  G1 = list(V = diag(4), n = 4))),
              family = "categorical",
              data = d,
                nitt=30000,
                pl=TRUE)

But, I have quasi-complete separation in my data and if I well understand it is better to use gelman.prior in this case? Is that right?
So I want to change for a model (with the gelman prior) like that :
prior = list(B=list(mu=rep(0,12),V=gelman.prior(~-1 + trait*AP2 - AP2, data=d, scale=1+pi^2/3)), R = list(fix=1, V=0.5 * (I + J), n = 4),G = list(G1 = list(V = diag(4), n = 4)))

The problem is with the matrix V, I can't use -1 + trait*AP2 - AP2 because in the prior trait doesn't exist. I understand why it can't be use and so doesn't work but I want to know if there is another way to do that?


2)      Then, my effective sample sizes are very small in some case. If I understand, the better is to have these values close to the sample size given in the model? Is that correct? My sample size is 2700 but in the outut the eff.sample avec smaller...I tried to increase the number of iteration, here is the output :

Iterations = 3001:29991
Thinning interval  = 10
Sample size  = 2700
 DIC: 1319.542
....
              post.mean l-95% CI u-95% CI eff.samp  pMCMC
traitM.1        -2.2164  -3.2787  -1.3468   11.338 <4e-04 ***
traitM.2         0.5711   0.0387   1.1159   84.700 0.0341 *
traitM.4        -0.5480  -1.2154   0.1264   40.578 0.1015
traitM.5        -1.3570  -2.4205  -0.4973   13.702 <4e-04 ***
traitM.1:AP21   -7.3803 -12.2210  -3.1333    4.068 <4e-04 ***
traitM.2:AP21   -3.1508  -4.2727  -1.8902  208.868 <4e-04 ***
traitM.4:AP21   -2.6099  -3.8932  -1.2076  149.046 <4e-04 ***
traitM.5:AP21   -4.9783  -8.0197  -2.5096   21.507 <4e-04 ***
traitM.1:AP22   -2.6248  -4.0651  -1.3906   38.690 <4e-04 ***
traitM.2:AP22   -2.9709  -3.8151  -2.0987  202.438 <4e-04 ***
traitM.4:AP22   -3.5217  -4.6169  -2.4356   52.576 <4e-04 ***
traitM.5:AP22   -3.3705  -4.9749  -2.0923   25.030 <4e-04 ***


How can I change that? Is it a problem to interpret the results?

Thank you very much for your help,
Mathilde


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