### Model 3: 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[j] + (1 - e[j])*like[j]*(1 - p[j]) 
   llike[j] <- log(max(0.00000000001, min(0.99999999999, zerolike[j])))
   
   tp[j] <- exp(alpha[Treatment[j]] + b[Block[j]])
   mu[j] <- log(tp[j])

   logit(Q1[j]) <- (beta[1] + beta[2]*mu[j])
   p[j] <- max(0.00000000001, min(0.99999999999, Q1[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  

 
 # Probabilities of zero
 
 p2[1]  <- (p[4]  + p[13] + p[30] + p[36])/4 
 p2[2]  <- (p[5]  + p[16] + p[29] + p[33])/4 
 p2[3]  <- (p[1]  + p[17] + p[28] + p[32])/4 
 p2[4]  <- (p[6]  + p[20] + p[23] + p[35])/4 
 p2[5]  <- (p[9]  + p[12] + p[25] + p[37])/4 
 p2[6]  <- (p[2]  + p[11] + p[27] + p[38])/4 
 p2[7]  <- (p[10] + p[18] + p[21] + p[31])/4 
 p2[8]  <- (p[7]  + p[14] + p[26] + p[34])/4 
 p2[9]  <- (p[8]  + p[15] + p[22] + p[39])/4 
 p2[10] <- (p[3]  + p[19] + p[24] + p[40])/4 
 
 
 # Priors
 
  for (i in 1:10)
   {  
  alpha[i]~ dnorm(0.01, 0.1)  
   }

 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)
  }
}