[R-sig-ME] MCMCglmm covariance matrix specification

[Walid Crampton-Mawass]

Hey all,

Hope you are doing well during this time!

I have been racking my brain for weeks on how to do model this issue but I
have found nothing other than one old answer by Jarrod Hadfield (
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2015q4/024036.html) which
recommends using an antedepedence model. Here is the issue:

I have constructed a bivariate animal model (trait1, trait2) with a random
interaction with the additive genetic random effect and the residual
variance,i.e. (trait:env):animal. The interaction variable is a categorical
environmental variable of 3 levels (Low, Mid, High). So my
variance-covariance matrix has a 6x6 shape (2traitsx3env). Hence, the
matrix would include both among-trait covariances within the same env and
between env, and cross-env covariances for the same trait:

trait1:low trait1:mid trait1:high trait2:low trait2:mid trait2:high
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
(1 represent variances, 0 represent covariances)

I have already run the model with both the idh() and us() specification. In
the first case, no covariances are calculated at all, only variances are
calculated. In the second case, all types of covariances are calculated.

I need help figuring out how to specify the variance-covariance matrix in
MCMCglmm (and prior) in a way to tell the model not to estimate the
cross-env covariances, only the among-trait covariances should be
estimated:
trait1:low trait1:mid trait1:high trait2:low trait2:mid trait2:high
1 x x 0 x x
x 1 x x 0 x
x x 1 x x 0
0 x x 1 x x
x 0 x x 1 x
x x 0 x x 1
(1 represent variances, 0 represent covariances to be estimated, x
represent covariances fixed at 0, i.e. not estimated)

any help would be appreciated!
-- 
Walid Crampton-Mawass
Ph.D. candidate in Evolutionary Biology
Population Genetics Laboratory
University of Québec at Trois-Rivières
3351, boul. des Forges, C.P. 500
Trois-Rivières (Québec) G9A 5H7
Telephone: 819-376-5011 poste 3384

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