Flexible extension of mu & tau into P dimensions. Below is an example. This would need more work and the main problem is that you can't have full pooling on some parameters and non-full on others.
functions {
#include /functions/prior_increment.stan
}
data {
int<lower=0> P; //number of parameters -- CURRENTLY IT HAS TO BE 2, more will fail
int<lower=0> N; // total number of observations
int<lower=0> K; // number of sites
int<lower=0> Nc; //number of covariates (fixed effects)
matrix[N,Nc] X; //covariate values (design matrix for FE)
int pooling_type[P]; //0 if none, 1 if partial, 2 if full
int joint_prior; //0 if no, 1 if yes, but 1 requires all pooling == 1
int<lower=0,upper=K> site[N];
// vector<lower=0,upper=1>[N] treatment;
matrix[N, P] U;
// priors:
// joint prior for the mean
int prior_hypermean_fam;
matrix[P, 3] prior_hypermean_val;
vector[P] prior_hypermean_mean;
matrix<lower=0>[P, P] prior_hypermean_scale;
//dispersions for effect and baselines:
int prior_hypersd_fam;
matrix[P, 3] prior_hypersd_val;
//correlations (only LKJ allowed for now)
int prior_hypercor_fam;
real prior_hypercor_val;
//fixed effects (same dist. for all betas)
int prior_beta_fam;
matrix[Nc, 3] prior_beta_val;
//cross-validation variables:
int<lower=0> N_test;
int<lower=0> K_test;
matrix[N_test, Nc] X_test;
int<lower=0, upper=K> test_site[N_test];
int<lower=0, upper=1> test_treatment[N_test];
// NORMAL specific:
vector[N] y;
vector[N_test] test_y;
vector[K_test] test_sigma_y_k;
}
transformed data {
int K_pooled; // number of modelled sites if we take pooling into account
if(pooling_type == 2)
K_pooled = 0;
if(pooling_type != 2)
K_pooled = K;
}
parameters {
// corr_matrix[P] Omega; // prior correlation
cholesky_factor_corr[P] L_Omega[joint_prior? 1: 0];
vector<lower=0>[P] hypersd[pooling_type == 1? 1: 0]; // prior scale
vector[P] mu[pooling_type != 0? 1: 0];
matrix[P,K] eta[pooling_type != 2? 1: 0];
vector[Nc] beta;
// NORMAL specific:
vector<lower=0>[K] sigma_y_k;
}
transformed parameters {
matrix[P,K] theta_k[pooling_type != 2? 1: 0];
matrix[P,P] tau[pooling_type == 1? 1: 0];
if(pooling_type == 0)
theta_k[1] = eta[1];
if(pooling_type == 1){
if(joint_prior)
tau[1] = diag_pre_multiply(hypersd[1], L_Omega[1]);
else
tau[1] = diag_matrix(hypersd[1]);
theta_k[1] = rep_matrix(mu[1], K) + tau[1] * eta[1];
}
}
model {
vector[N] y_mean;
if(N > 0){
if(Nc == 0)
y_mean = rep_vector(0.0, N);
else{
y_mean = X*beta;
for(p in 1:Nc)
target += prior_increment_vec(prior_beta_fam, beta, to_vector(prior_beta_val[p]));
}
if(pooling_type != 2){
for(p in 1:P)
y_mean += U[, p] .* to_vector(theta_k[1][p, site]);
}else{
for(p in 1:P)
y_mean += U[, p] * mu[1][p];
}
}
if(joint_prior){
mu[1] ~ multi_normal(prior_hypermean_mean, prior_hypermean_scale);
L_Omega[1] ~ lkj_corr_cholesky(prior_hypercor_val);
}else {
for(p in 1:P){
if(pooling_type > 0)
target += prior_increment_real(prior_hypermean_fam, mu[1][p], to_vector(prior_hypermean_val[p]));
else
target += prior_increment_vec(prior_hypermean_fam, to_vector(eta[1][p,]), to_vector(prior_hypermean_val[p]));
if(pooling_type == 1) {
to_vector(eta[1][p,]) ~ std_normal();
target += prior_increment_real(prior_hypersd_fam, hypersd[1][p], to_vector(prior_hypersd_val[p]));
}
}
}
y ~ normal(y_mean, sigma_y_k[site]);
}
generated quantities {
// to do this, we must first (outside of Stan) calculate SEs in each test group,
// i.e. test_sigma_y_k`
}
Flexible extension of mu & tau into P dimensions. Below is an example. This would need more work and the main problem is that you can't have full pooling on some parameters and non-full on others.