------ R code -------
library(rstan)

# Reading dataset
data <- read.table("p1_data_001.txt",header=T)
y <- data[,10]

# Constructing addtive relationship matrix
ped <- data
n.ped <- length(ped[,1])
a.mat <- matrix(0,n.ped,n.ped)
a.inv <- matrix(0,n.ped,n.ped)
f <- array(0,n.ped)
tt <- c(1.0,-0.5,-0.5)

for(i in 1:n.ped){
  a.mat[i,i] <- 1
  if(ped[i,2]!=0 && ped[i,3]!=0){
    a.mat[i,i] <- a.mat[i,i]+0.5*a.mat[ped[i,2],ped[i,3]]
    a.mat[1:i-1,i] <- 0.5*(a.mat[1:i-1,ped[i,2]]+a.mat[1:i-1,ped[i,3]])
  }else if(ped[i,2]==0 && ped[i,3]!=0){
    a.mat[1:i-1,i] <- 0.5*(a.mat[1:i-1,ped[i,3]])
  }else if(ped[i,2]!=0 && ped[i,3]==0){
    a.mat[1:i-1,i] <- 0.5*(a.mat[1:i-1,ped[i,2]])
  }
  a.mat[i,1:i-1] <- a.mat[1:i-1,i]
  f[i] <- a.mat[i,i]-1
}

# Setting fixed effect
n.fixed <- 2
n <- length(data[,1])
sex <- matrix(0,n,1)
for(i in 1:n){
  if(data[i,4]=='M'){
    sex[i] <- 1
  }
  else if(data[i,4]=='F'){
    sex[i] <- 2
  }
}

# Setting incident matrix
X <- matrix(0,n,n.fixed)
Z <- matrix(0,n,n.ped)
for(i in 1:n){
	X[i,sex[i]] <- 1
	Z[i,data[i,1]] <- 1
}

# Implementing NUTS by Stan
data_stan <- list(J=n.fixed, N=n, K=n.ped, X=X, Z=Z, Y=y, A=a.mat)  

fit <- stan(file='test.stan', data=data_stan, seed=1234, chain = 1, iter = 10000, warmup = 1000)

------ test.stan file------
data {
  int<lower=1>    J; // number of fixed effects
  int<lower=1>    K; // number of all animals
  int<lower=1>    N; // number of observations
  matrix[N,J]     X; // Fixed effects design matrix
  matrix[N,K]     Z; // Random effects design matrix
  vector[N]       Y; // response variable
  matrix[K,K]     A; // relationship matrix
}
transformed data{
  matrix[K,K] LA;
  LA = cholesky_decompose(A);
}
parameters {
  vector[K]  a_decompose; // breeding values
  vector[J] b; // fixed effects
  real<lower=0> sigma_G; // genetic standard deviation
  real<lower=0> sigma_R; // residual standard deviation
}
model {
    vector[N] mu;
    vector[K] a;
    a_decompose ~ normal(0, 1);
    a = sigma_G * (LA * a_decompose);
    mu = X * b + Z * a;
    Y ~ normal(mu, sigma_R);
    to_vector(b) ~ normal(0, 1);
    sigma_G ~ student_t(4, 0, 1);
    sigma_R ~ student_t(4, 0, 1);
}
generated quantities{
  real sigma_U;
  real sigma_E;
  sigma_U = sigma_G * sigma_G; // genetic variance
  sigma_E = sigma_R * sigma_R; // residual variance
}