uncensor_me.stan

// trying out a censoring thing


data 
{
  int<lower=2> K;             // there are K categories for data y
  int<lower=1> N;             // N obersevations
  int<lower=1,upper=K> y[N];  // outcome variable
  int<lower=1,upper=11> x[N]; // predictor variable
}

parameters 
{
  real mu;                    // mean of log of latent variable
  real<lower=0> sigma_sq;     // variance of log of latent variable
  real 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 
{
  exp(mu) + 12.7 ~ normal(75738,20000);      // mean of income is distruted with mean and standard deviation from US Census (technically not normal beause stricty positive) NB: NEED TO ADD LOG JACOBIAN HERE!
  sigma ~ cauchy(0,10);           // weak prior (half cauchy due to restriction)
  latent_y ~ normal(mu, sigma);   // latent_y = log(income) which is normal
  for(n in 1:N) 
  {
    if(y[n] == 1) 
    {
      target += normal_lcdf(5000 | mu, sigma);
    } 
    else if(y[n] == 2) 
    {
      target += log_diff_exp(normal_lcdf(7500 | mu, sigma),
                             normal_lcdf(5000 | mu, sigma));
    } 
    else if(y[n] == 3) 
    {
      target += log_diff_exp(normal_lcdf(10000 | mu, sigma),
                             normal_lcdf(7500  | mu, sigma));
    }
    else if(y[n] == 4) 
    {
      target += log_diff_exp(normal_lcdf(12500 | mu, sigma),
                             normal_lcdf(10000 | mu, sigma));
    }
    else if(y[n] == 5) 
    {
      target += log_diff_exp(normal_lcdf(15000 | mu, sigma),
                             normal_lcdf(12500 | mu, sigma));
    }
    else if(y[n] == 6) 
    {
      target += log_diff_exp(normal_lcdf(20000 | mu, sigma),
                             normal_lcdf(15000 | mu, sigma));
    }
    else if(y[n] == 7) 
    {
      target += log_diff_exp(normal_lcdf(25000 | mu, sigma),
                             normal_lcdf(20000 | mu, sigma));
    }
    else if(y[n] == 8) 
    {
      target += log_diff_exp(normal_lcdf(30000 | mu, sigma),
                             normal_lcdf(25000 | mu, sigma));
    }
    else if(y[n] == 9) 
    {
      target += log_diff_exp(normal_lcdf(35000 | mu, sigma),
                             normal_lcdf(30000 | mu, sigma));
    }
    else if(y[n] == 10) 
    {
      target += log_diff_exp(normal_lcdf(40000 | mu, sigma),
                             normal_lcdf(35000 | mu, sigma));
    }
    else if(y[n] == 11) 
    {
      target += log_diff_exp(normal_lcdf(50000 | mu, sigma),
                             normal_lcdf(40000 | mu, sigma));
    }
    else if(y[n] == 12) 
    {
      target += log_diff_exp(normal_lcdf(60000 | mu, sigma),
                             normal_lcdf(50000 | mu, sigma));
    }
    else if(y[n] == 13) 
    {
      target += log_diff_exp(normal_lcdf(75000 | mu, sigma),
                             normal_lcdf(60000 | mu, sigma));
    }
    else if(y[n] == 14) 
    {
      target += log_diff_exp(normal_lcdf(100000 | mu, sigma),
                             normal_lcdf(75000  | mu, sigma));
    }
    else if(y[n] == 15) 
    {
      target += normal_lccdf(100000 | mu, sigma);
    }
      
  }

}