Divergent transitions and other warnings for binomial model describing spider feeding rates

Modeling
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3

Wow, that’s an interesting system!

Based on this block:

  for (k in 1:K) {
    aj[k] ~ normal(a_mean, a_sd);
  }
  
  a_mean ~ normal(30, 15);
  
  a_sd ~ normal(0, 10);

I think this corresponds to centered parameterization which notoriously causes divergences. Case study here is a very accessible description of why (Diagnosing Biased Inference with Divergences), and shows that you could recode the hierarchical component here using a non-centered parameterization.

To follow @andre.pfeuffer comments regarding the beta-binomial, I believe that a clever implementation of hierarchical terms could be an alternate approach to add observation-level variability, see here Beta-Binomial: Why not a default family in the package? - #2 by paul.buerkner.