[R-sig-ME] MCMCglmm rcov term

[Ingleby, Fiona]

Dear all,

I am using the MCMCglmm package to form a model with a multivariate response (three principal components), two fixed effects (temperature and food with two factor levels each), and isoline (or genotype, with 60 factor levels) as a random effect. I'm also interested in the interaction between isoline and both food and temperature, and have therefore included these interactions in the random effects. My prior and model therefore look like this:

prior<-list(R=list(V=diag(3),nu=2),G=list(G1=list(V=1,nu=0.02),
G2=list(V=1,nu=0.02),G3=list(V=1,nu=0.02),G4=list(V=1,nu=0.02)))

model<-MCMCglmm(cbind(PC1,PC2,PC3)~trait+Temperature*Food-1,
random=~Temperature:Isoline+Food:Isoline+Isoline+Isoline:Food:Temperature,rcov=~us(trait):units,
prior=prior,data=data,family=rep("gaussian",3),verbose=F)

My problem is that I am struggling to understand the use and interpretation of the 'rcov' term. I think I understand that as I have written it in the above model, I have defined a unique residual for each of the PCs (trait) for each individual (unit)?

When I call summary(model), I get this output table relating to the rcov term:

 R-structure:  ~us(trait):units

                      post.mean l-95% CI u-95% CI eff.samp
PC1:PC1.units  10.67864  10.0780  11.2944   1000.0
PC2:PC1.units   0.10204  -0.1432   0.3343   1000.0
PC3:PC1.units   0.01738  -0.1224   0.1665   1000.0
PC1:PC2.units   0.10204  -0.1432   0.3343   1000.0
PC2:PC2.units   3.18642   3.0058   3.3625   1000.0
PC3:PC2.units  -0.83016  -0.9082  -0.7585    727.5
PC1:PC3.units   0.01738  -0.1224   0.1665   1000.0
PC2:PC3.units  -0.83016  -0.9082  -0.7585    727.5
PC3:PC3.units   1.06151   1.0092   1.1272   1000.0

I'm not quite sure what this means. It seems to be that there is a lot of variance in PC1, slightly less in PC2, and slightly less again in PC3, and very low covariance between different PCs. These values are similar to the individual-level phenotypic covariance matrix that I can get directly from my data using the cov(data) R command. Given my current understanding of the rcov term, it makes sense that these are similar, but since I'm not sure about how I'm using the rcov term in this model, I can't be sure of my interpretation either. Can anyone clarify this for me? I also thought that, IF the covariance between my PCs is nearly 0, should I use the 'idh' matrix instead of an unstructured one? Additionally, I am more interested in covariance between my PCs at the genotype level rather than the individual level, and so I tried to see if I could look at this by using a slightly different rcov term in my model:

rcov=~us(trait):units:Isoline

I guess I was trying to group the individuals by isoline, but whatever this command actually does, the resulting output table is almost identical to that from the previous model, and so I don't think I achieved what I meant to. I would really appreciate it if anyone has any idea how to do this correctly, or if anyone could explain what I have done here and why the two models might give near-identical output.

I would be really grateful for any help.

Thanks,

Fiona

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Fiona C Ingleby

http://biosciences.exeter.ac.uk/cec/staff/postgradresearch/fionaingleby/

Centre for Ecology and Conservation
University of Exeter, Tremough Campus
Cornwall
TR10 9EZ

Tel: 01326 371852