Some kind of rounding thing.stan

# trying out a rounding thing


functions
{
  int income_rounding(real log_income)    // function to transform latent log income into NSFG categories
  {
    real inc;
    inc = exp(log_income);
    
    if (inc < 5000) 
      return 1;
    else if (inc < 7500) 
      return 2;
    else if (inc < 10000) 
      return 3;
    else if (inc < 12500) 
      return 4;
    else if (inc < 15000) 
      return 5;
    else if (inc < 20000) 
      return 6;
    else if (inc < 25000) 
      return 7;
    else if (inc < 30000) 
      return 8;
    else if (inc < 35000) 
      return 9;
    else if (inc < 40000) 
      return 10;
    else if (inc < 50000) 
      return 11;
    else if (inc < 60000) 
      return 12;
    else if (inc < 75000) 
      return 13;
    else if (inc < 100000) 
      return 14;
    else 
      return 15;
  }
}


data 
{
  int<lower=2> K;             // there are K categories for data y
  int<lower=0> N;             // N obersevations
  int<lower=1,upper=K> y[N];  // outcome variable
  int x[N];                   // predictor variable
  //vector[K-1] c;              // cutoff points for latent outcome variable
}

parameters 
{
//  real mu;                    // mean of log of latent variable
  real<lower=0> sigma_sq;     // variance of log of latent variable
  vector latent_y[N];         // latent variable = log income
  real beta;                  // coefficient on predictor variable (slope)
  real alpha;                 // intercept
}

transformed parameters 
{
  real<lower=0> sigma;        // standard deviation of log income
  sigma = sqrt(sigma_sq);     // standard deviation of log income
  
}

model 
{
  latent_y ~ normal(alpha + beta*x, sigma);   // income is log normal
//  latent_y = alpha + beta*x;      // linear model
  
  y = income_rounding(latent_y)   // relationship between latent log income and NSFG income categories
}