Choosing priors in brms for interaction term and covariance matrix

[ShabnamShadloo]

I am trying to model a proportional zero inflated response variable. The number of sample sizes are not the same throughout.

I have a covariance matrix resulted from a phylogenetic tree as a random effect. I have a categorical (diet with three levels) and two other continues (landImpact and OceanImpact) and one binary (method) fixed variables. Land impact and ocean impact cannot be below zero. I have done Z score normalization on them.

The model is so complicated and I am new to Bayesian modeling, though brms is the only package I could find that works for my data.

refModel <- brm(
   bf(
    positive | trials(sampleSize) ~  diet:LandImpactZ + diet:OceanImpactZ +  method +
     (1 | gr(speciesPhylo, cov = phylo_cor)) + (1|study)),  
  data = data, 
  family = zero_inflated_binomial(),  
  data2 = list(phylo_cor = phyloCor),
  prior = priors
  )

I am struggling to find priors for them. The default prior set for response is beta(1, 1). Without looking at data, I expect 20% be zero. So would beta(2,7) make sense? I’m also confused about setting priors for the interaction term. I don’t think I should consider the variables separately, but I can’t figure out how to consider the interaction for creating a prior.
Also, the default priors for the rest of the parameters would result in conflict in intercept and in phylogeny. There are 71 rows and columns in the phylogeny matrix. Can get rid of the conflict?

I hope it makes sense and it’s easy to follow.
Thank you so much for reading it!

[Corey.Plate]

I don’t know much about zero-inflated models, but if you’re trying to model percentages with a beta distribution, and you want it to be centered around 20%, you can calculate the empirical mean as α/(α+β) = 1/5, which gives that β = 4α. α and β are both [1,∞), but the higher they are the lower the variance of the prior distribution and the closer the mode is to 0.2 as well. The least informative, convergent, beta distribution with mean 0.2 is Beta(1,4).

[ShabnamShadloo]

Thanks a lot @Corey.Plate