### Model 2: Lognormal distribution

# Model

model{
 pi <- 3.141593
 for(j in 1:n){
   zeros[j] <- 0
   zeros[j] ~  dpois(zeros.means[j])  
   zeros.means[j] <- -llike[j] + 10000
   
   like[j] <- exp(-log(Y[j]) - log(phi) - (1/2)*log(2*pi) - pow(log(Y[j]) - mu[j], 2)/(2*pow(phi, 2))) 
   
   e[j]  <- equals(Y[j], 0.000001)
   zerolike[j] <- e[j]*p[Treatment[j]] + (1 - e[j])*like[j]*(1 - p[Treatment[j]]) 
   llike[j] <- log(max(0.00000000001, min(0.99999999999, zerolike[j])))
   
   tp[j] <- exp(beta[1] + beta[2]*logit(p[Treatment[j]]) + b[Block[j]])
   mu[j] <- log(tp[j])
   }
 
 
 # Conditional medians
 
 tp2[1]  <- (tp[4]  +tp[13] + tp[30] + tp[36])/4 
 tp2[2]  <- (tp[5]  +tp[16] + tp[29] + tp[33])/4 
 tp2[3]  <- (tp[1]  +tp[17] + tp[28] + tp[32])/4 
 tp2[4]  <- (tp[6]  +tp[20] + tp[23] + tp[35])/4 
 tp2[5]  <- (tp[9]  +tp[12] + tp[25] + tp[37])/4 
 tp2[6]  <- (tp[2]  +tp[11] + tp[27] + tp[38])/4 
 tp2[7]  <- (tp[10] +tp[18] + tp[21] + tp[31])/4 
 tp2[8]  <- (tp[7]  +tp[14] + tp[26] + tp[34])/4 
 tp2[9]  <- (tp[8]  +tp[15] + tp[22] + tp[39])/4 
 tp2[10] <- (tp[3]  +tp[19] + tp[24] + tp[40])/4 
 
 
  # Priors
 
 for (i in 1:10){
   p[i] ~ dbeta(1, 1)
 }

  beta[1] ~ dnorm(0.01, 0.1)   
  beta[2] ~ dnorm(0.01, 0.1)I(, 0)   

  phi ~ dgamma(0.01, 0.01)
  
  B <- 0.1                        
  inv.B.squared <- 1/pow(B, 2)
  z ~ dnorm(0, inv.B.squared)      
  chisq.1 ~ dgamma(0.5, 0.5)       
  s.b <- abs(z)/sqrt(chisq.1)      
  prec.b <- 1/pow(s.b, 2)

  for(i in 1:8){
    b[i] ~ dnorm(0, prec.b)
  }
}