# [R-sig-ME] G vs R posterior correlation in bivariate MCMCglmm

Xav Harrison xav.harrison at gmail.com
Wed Oct 26 09:46:45 CEST 2016

```Hi Folks

A potentially rookie question here, but here goes.

I'm using MCMCglmm to fit a bivariate response model where one response is
a Poisson count of pathogen load (Disease) and one is a Gaussian
phentotypic measure of the host (Phenotype).

I've fit a model with fixed effects that one would expect to influence each
of these predictors, and including a random effect of site, of the form:

prior1<-list(R=list(V=diag(2), nu=3),G=list(G1=list(V=diag(2),nu=3, alpha.mu
=c(0,0),alpha.V=diag(2)*1000)))

MCMCglmm(cbind(Disease,Phenotype) ~ trait-1 +
trait:predictors,rcov=~us(trait):units,random=~us(trait):site,family=c("poisson","gaussian"),prior=prior1,verbose=F,nitt=42000,burnin=2000,thin=20)

The golden egg here, and my hypothesis, is that after accounting for some
predictors there will be a negative posterior correlation between the
response traits, where the posterior correlation is calculated as:

Cov(Disease,Phenotype) / sqrt(Var(Disease)*Var(Phenotype))

My question is whether this correlation is relevant at the G structure
level (Site random effect) or at the R structure level, which I take to be
the residual variance at the observation (individual) level?

I suspect the answer is the latter, but I'm struggling to interpret what it
means if there is a negative correlation at the Site level? Does it mean
that the variances of the two traits at the site level are not independent,
in that higher values in one trait for a site tend to produce lower values
for the other?

Any help greatly appreciated.

Cheers

Xav

--
-------------------------------------------------------
Dr Xavier Harrison
Research Fellow
Institute of Zoology
Regent's Park
London NW1 4RY
www.zsl.org/xavierharrison
+44 (0) 207 449 6621

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