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// Multivariate Regression Example
// Taken from stan-reference-2.8.0.pdf p.66
data {
int<lower=0> N; // num individuals
int<lower=1> K; // num ind predictors
int<lower=1> J; // num groups
int<lower=1> L; // num group predictors
int<lower=1,upper=J> jj[N]; // group for individual
matrix[N,K] x; // individual predictors
row_vector[L] u[J]; // group predictors
vector[N] y; // outcomes
}
parameters {
corr_matrix[K] Omega; // prior correlation
vector<lower=0>[K] tau; // prior scale
matrix[L,K] gamma; // group coeffs
vector[K] beta[J]; // indiv coeffs by group
real<lower=0> sigma; // prediction error scale
}
model {
tau ~ cauchy(0,2.5);
Omega ~ lkj_corr(2);
to_vector(gamma) ~ normal(0, 5);
{
row_vector[K] u_gamma[J];
for (j in 1:J)
u_gamma[j] <- u[j] * gamma;
beta ~ multi_normal(u_gamma, quad_form_diag(Omega, tau));
}
{
vector[N] x_beta_jj;
for (n in 1:N)
x_beta_jj[n] <- x[n] * beta[jj[n]];
y ~ normal(x_beta_jj, sigma);
}
}
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