[R-sig-ME] MCMCglmm: multivariate response with phylogenetic structure

[Kyle Edwards]

Hello,

I am looking for some advice on how to specify an MCMCglmm model with a multivariate response, while accounting for potential phylogenetic structure in the residuals. The data consist of 4 traits (tr1 - tr4), with each trait measured a maximum of one time for each of 27 species (there is some missing data, but that does not appear to be problematic for these analyses). To begin with, following chapter 5 in the course notes, I fit the following model without phylogenetic information:

mod = MCMCglmm(cbind(tr1, tr2, tr3, tr4) ~ trait-1, rcov = ~us(trait):units, data = my.data, family = rep("gaussian", 4))

This model converges quickly and gives sensible results similar to those I have found using other approaches. 

I would next like to incorporate a phylogenetic tree for these species, to test whether this alters the estimated trait correlations. If I understand correctly, this is implemented in MCMCglmm using a combination of the 'random' and 'pedigree' arguments, or a combination of the 'random' and 'ginverse' arguments. So I would expect to include these terms in the model: 

random =~ us(trait):species, pedigree = my.phylogeny,

where the names of the species are the tips of the phylogeny. 

However, I am confused about how to model the 'rcov' argument, once this random effect term is introduced. Because each species is only observed once, there is no residual variation within species, and so it seems this random effect term should make the rcov term in my original model redundant. How should one specify the residual variation in this case? If I fit a model with "rcov = ~us(trait):units, random =~ us(trait):species", it is much slower to converge and the posterior distributions of the trait correlations at both levels are much wider than in the original model. This occurs with or without the pedigree argument included, and it makes sense that I shouldn't be able to separately estimate all these parameters. 

Thanks for any insight into this issue,

Kyle

Kyle Edwards
Postdoctoral Research Associate
Kellogg Biological Station
Michigan State University

edwar466 at msu.edu