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

[Jarrod Hadfield]

Hi,

If you use the pedigree option you need to make sure that the column  
of species names is called "animal". The pedigree option has been  
superseded by the ginverse argument which allows more flexibility. To  
use this you can retain species in your random formula and then pass  
ginverse(species=Ainv) to MCMCglmm where Ainv can be obtained using  
inverseA(tree)$Ainv.

If you have just modelled species effects as uncorrelated random  
effects then they are equivalent to the residuals and so the two  
covariance matrices cannot be separately estimated as you state. This  
is not the case with a phylogenetic effect because the correlation  
structure allows the effects to be separated. However, separating them  
can still be difficult so you should expect wider credible intervals.  
With 27 species and two 4x4 covariance matrices I think the precision  
of the estimates will be very low and the prior will have a large  
effect.

Cheers,

Jarrod





Quoting Kyle Edwards <kedwards at ucdavis.edu> on Tue, 6 Mar 2012 23:38:02 -0800:

> 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
>
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>



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