Dirichlet Multinomial model in JAGS with categorical X

Question

Can someone help with JAGS code for a Bayesian multinomial logistic model with one categorical X variable (Dirichlet prior)? My representative sample is the matrix "z" in the code below that represents the 3 outcomes and "site", in the bottom line of code, is the categorical x variable.

I can get the code that estimates each of the 3 outcomes but I'm stumped on how to add a categorical X (hospital site).

I would like to use the first outcome, z[, 1], as the reference and 'a' as the reference for 'site'.

Here is example code that estimates the outcomes (NO categorical X). This is what I have so far. Any help on extending this model with X would be appreciated.

library('rjags')
z <- matrix(c(rep(1,70), rep(0,30),
         rep(0,70), rep(1,22), rep(0,8),
         rep(0,92), rep(1,8)),
         nrow=100, ncol=3)

## The model ##
modelString = "
model
{
  for (j in 1:K)
  {
  alpha[j] <- 1
  }
  #Prior
  pi ~ ddirch(alpha[1:K])

  for (i in 1:N)
  {
  z[i, 1:K] ~ dmulti(pi, 1)
  }
}
"
writeLines( modelString , con="TEMPmodel.txt" )

#Run jags
jags <- jags.model('TEMPmodel.txt',
                   data = list('z' = z,
                               'N' = nrow(z),
                               'K' = ncol(z)),
                   n.chains = 4,
                   n.adapt = 1000)

mcmc.samples <- coda.samples(jags,
                             c('pi'),
                             2500)
#Estimates are similar to observed data
summary(mcmc.samples)

#5 category predictor hospital site to add to model
set.seed(1)
site <- sample(rep(letters[1:5], 20), 100)