var
   Y[N], pupil[N], school[N], LRT[N], LRT2[N], VR[N,2], Gender[N],  
   School.gender[N,2], School.denom[N,3], alpha[M,3], beta[8], mu[N], 
   tau[N], sigma2[N], theta, phi, min.var, max.var, gamma[3], T[3,3], 
   Sigma[3,3], mn[3], prec[3,3], R[3,3], rank[M], greater.than[M,M];
model {
   for(p in 1:N) {

      Y[p] ~ dnorm(mu[p], tau[p]);
      mu[p] <- alpha[school[p],1] + alpha[school[p],2]*LRT[p] 
               + alpha[school[p],3]*VR[p,1];
      log(tau[p]) <- theta + phi*LRT[p];
      sigma2[p] <- 1/tau[p];
      LRT2[p] <- pow(LRT[p],2);

   }
   min.var <- exp(-(theta + phi * (-34.6193))); # lowest LRT score = -34.6193
   max.var <- exp(-(theta + phi * (37.3807)));  # highest LRT score = 37.3807

   # Priors for fixed effects:
   for (k in 1:8) {  beta[k] ~ dnorm(0.0, 0.0001);   }
   theta ~ dnorm(0.0, 0.0001); phi ~ dnorm(0.0, 0.0001);

   # Priors for random coefficients:
   for (j in 1:M) {
      alpha[j,] ~ dmnorm(gamma[], T[,]); 
   }
 
   # Hyper-priors:
   #gamma[] ~ dmnorm(mn[], prec[,]);
   for (k in 1:3) {
      gamma[k] ~ dnorm(mn[k], prec[k,k]);
   }

   T[,] ~ dwish(R[,],3);
   Sigma[,] <- inverse(T[,]);

   # Compute ranks:
   #for (j in 1:M) {
   #   for (k in 1:M) {
   #      greater.than[j,k] <- step(alpha[k,1] - alpha[j,1]);
   #   }
   # 
   #    rank[j] <- sum(greater.than[j,]);  # rank of school j
   #}
}
