model {

  # DATA
  
  for (i in 1:N) {
    for (j in 1:J) {
      y[i,j] <- yy[i + (j-1)*N]
    }
  }

  # LIKELIHOOD AND LATENT CLASS INDICATORS

  for (i in 1:N) {
    for (j in 1:J) {
      y[i,j] ~ dbern( py[i,j] )
      py[i,j] <- p[j,1]*z[i] + p[j,2]*(1-z[i])
    }
  }

  for (i in 1:N) {
    z[i] ~ dbern( lambda )
  }

  # PRIORS

  lambda ~ dunif(0,1)

  p[1,1] ~ dunif(0,1)
  p[1,2] ~ dbeta(1,1)I(0,p[1,1])
  # or equivalently p[1,2] ~ dunif(0,p[1,1])
  
  for (j in 2:J) {
      p[j,1] ~ dunif(0,1)
      p[j,2] ~ dunif(0,1)
    }
  }
  
}