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bayes_raking_32.stan
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bayes_raking_32.stan
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/*
bayes_raking.stan with generate quantities
*/
data {
// dimension parameters following paper section 2.1
int <lower=0> D; // Number of marginals
int <lower=0> J; // Number of cells include empty cells
matrix[D, J] L; // Loading matrix (binary)
int <lower=0> Nmargin[D]; // Known marignals
int <lower=0> Ntotal; // Total population size: Can be calculated based on marginals distribution
// Observed data: cell size related
int <lower=0> ncell[J]; // Observed cells sizes
// Models for inclusion mechanism
int <lower=0> ps; // Number of parameters in inclusion probability model section 2.4
matrix[J, ps] pdesign_J;
// Observed data: cell outcome related
int <lower=0> non_empty_J; // Number of non-empty cells
int <lower=1> y_id[non_empty_J]; // helper id to match the location
vector[non_empty_J] y_ave_non_empty; // Sample cells' mean
vector[non_empty_J] y_sum_of_square_non_empty; // Sample cell's sum of square
vector[non_empty_J] y_total; // Sample cells size
// Models for outcome
int py;
matrix[non_empty_J, py] ydesign_non_empty;
// Models to predict outcome: Since some of the cells are empty, but we can still estimate the potential outcome
matrix[J, py] ydesign_J;
// Generated Quantities:
int <lower=0> D_quant; // Dimention of marginals
matrix[D_quant, J] L_quant; // Loading matrix
}
parameters {
vector[ps] pbeta;
vector<lower=0>[J] Nhat;
}
transformed parameters {
vector[J] pselect;
pselect = inv_logit(pdesign_J * pbeta);
}
model {
// parameters related with model
vector[non_empty_J] f;
for (i in 1:non_empty_J) {
f[i] = 1 / pselect[y_id[i]];
}
// Model
Nmargin ~ poisson(L * Nhat); // Margins prior
for(i in 1:J) {
if(ncell[i] == 0)
Nhat[i] ~ cauchy(20, 3);
}
ncell ~ poisson(Nhat .* pselect); // Inlcudesion mechanism
for(i in 1:non_empty_J) {
if (y_total[i] > 1) {
y_ave_non_empty[i] ~ normal(f[i], f[i] / sqrt(y_total[i])); // Survey outcome
(y_sum_of_square_non_empty[i] / pow(f[i], 2)) ~ chi_square(y_total[i] - 1);
target += log(fabs(0.5 * pow(f[i], -1.5)));
} else {
y_ave_non_empty[i] ~ normal(f[i], f[i]); // Survey outcome
}
}
}
generated quantities {
real ymean; // estimator of ymean
vector[D_quant] ymarginals; // estimator of marginals outcome
vector[J] f_pred;
f_pred = 1 ./ pselect;
ymean = sum(f_pred .* Nhat) / sum(Nhat);
ymarginals = L_quant * (f_pred .* Nhat) ./ (L_quant * Nhat);
}