Hey guys, I’m trying to set up a multivariate animal model, which is just a random intercept model with a known covariance matrix between individuals (which is derived from a pedigree), and an unknown covariance matrix (G) between traits that gets Kronecker multiplied by the known between-individua…

Ok, so I came back to this model this week and finally found a solution that is fast and well behaved enough to be useful. Looking into the code from this paper I found a formulation of the A⊗G Kronecker product that honestly had me banging my head against a wall for not thinking of it before. My i…

Sorry nobody replied earlier. I’m still getting used to dealing with Discourse and trying not to get the first reply in on everything. You probably don’t want to fully blow out this Kronecker result (this came up recently on our old mailing list). We should have examples of that. It won’t not wo…

Hey Bob, Thanks for the reply. This was the simplest multivariate model I could think of, but I’ve moved to an univariate model to work things out. The idea is to model a continuous response in N individuals as a regression with random intercepts, given a known covariance between random intercepts…

I think the default chol in R returns an upper triangular Cholesky factor. cholesky_decompose in Stan returns a lower triangular one. I think the way you’ve written the Stan code you want to use a lower triangular one (so just transpose it before you pass it in, or do the Cholesky factorization ins…

Thanks, Ben, good catch. I moved the Cholesky decomposition to the Stan code and now I’m getting sensible estimates. However, for some combinations of random intercept variance and residual variance, I get a warning on Bayesian Fraction of Missing Information being low in all chains. The estimates a…

I honestly don’t really know what that diagnostic is. I Googled it, and came across this discussion: https://groups.google.com/forum/#!topic/stan-dev/uJhsapVwlk8 Seems relevant :D

That diagnostic is interesting (and Michael’s arXiv papers have good stuff on it) but I don’t think he has disseminated clear recommendations on interpretation (turns out to be hard).

Just reread this – for some combinations of random intercept variance and residual variance, is there any indication what combinations of parameters are causing this? Might give you an idea what part of the model is being weird.

I get the warnings when the proportion of variance associated with the random intercepts is higher than the residual variance. That’s not really common in practice, but is there any alternative way to parametrize this?

The E-BFMI quantifies how effective the momentum resampling step of Hamiltonian Monte Carlo is – the smaller the number the harder it is to explore all of the energy level sets with nontrivial probability. In particular, for sufficiently small values this step loses some important guarantees which …

I just did a bunch of chains with random intercepts at around 0.7 of the total variance, scaling so the random intercept variance and residual variance was around 1, put N(0, 1) priors on everything and got E-BMFI between 0.24 and 0.34. All the estimates are consistent with the simulated values, so …

Multivariate animal model

Modeling

Zhanglong September 21, 2020, 8:40am 15

Hi @diogro, I am not sure if you are still working on this topic, and I have a solution at here that runs faster than your code. I much appreciate you providing the stan code. It is inspiring. Thank you.

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Multivariate animal model

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