model {

  itofpprior[1:2] ~ ddirch(alphafp[])

  # Uninformative priors for logistic regression weights  
  logoffset ~ dnorm(0.0, 0.01)
  loglit ~ dnorm(0.0, 0.01)
  logito ~ dnorm(0.0, 0.01)
  loguetz ~ dnorm(0.0, 0.01)

  titodist[1,1,1:2] ~ ddirch(alphatito1[])
  titodist[1,2,1:2] ~ ddirch(alphatito1[])
  titodist[2,1,1:2] ~ ddirch(alphatito2[])
  titodist[2,2,1:2] ~ ddirch(alphatito1[])
  titodist[3,1,1:2] ~ ddirch(alphatito2[])
  titodist[3,2,1:2] ~ ddirch(alphatito1[])
  titodist[4,1,1:2] ~ ddirch(alphatito2[])
  titodist[4,2,1:2] ~ ddirch(alphatito1[])

  for( p in 1 : N) {
       itopfp[p] ~ dcat(itofpprior[])
  }

  for( i in 1 : M ) {
	itofp[i] <- step(itopfp[parent1[i]] + itopfp[parent2[i]] - 3) + 1
	tito[i] ~ dcat(titodist[ito[i],itofp[i],])

        val[i] <- logoffset + loglit*(lit[i]-1) + logito*(tito[i]-1) + loguetz*(uetz[i]-1)
	ppiprior[i] <- 1 / (1 + exp(val[i]))
	ppi[i] ~ dbern(ppiprior[i])
  }

}