## Model with random effects represented by hidden covariate b[i] 
model {
   alpha0 ~ dnorm(0.0,1.0E-6);  # intercept
   alpha1 ~ dnorm(0.0,1.0E-6);  # seed coeff
   alpha2 ~ dnorm(0.0,1.0E-6);  # extract coeff
   alpha12 ~ dnorm(0.0,1.0E-6);
   sigma ~ dexp(1.0);     
   for (i in 1:N) {
      b[i] ~ dnorm(0.0,1.0);
      logit(p[i]) <- alpha0 + alpha1*x1[i] + alpha2*x2[i] +
                     alpha12*x1[i]*x2[i] + sigma * b[i];
      r[i] ~ dbin(p[i],n[i]);
   }
 }

