################# Model ########################

# Mixture of regressions with logit 
model 
{
   # model for observable responses: j is replication

 for(j in 1:t){    # j: time point
   for(i in 1:N){      # i: line id
      y[i,j]~dnorm(mu[j,grp[i]],tau[grp[i]])  
   } 

   for(i1 in 1:G){
    mu_rand1_temp[j,i1,1]<- gam[i1,1]*z[j,1]
    for(i2 in 2:nknots){
      mu_rand1_temp[j,i1,i2]<- mu_rand1_temp[j,i1,(i2-1)]+gam[i1,i2]*z[j,i2]
    }   
    mu_rand1[j,i1]<- mu_rand1_temp[j,i1,nknots]
   }
   
 
   for(i1 in 1:G){
    mu_fix_temp[j,i1,1]<- beta[i1,1]*x[j,1]
    for(i2 in 2:n_beta){
      mu_fix_temp[j,i1,i2]<- mu_fix_temp[j,i1,(i2-1)]+beta[i1,i2]*x[j,i2]
    }   
    mu_fix[j,i1]<- mu_fix_temp[j,i1,n_beta]
   }
   

   for(i1 in 1:G){
      mu[j,i1] <- mu_fix[j,i1]+ mu_rand1[j,i1]  
   
    }


 


}

 

   for(i in 1:N){   
    grp_multino[i, 1 : G] ~ dmulti( pi_test[i, 1 :G],1)
    for (i1 in 2:G) {
      log(ex[i,i1]) <- alpha[(i1-1),1] +alpha[(i1-1),2]*w[i,1] +alpha[(i1-1),3]*w[i,2] +alpha[(i1-1),4]*w[i,3] +alpha[(i1-1),5]*w[i,4]  
    }
    log(ex[i,1]) <- 0 
    sump[i] <- sum(ex[i,1:G])
    for(j in 1:G){
     pi_test[i,j] <- ex[i,j]/ sump[i]
    } 

    grp_temp[i,1]<- grp_multino[i, 1]
    for(i1 in 2:G){
      grp_temp[i,i1]<- grp_temp[i,i1-1]+i1*grp_multino[i, i1]
    }   
    grp[i]<- grp_temp[i,G] 
   } 


 ########## priors
  
  for(i in 1:nknots){  
   for(i1 in 1:G){  
    gam[i1,i]~dnorm(0, tau_b[i1])
   }
  } 
  for(i in 1:n_beta){  
   for(i1 in 1:G){  
    beta[i1,i]~dnorm(zero[1], R_1[1,1])
   }
  } 

  for(i in 1:n_alpha){  
   for(i1 in 1:(G-1)){  
    alpha[i1,i]~dnorm(zero[1], R_1[1,1])
   }
  } 



  


  for(i in 1:G){   
   tau[i]~dgamma(0.01, 0.01)
   s[i]<-1/tau[i]    
   tau_b[i]~dgamma(0.01, 0.01)
   s_b[i]<-1/tau_b[i]
  }
     

 
}
# end model








################# Data ########################
list(t=3.60000E+01, G=4.00000E+00, N=3.70000E+01, nknots=3.60000E+01, n_beta=2.00000E+00, n_alpha=5.00000E+00, y= structure(.Data= c(4.05119E+00, 5.76548E+00, 5.62262E+00, 7.76548E+00, 1.09083E+01, 1.14798E+01, 1.29083E+01, 1.43369E+01, 1.57655E+01, 1.63369E+01, 1.79083E+01, 1.96226E+01, 2.44512E+01, 2.24798E+01, 2.36226E+01, 2.39083E+01, 2.53369E+01, 2.57655E+01, 2.67655E+01, 2.67655E+01, 2.61940E+01, 2.11940E+01, 9.30833E+00, -1.37738E+00, -1.23774E+01, -2.05202E+01, -2.53774E+01, -2.98060E+01, -3.29488E+01, -3.45202E+01, -3.50631E+01, -4.08060E+01, -4.15202E+01, -4.02345E+01, -4.36345E+01, -4.00774E+01, -2.94500E+01, 9.40714E+00, 2.39786E+01, -6.07857E+00, -2.25929E+01, -2.48786E+01, -3.23071E+01, -4.23929E+01, -5.88786E+01, -7.85929E+01, -8.60214E+01, -9.54500E+01, -1.04593E+02, -1.26593E+02, -1.48021E+02, -1.57450E+02, -1.36021E+02, -1.05650E+02, -1.88786E+01, 1.80929E+01, 1.02264E+02, 1.73693E+02, 2.06264E+02, 1.97121E+02, 1.87264E+02, 1.62550E+02, 1.28264E+02, 5.81214E+01, 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0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00))





############ Initial values ###################

list(grp_multino= structure(.Data= c(1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 1.00000E+00, 0.00000E+00, 0.00000E+00), .Dim=c(37, 4)), beta= structure(.Data= c(2.37020E+01, -1.39558E+00, -2.18143E+01, 1.21406E+00, -4.80218E+01, 2.76849E+00, -5.60083E+01, 3.18164E+00), .Dim=c(4, 2)), gam= structure(.Data= c(-1.51427E-01, -9.93510E-02, 2.27561E+00, 2.72751E+00, -1.71999E+00, 5.98073E-01, 2.12732E+00, -1.27150E+00, 7.61226E-01, -6.94390E-01, -6.38425E-01, -7.19402E-01, -1.92556E+00, 9.05831E-01, 2.04170E+00, -3.02519E+00, -6.26189E+00, 5.95026E-01, 4.88265E+00, 6.65637E+00, -2.06471E+00, -4.52512E+00, 1.88833E+00, 8.42662E-01, 3.76337E-01, 2.32680E+00, -1.28912E+00, 2.70554E+00, -1.30244E+00, 1.82565E+00, -3.98879E+00, 1.48314E+00, 5.63224E+00, 1.95091E+00, 1.66300E+00, -1.08170E+00, -3.05422E-02, -2.29524E-01, 5.87372E+00, 5.92590E+00, -9.19938E-01, 4.86469E+00, 3.51555E+00, 2.93383E+00, 9.10220E+00, -2.02511E+00, 3.69390E+00, 5.67367E+00, -3.72436E-01, 2.58050E+00, 1.08660E+00, 8.59136E-01, -2.36255E+00, 6.19752E+00, -6.41903E+00, 2.60614E+00, -6.58069E-01, -5.31849E+00, 5.25566E+00, 5.35640E+00, 5.78609E+00, -1.46262E+00, 2.83540E+00, -2.09343E+00, 2.50986E+00, 1.18518E+01, -6.92790E+00, 9.96562E+00, 1.02762E+01, -9.97085E-01, 6.07130E+00, -7.14913E-01, 1.24551E-01, 2.25426E-01, 2.87040E-02, 9.58117E-02, -1.47987E-01, 4.55401E-01, -1.10096E+00, 1.50407E-02, -2.65966E-01, 2.77922E-01, -1.21712E+00, -9.84803E-01, 1.26978E+00, -1.01078E+00, 1.32747E-01, 1.64660E+00, 2.57664E+00, -2.53025E-01, -1.97365E+00, -1.70855E+00, -4.87152E-01, 1.73867E+00, -1.31202E+00, 2.77196E-01, -2.03319E+00, 1.77159E+00, 8.76789E-01, 2.57689E+00, 3.21924E+00, 9.26131E-01, 4.64481E+00, 4.85739E+00, -2.20314E-01, -5.65421E+00, 3.73912E+00, 1.04768E+00, -5.70219E-01, 6.50237E-01, 6.38911E+00, 6.87502E+00, 3.03361E+00, 7.97958E+00, 2.46233E+00, 4.61243E+00, 7.21204E+00, -9.69584E-01, 3.34044E+00, 3.28194E+00, 2.69547E+00, 3.85971E+00, 4.99549E+00, 1.36889E+00, -9.18620E+00, 2.87850E+00, 1.04784E+00, 1.07758E+01, -2.27879E+00, -4.53177E+00, 1.51518E+00, 1.84237E+01, 6.93657E+00, 4.64260E+00, 1.14841E+01, 9.77636E-01, 1.04475E+01, 1.85684E+01, -5.17889E-01, 1.79034E+01, 1.46963E+01, -6.21521E+00, 1.14215E+01, -5.50773E-03), .Dim=c(4, 36)), alpha= structure(.Data= c(0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00), .Dim=c(3, 5)), tau=c(1.00000E+02, 1.00000E+02, 1.00000E+02, 1.00000E+02), tau_b=c(1.00000E+02, 1.00000E+02, 1.00000E+02, 1.00000E+02))