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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