[bugsicon]

model {
      for (i in 1:N) {
            r[i] ~ dbin(p[i], n[i])
            b[i] ~ dnorm(0, tau)
            logit(p[i]) <- alpha0 + alpha1 * x1[i] + alpha2 * x2[i]
                              + alpha12 * x1[i] * x2[i] + b[i]
      }
      alpha0 ~ dnorm(0, 1.0E-6)
      alpha1 ~ dnorm(0, 1.0E-6)
      alpha2 ~ dnorm(0, 1.0E-6)
      alpha12 ~ dnorm(0, 1.0E-6)
      tau ~ dgamma(0.001, 0.001)
      sigma <- 1 / sqrt(tau)
}