Dear list users,

I wonder if anyone would be able to help me with a problem which I've been
trying to solve for quite some time. I want to run a bivariate random
regression, where the two dependent variables are body weight and lifetime
breeding success. Body weight is measured multiple times per individual,
while LBS is measured once. I then want to fit two random slopes in the
individual-level variance component for body weight- I x A and I x E. The
key is then to estimate the individual-level covariances involving LBS to
look for evidence of selection on body weight and individual slopes of
weight on A and E. Finally, I would like to fix the residual variance in
LBS to close to zero (I appreciate that it is impossible to fix it to
exactly zero), but I would like the residual variance in body weight to
vary across four quartiles of E (EQ).

I've been having two issues. Firstly, how to fix the residual variance in
LBS to zero, while allowing that for body weight to vary freely. The
problem is that when I specify "rcov = ~idh(trait:EQ):units", the resulting
8 x 8 VCV matrix (where only the variances are estimated), rather than
havig elements 1-4 being the four residual variances in weight and elements
5-8 being those for LBS, has the weight variances at the diagonal locations
1,3,5, and 7 and those for LBS at 2,4,6, and 8. In the former scenario, it
would be easy to fix the residual variances in LBS by using V = 0.001, fix
= 5 in the prior specification, but since the weight and LBS residual
variances alternate, this is not possible. I am yet to find a way to fix
specific variances in the residual structure. I have been able to do this
in ASReml, but the distribution of LBS is far from Gaussian, hence checking
it in MCMCglmm.

The second issue is that I have found it very difficult (even without
fixing residual variances in any way) to obtain satisfactory diagnostics-
in particular, the autocorrelation is very high for the individual VCV
components involving LBS and the random slopes, even with a run as long as
10 million iterations. I though that treating LBS as zero-inflated could
help, but have been unable it work out how to incorporate the necessary
zipoisson prior specifications into a bivariate model.

If anyone has any thoughts on fixing individual elements of the R
structure, or on sue of zipossion errors in bivariate models, I'd be very
grateful and pleased to hear from you.

Many thanks and best wishes,
Adam

A "basic" model is shown below. Nothing is fixed, but it illustrates the
structure of the model:

prior.x0 = list (R = list (V = diag(8), n = 0.002),
              G = list (G1 = list (V = diag(4), n = 0.002),
                        G2 = list (V = 1, n = 0.002),
                        G3 = list (V = diag(2), n = 0.002),
                G4 = list (V = 1, n = 0.002)))

model.x0<-MCMCglmm(cbind(WT, LBS) ~ trait-1 + some fixed effects,
      random = ~ us(trait + at.level(trait,1):E + at.level(trait,1):Age):ID
+ us(at.level(trait,1)):Year + us(trait):MumID + us(at.level(trait,2)):BY,
      rcov = ~idh(trait:EQ):units, data = data, family = c("gaussian",
"poisson"), nitt = , burnin = , thin = ,
      DIC = TRUE, prior = prior.x0, verbose = TRUE)










-- 
Adam Hayward
Post-Doctoral Research Associate
Department of Animal and Plant Sciences
Alfred Denny Building
University of Sheffield
Western Bank
Sheffield S10 2TN
UK
http://www.huli.group.shef.ac.uk/adam-personal.html
http://adhayward.wordpress.com/
https://twitter.com/adhayward18

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