G vs R posterior correlation in bivariate MCMCglmm
Hi, If the relationship between the two is causal - lets say phenotype affects disease - then the regression at the two levels will be identical: COV(Disease, phenotype)/VAR(phenotype) is the same at the site level and the units level. However, they can easily differ. Imagine that the amount of resource varies between sites, but within sites all individuals have access to the same amount of resource. If there is a trade-off then, for a given amount of resource, there will be a positive relationship (if high values of the phenotype are 'good') between the two variables observed at the units level. However, imagine that as the amount of resource increases individuals can increase their phenotype but also reduce the amount of disease. As a consequence the between site correlation may well be negative. So, correlations at both levels tell you something interesting. However, it should be noted that if you can assume causality you are better just fitting a univariate model with phenotype in as a predictor: you get an increase in precision for your assumption. Cheers, Jarrod
On 26/10/16 08:46, Xav Harrison wrote:
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
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