[R-sig-ME] MCMCglmm covariance matrix specification

[Srivats Chari]

Hey Walid,

I had a similar problem a few months ago, I didn't want 1 trait to have any
covariance. I was not able to find a solution to it but after reading
several articles, I figured out a way.

Instead of not calculating the covariances at all (which I am not sure if
it's possible), you can set the value to 0 in the prior.

Here is my example-
I have 9 traits and I do not want my last trait to covary with any other
trait. Hence I set it to a very low value (0.001) for the within individual
covariance and use the fix command to specify which trait it is (in this
instance  my 9th trait).

final_priorv1 <- list(R = list(V =diag(c(1,1,1,1,1,1,1,1,0.001),9,9), nu =
0.002, fix = 9),
                      G = list(G1 = list(V = diag(9), nu = 9,
                                         alpha.mu = rep(0, 9),
                                         alpha.V  = diag(25^2,9,9))))

Remember this is within individual variance set to 0.001, you will still be
calculating the among individual covariance.

Found this solution from Dr. Houslay's MCMCGlmm Tutorial page 14. Link
here-->
https://tomhouslay.files.wordpress.com/2017/02/indivvar_mv_tutorial_mcmcglmm.pdf
Something similar from his other tutorial page 31-->
https://tomhouslay.files.wordpress.com/2017/02/indivvar_plasticity_tutorial_mcmcglmm1.pdf

With this prior, I was able to use the unstructured (us) covariance matrix
and I was able to get what I needed.

I feel what you are looking for is fairly similar, and I believe this
solution might work for you.

 Happy coding!

Regards,
Srivats.

Srivats Chari
<https://sites.google.com/ucd.ie/wildl-ecol-behav-at-ucd/people#h.p_DyWP_UxHDqgq>
Post-Graduate Research Student
Twitter- @WildlifeVats <https://twitter.com/WildlifeVats>

Laboratory of Wildlife Ecology and Behaviour
<https://sites.google.com/ucd.ie/wildl-ecol-behav-at-ucd>
School of Biology and Environmental Science (SBES),
University College Dublin (UCD).


On Wed, Feb 24, 2021 at 6:29 PM Walid Crampton-Mawass <
walidmawass10 using gmail.com> wrote:

> 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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>
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