data{

  int<lower=0> N; //number of nests
  int cens[N]; //id for censored nests "1", and fully decayed nests ""
  int days_to_event[N]; //days until full decay (or until last observation day if censored)
  int F [N]; //forest type
  int E [N]; //nest exposure
  int P [N]; //nest position
  int C [N]; //construction type
  int H [N]; //nest realtive height
  int W [N]; //average rainfall
  int S [N]; //average number of stroms
  int D [N]; //differential temperature at construction
  int R [N]; //rain at construction
  int SP[N]; //tree species
  
}
  
parameters{

//////////Define factor specific parameters, and number of levels within each

  vector[2]  f;  //forest type
  vector[2]  e;  //nest exposure
  vector[2]  p;  //nest position
  vector[2]  c;  //nest construction type
  vector[3]  h;  //nest realtie height
  vector[3]  w;  //average rainfall
  vector[3]  s;  //average number of storms
  vector[3]  d;  //differential temperature at construction
  vector[2]  r;  //rain at construction
  vector[11] sp; //tree species 
  real<lower=0> theta; //rate parameter, has to be positive
}

transformed parameters{

vector<lower=0>[N] mu; //defines decay time of each nest, has to be positive

for ( i in 1:N ) {
    
    mu[i] = f[F[i]]+e[E[i]]+p[P[i]]+c[C[i]]+h[H[i]]+w[W[i]]+s[S[i]]+d[D[i]]+r[R[i]]+sp[SP[i]]; //linear model
    mu[i] = exp(mu[i]); //link function : exp of mu. mu has to be positive 
  
  }
}

model{

/////////////Define priors for parameters, on the log scale

  f ~ normal(0,5);
  e ~ normal(0,5);
  p  ~ normal(0,5);
  c  ~ normal(0,5);
  h ~ normal(0,5);
  w  ~ normal(0,5);
  d ~ normal(0,5);
  r ~ normal(0,5);
  s  ~ normal(0,5);
  sp ~ normal(0,5);
  theta ~ gamma (0.1,0.1);

  
  for ( i in 1:N ) 
    if ( cens[i] == 1 ) target += gamma_lccdf(days_to_event[i] | mu[i] * theta , theta);//censored nests, modelled using complementary cumulative gamma distribution 
    for ( i in 1:N ) 
      if ( cens[i] == 0 ) days_to_event[i] ~ gamma( mu[i] * theta, theta); // fully decayed nests, modelled using gamma distribution
}

generated quantities{

/////////////////Define quantities to be calculated 

real Decay; //Average decay time

////////////Define main effects

//Forest type
matrix [N,2] D_F;
vector [2]   Dec_F;
//Exposure
matrix [N,2] D_E;
vector [2]   Dec_E;
//Position
matrix [N,2] D_P;
vector [2]   Dec_P;
//Constructon type
matrix [N,2] D_C;
vector [2]   Dec_C;
//Relative height
matrix [N,3] D_H;
vector [3]   Dec_H;
//Average rain
matrix [N,3] D_W;
vector [3]   Dec_W;
//Average storms
matrix [N,3] D_S;
vector [3]   Dec_S;
//DIfferential temperature
matrix [N,3] D_T;
vector [3]   Dec_T;
//Rain at construction
matrix [N,2] D_R;
vector [2]   Dec_R;
//Tree species
matrix[N,11] D_SP;
vector[11]   Dec_SP;

/////////////////Calculate main effects
for (i in 1:N){
  for(j in 1:2){

    D_F[i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] +  f[j]);
    D_E[i,j]  = exp(f[F[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] +  e[j]);
    D_P [i,j]  = exp(f[F[i]] + e[E[i]] + m[M[i]] + dr[DR[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] + p[j]);
    D_M [i,j]  = exp(f[F[i]] + e[E[i]] + p[M[i]] + dr[DR[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] + m[j]);
    D_DR[i,j]  = exp(f[F[i]] + e[E[i]] + m[M[i]] + p[P[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] +  dr[j]);
    
  }
  
  for(j in 1:3){

    D_HT[i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + f[F[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]]  + ht[j]);
    D_R [i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + f[F[i]] + ht[HT[i]] + s[S[i]] + mt[MT[i]] + sp[SP[i]] + r[j]);
    D_S [i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + f[F[i]] + r[R[i]] + ht[HT[i]] + mt[MT[i]] + sp[SP[i]] + s[j]);
    D_MT[i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + f[F[i]] + r[R[i]] + s[S[i]] + ht[HT[i]] + sp[SP[i]]  + mt[j]);

  }
  
  for(j in 1:11){
    D_SP[i,j]  = exp(e[E[i]] + p[P[i]] + m[M[i]] + dr[DR[i]] + ht[HT[i]] + r[R[i]] + s[S[i]] + mt[MT[i]] + f[F[i]] + sp[j]);
  }
  
}

////////////Calculate mean decay time for each category
for(j in 1:2){
  Dec_F[j] = mean(D_F[,j]);
  Dec_E[j] = mean(D_E[,j]);
  Dec_P [j] = mean(D_P[,j]);
  Dec_M [j] = mean(D_C[,j]);
  Dec_DR[j] = mean(D_R[,j]);
}

for(j in 1:3){
  Dec_HT[j] = mean(D_HT[,j]);
  Dec_R [j] = mean(D_W[,j]);
  Dec_S [j] = mean(D_S[,j]);
  Dec_MT[j] = mean(D_T[,j]);
}

for (j in 1:11){
  Dec_SP[j] = mean(D_SP[,j]);
}

////////////Calculate overall mean decay time
Decay = mean(mu);

}