# Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used repeated measures, I wanted to fit random intercepts for participants. The only package that should be able to fit multivariet hierarchical regression I find is MCMCglmm. I was able to mix informations from course notes (included in package) and forums to specify priors which was accepted by model and gave similar answers as mancova. I would like to know though, how much uninformative my prior was, and how to specify least informative proper prior and how to specify uninformative improper prior.

All variables in model are kardinal.

what I used and worked:

prior<-list(R=list(V=diag(2)/2,nu=0.05),
G=list(G1=list(V=diag(2)/2,nu=0.05)))

fit_MM <- MCMCglmm(cbind(xpos, ypos) ~ trait +
(atribute1+atribute2+atribute3+atribute4+atribute5)^5 - 1,
random = ~us(trait):id, rcov = ~us(trait):units, prior = prior,
data = selected_data, family = c("gaussian", "gaussian"),  verbose = FALSE)


I have really lot's of data, so mixing, corelations and interactions are looking good. Also, if I would like to add random slopes for some atributes and responses, I expect I should add: +us(trait:atribute):id to random term, but I have absolutly no idea, how should prior for this look.

Thank you very mutch for any answer.

As of uninformative priors: the prior You described can be 'eased' further by decreasing the degree of belief (nu). Note that You can achieve practically flat improper priors by specifying nu of variance components to be zero (see Hadfield's Course Notes). I wouldn't recommend using improper priors though, because they can make inference from the model challenging (or even meaningless), and improper priors can lead to zero values of variance components, or MCMC chains more easily get stuck at given parameter values (produce reducible chains).
Specifying us(trait:atribute):id is indeed a correct way to have random slopes, and in this setup You won't need to change the dimension of variance matrix of G1 from 2.