Categorical response phylogenetic model brms

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@jonnations is right that variance for categorical model is meaningless (and thanks for looking into this question, it is appreciated!). To expand a bit: the responses are coded as integers, so R will happily compute the variance, but the number does not make sense, because by reordering the levels (which does not matter in the real world), you can get quite different variances:

var(c(1,1,1,1,1,2,2,3,3,3,3,3,3,3,3))
#[1] 0.8857143
var(c(1,1,1,1,1,3,3,2,2,2,2,2,2,2,2))
#[1] 0.4571429
>

Some stuff that could make sense (but really, you need to think if it is appropriate for the scientific question you are asking):

Definitely - for some types of questions, interpreting the sd could be directly relevant (although interpretation of parameters of multinomial models is a bit tricky).

Additionally:

  • You can interpret categorical regression as a set of pairwise binary comparisons. I.e. you can compute the odds between each pair of categories. You can then compute ICC for each logistic regression either as you do, by computing the variance directly, or via the analytic formula outlined for example here: Calculating Intra-Cluster Correlation (ICC) for the Group-Level Effect in a Multinomial GLMM (the topic discuss problem similar to yours, but there actually isn’t a solution, but it starts with the binary case)
  • While variance is meaningless for a multinomial distribution, there are other quantities that are meaningful, most notably entropy. So you could compute how much entropy is accounted for by the phylogenetic signal. Once again, whether this number is relevant depends heavily on the question you are trying to answer, so it might be useful to share the scientific background of the model.

Also, comparing an intercept-only model to a model with phylogeny via loo might (and might not) be sensible for your question (this is a bit of a tough topic, where reasonable people don’t necessarily agree what is best, see Hypothesis testing, model selection, model comparison - some thoughts for my current best take).

Best of luck with your model!

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