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data {
int<lower=1> D; // Dimensions
int<lower=0> N_obs; // Number of "observed observations" (with T = 1)
int<lower=0> N_cens; // Number of "censored observations" (with T = 0)
int<lower=1> M; // Number of judges
int<lower=1> K; // Number of groups
real<lower=0> sigma_tau;
int<lower=1, upper=M> jj_obs[N_obs]; // judge_ID
int<lower=1, upper=M> jj_cens[N_cens]; // judge_ID
int<lower=1, upper=K> kk_obs[N_obs]; // Grouping
int<lower=1, upper=K> kk_cens[N_cens]; // Grouping
int<lower=0, upper=1> dec_obs[N_obs]; // Positive decisions
int<lower=0, upper=1> dec_cens[N_cens]; // Negative decisions
row_vector[D] X_obs[N_obs]; // Private features of "observed observations" (with T = 1)
row_vector[D] X_cens[N_cens]; // Private features of "censored observations" (with T = 1)
int<lower=0, upper=1> y_obs[N_obs]; // Observed outcomes
}
parameters {
vector[N_obs] Z_obs;
vector[N_cens] Z_cens;
real alpha_T[M]; // Judge-specific intercepts
vector[D] beta_XT[K];
vector[D] beta_XY[K];
vector<lower=0>[K] beta_ZT_raw; // Coefficient for the latent variable.
vector<lower=0>[K] beta_ZY_raw; // Coefficient for the latent variable.
real<lower=0> tau_XT;
real<lower=0> tau_XY;
real<lower=0> tau_ZT;
real<lower=0> tau_ZY;
}
transformed parameters{
vector<lower=0>[K] beta_ZT_cumulative;
vector<lower=0>[K] beta_ZY_cumulative;
vector<lower=0>[K] beta_ZT;
vector<lower=0>[K] beta_ZY;
beta_ZT[1] = beta_ZT_raw[1];
beta_ZY[1] = beta_ZY_raw[1];
if(K >= 2){
beta_ZT[2:] = tau_ZT * beta_ZT_raw[2:];
beta_ZY[2:] = tau_ZY * beta_ZY_raw[2:];
}
beta_ZT_cumulative = cumulative_sum(beta_ZT);
beta_ZY_cumulative = cumulative_sum(beta_ZY);
}
model {
Z_obs ~ std_normal();
Z_cens ~ std_normal();
tau_XY ~ normal(0, sigma_tau);
tau_XT ~ normal(0, sigma_tau);
tau_ZY ~ normal(0, sigma_tau);
tau_ZT ~ normal(0, sigma_tau);
beta_XT[1] ~ std_normal(); // first group
beta_XY[1] ~ std_normal();
beta_ZT_raw ~ std_normal();
beta_ZY_raw ~ std_normal();
if(K >= 2){
for(i in 2:K){ // random walk prior here
beta_XT[i] ~ normal(beta_XT[i-1], tau_XT); // ith group
beta_XY[i] ~ normal(beta_XY[i-1], tau_XY);
}
}
for(i in 1:N_obs){
dec_obs[i] ~ bernoulli_logit(alpha_T[jj_obs[i]] + X_obs[i] * beta_XT[kk_obs[i]] + beta_ZT_cumulative[kk_obs[i]] * Z_obs[i]);
y_obs[i] ~ bernoulli_logit(X_obs[i] * beta_XY[kk_obs[i]] + beta_ZY_cumulative[kk_obs[i]] * Z_obs[i]);
}
for(i in 1:N_cens)
dec_cens[i] ~ bernoulli_logit(alpha_T[jj_cens[i]] + X_cens[i] * beta_XT[kk_cens[i]] + beta_ZT_cumulative[kk_cens[i]] * Z_cens[i]);
}
generated quantities {
real<lower=0, upper=1> y_est[N_cens];
for(i in 1:N_cens){
y_est[i] = inv_logit(X_cens[i] * beta_XY[kk_cens[i]] + beta_ZY_cumulative[kk_cens[i]] * Z_cens[i]);
}
}