Hey @cmcd! Thank you for not abandoning me!
So, my data has considerable phylogenetic signal (i.e. data are phylogenetically clumped), as measured by Moran’s I or any other metric. I was prepared to agree that there must be something wrong with the covariance structure, as you suggested, even though I can’t really imagine where it might have gone wrong. The phylogeny itself comes from a widely used source (birdtree.org) and was transformed into a variance-covariance matrix with ape::vcv(), which is standard practice as far as I’m aware.
But then I decided to test whether phylogenetic signal has some role in inflating variance, as you imagined, by simulating some data. I simulated data under a Poisson distribution in the presence or absence of phylogenetic signal. The Poisson’s lambda is based on a subset of the data in the first post. For each dataset, I fitted a brms model predicted by (1|species) and (1|gr(species, cov = A)). Here’s what I found:
Turns out that phylogenetic signal does influence variance, but in the opposite direction! The covariance matrix is only inflating variance in the presence of phylogenetic signal (i.e., phylogenetic correlation).
I’m clueless! Could it be that phylogenetic correlation is so high that the model can’t handle it even with a covariance matrix, thereby affecting the model’s accuracy? But then how come the model’s prediction is spot-on without the covariance matrix, right?