NSFG.stan

# This is the stan code to implement the model

data 
{
  int<lower=1> N;         // number of observations
  int<lower=1> G;         // number of clusters
  vector[N] y;            // the predicted variable (income)
  vector[N] x;            // the predictor variable (education)
}

parameters 
{
  vector<lower=1> alpha;    // intercept for each cluser
  vector beta;              // slope for each cluster 
  vector[2] mu;             // intercept and slope means
  vector[2] sigma;          // intercept and slope standard errors
  corr_matrix[2] rho;       // correlation matrix for intercept and slope
}

transformed parameters 
{
  vector[2] params = [log(alpha) beta]';     // put log_intercept and slope into a vector
  cov_matrix[2] S = diag_matrix[sigma] * rho * diag_matrix[sigma];  // formula for covariance matrix of intercept and slope
}

model 
{  
  z ~ normal(0,1);
  mvz ~ multi_normal([0 0]',[[1 0] [0 1]]);
  rho ~ lkj_corr(2);       // rho has LKJcorr distribution
  
  log(y) = log(75000) + z*log(446); // distribution of household income is log normal with mean 75 000 and standard error 446
  params = mu + mvz*S;   // log_intercept and slope are distributed multivariate normal with mean mu and covariance matrix S
  
}