[R-sig-ME] set up of priors in MCMCglmm for phylogenetic mixed models

[albrechj at staff.uni-marburg.de]

Dear list,

I want to us MCMCglmm to fit phylogenetic mixed models. I would like  
to fit models for three response variables. The data is based on  
observations from 15 plant species in 13 study sites across two years,  
but the dataset is not completely full factorial with respect to the  
random grouping factors. The dataset is relatively small (n = 128).

The error families of the three response variables are gaussian,  
multinomial2 (i.e., binomial), and ztpoisson (zero-truncated poisson).

The models look as follows:
###############################################################
# model 1, Gaussian
prior1 <- list(R=list(V=1, nu=0),
                      G=list(G1=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3),
                             G2=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3),
                             G3=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3)))

model1 <- MCMCglmm(fixed = plant_d ~ s.fruit_density_con * s.phen_d,
                                            random = ~ plant_species +  
site + year,
                                            ginverse =  
list(plant_species = Ainv), prior = prior1,
                                            data = data_complete,  
nodes = "TIPS", family = "gaussian",
                                            nitt = 1.5e6, thin = 1e3,  
burnin = 5e5)

###############################################################
# model 2, multinomial2 (binomial)
prior2 <- list(R=list(V=1, nu=0),
                      G=list(G1=list(V=1, nu=1e3, alpha.mu=0, alpha.V=1),
                             G2=list(V=1, nu=1e3, alpha.mu=0, alpha.V=1),
                             G3=list(V=1, nu=1e3, alpha.mu=0, alpha.V=1)))

model2 <- MCMCglmm(fixed = cbind(removal, total_rem) ~  
s.fruit_density_con * s.phen_d,
                                            random = ~ plant_species +  
site + year,
                                            ginverse =  
list(plant_species = Ainv), prior = prior2,
                                            data = data_complete,  
nodes = "TIPS", family = "multinomial2",
                                            nitt = 1.5e6, thin = 1e3,  
burnin = 5e5)

###############################################################
# model 3, zero-truncated poisson
prior3 <- list(R=list(V=1, nu=0),
                      G=list(G1=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3),
                             G2=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3),
                             G3=list(V=1, nu=0, alpha.mu=0, alpha.V=1e3)))

model3 <- MCMCglmm(fixed = richness ~ s.fruit_density_con * s.phen_d,
                                            random = ~ plant_species +  
site + year,
                                            ginverse =  
list(plant_species = Ainv), prior = prior3,
                                            data = data_complete,  
nodes = "TIPS", family = "ztpoisson",
                                            nitt = 1.5e6, thin = 1e3,  
burnin = 5e5)


My question is now which priors should I use for these three models. I  
have searched the course notes and on the list for suggestions, and  
ended up with flat *improper* priors for the residual variance and  
parameter expanded priors for the (co)variance in the random terms.

In the second model (with the binomial family) I used *parameter  
expanded priors* for the random effects (see below), as suggested by  
Jarrod Hadfield based on de Villemereuil et al. (2013) Methods in  
Ecology and Evolution 4:260-275.

However, at this point I'am stuck and I don't know whether the priors  
are specified correctly.


Could anyone give advice on the correct specification of the priors  
for these models?

I would really appreciate any suggestions.

Thanks,

Jörg