Hi list members,

I am currently having some struggles with multiresponse models in MCMCglmm
and I hope some of you will be able to help. I've read through Jarrod's
excellent course notes but my understanding of these methods is still
pretty minimal and any feedback would be much appreciated.
I wish to compare repeatabilities and correlation structure between 4
behavioural traits across 2 populations for which I have repeated measures.
I am especially interested in knowing whether within and between-individual
correlations differ between populations. I am still unsure on the most
appropriate way to do so, my specific questions are listed below:

1) I chose to compare 3 different models: one with no fixed effects and
individuals as random effect (model1), one with fixed effects and
individuals as random effect (model2) and a third with fixed effects and
individuals nested within populations as random effects (model3, see code
below). I am using proportion data, so according to previous list messages
I can't base my model selection on DIC, correct? If so, what should I use
in order to select the best model?

2) Is it possible to extract posterior correlations for each population
directly from model 3? If not, does that mean these correlations should be
calculated by running model 2 on each population independently and then
reporting overlap of 95% credibility intervals?

3) Although autocorrelation is low and multiple chains seem to converge
fine, for a few components, I only get 80% of the effective size (~700-800
out of 1000 samples). Is this a big issue and does that imply the chain has
to be run longer or is this level acceptable?


Anyway, here's my code, please let me know if you see any blatant mistake
in it as well. Populations are referred as Site here.

prior.miw.1 <- list(R=list(V=diag(4), nu= 4), G=list(G1=list(V=diag(4),
nu=4, alpha.mu=c(0,0,0,0),alpha.V=diag(4)*1000))) # multivariate inverse
Wishart prior

model.1<- MCMCglmm(cbind(Act_prop, Act_up,Aggr_prop, Aggr_up,Bold_prop,
Bold_up, Vor_prop,Vor_up) ~ (trait-1), random=~us(trait):Id,
rcov=~us(trait):units,
family=c("multinomial2","multinomial2","multinomial2","multinomial2"),
prior=prior.miw.1,nitt=2500000,thin=2000, burnin=500000, data=Data.pr, pr=T)

model.2<- MCMCglmm(cbind(Act_prop, Act_up,Aggr_prop, Aggr_up,Bold_prop,
Bold_up, Vor_prop,Vor_up) ~ (trait-1) + trait:Size + trait:Condition +
trait:Condition_meanId+trait:Rearing,
random=~us(trait):Id, rcov=~us(trait):units,
family=c("multinomial2","multinomial2","multinomial2","multinomial2"),
prior=prior.miw.1,nitt=2500000, thin=2000,burnin=500000, data=Data.pr, pr=T)

model.3<- MCMCglmm(cbind(Act_prop, Act_up,Aggr_prop, Aggr_up,Bold_prop,
Bold_up, Vor_prop,Vor_up)~(trait-1) + trait:Size + trait:Condition +
trait:Condition_meanId + trait:Rearing,
random=~us(trait):Site:Id,rcov=~us(trait):units,
family=c("multinomial2","multinomial2","multinomial2","multinomial2"),
prior=prior.mig.1, nitt=2500000,
thin=2000, burnin=500000, data=Data.pr, pr=T)

posterior.mode(posterior.cor(model.3$VCV[,1:16])) # between-individual
correlations
posterior.mode(posterior.cor(model.3$VCV[,17:32])) # within-individual
correlations

Thanks a lot for your help!

Raphaël Royauté
PhD candidate
Dept Natural Resource Sciences
McGill University, Macdonald campus
21,111 Lakeshore Road
Ste Anne de Bellevue, Québec
H9X3V9, CANADA
Arthropod Ecology
Lab<https://exchange.mcgill.ca/owa/redir.aspx?C=e4876361842249258fa397812fba8f4e&URL=http%3a%2f%2farthropodecology.wordpress.com>

	[[alternative HTML version deleted]]

