I would like to perform a bivariate MCMC regression with boldness scores as the continuous response variable, aggression ranks as the ordinal response variable, trial numbers as fixed effect and individual ID (measured repeatedly) as random effect. I read somewhere that it is not advisable to run a bivariate model that includes a mix of ordinal response and continuous response variables. Therefore, the ordinal variable can be treated as a nominal variable because ranks are not important in this particular case for estimating (co)variance between-and within-individual ID in boldness and aggression.
My question is how to specify uninformative priors for such models with mixed response variables? I have been reading about priors, but I'm unable to grasp the concept. Maybe I need a fool's guide...Below is the code, and possible prior that I had set.
Prior1 = list(R = list(V = diag(2), nu = 0.002,fix=2), G = list(G1 = list(V = diag(2), nu = 2, alpha.mu = rep(0,2), alpha.V = diag(25^2,2,2)))) Mod<-MCMCglmm(cbind(scale(Boldness),Aggression) ~ trait-1 + trait:scale(Trial_Number, scale = FALSE),random =~ us(trait):IndividualID, rcov =~ us(trait):units, family = c("gaussian","threshold"), prior = Prior1, nitt=420000, burnin=20000, thin=100, verbose = TRUE, data = mydata)
Please note that I have fixed the residual variance using fix=2 in the prior because my second response variable are ordinal ranks. The model runs, without any apparent convergence issues or autocorrelation. However, I do not know if this is the right approach. Thank you very much in advance!