Help expanding a Dirichlet-Categorical model

Modeling
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1

Hello all,

I have been trying to implement a hierarchical Dirichlet-Categorical model in stan to model spatial variation in fish diets. Specifically, my interest is to obtain the probabilities of encounter for each prey category at a given site (theta). The hierarchical structure of the model needs to include a linear model with an intercept and a continuous covariate (fish size) with the softmax link function, which I did not manage to include. I have the model implemented in JAGS, but I’m having trouble translating it to STAN. What follows is what I have so far:

data {

int<lower=1> N_obs;     // number of observations
int<lower=1> N_prey;    // number of categories
int site[N_obs] ;       // categorical covariate
int N_sites;            // number of sites
int y[N_obs];           // outcomes

}

parameters {

    simplex[N_prey] theta[N_sites];
    vector<lower=0>[N_prey] alpha;
    
}

model {

for (k in 1:N_prey) {
  
  alpha ~ uniform(0,100);   // weak prior on alpha

}

for (n in 1:N_sites) {

  theta[n] ~ dirichlet(alpha);  

}

for (i in 1:N_obs)

  y ~ categorical(theta[site[i]]);

}

I would greatly appreciate if anyone could show me how to expand the model!