i am trying to study whether the age of participants covaries with other hyperparameters with the following model below:

I have a prior on L ~eta(23) and then separately set L(3,2)~beta(9,1) to see how a strong correlation between age and b1 effects the other parameters.

But for some reason, this had no effect on the model fits (parameters fits were the same with or without setting L).

any insight into what im missing?

thanks in advance

```
data {
// Metadata
int<lower=1> N;
int<lower=1> NJ; // number of total subjects;
// Number of total observations
array[N] int<lower=1> J; // Subject-indicator per observation
array[N] int<lower=1> K; // Bandit-indicator per observation
vector[NJ] age_zscored; // Z-scored age
vector[NJ] age_squared_zscored; // Z-scored age
// Data
array[N] int<lower=0, upper=1> Y; // Response (risky = 1, certain = 0)
array[N] int<lower=0, upper=1> R; // Outcome (reward = 1, nonreward = 0)
}
transformed data {
// int NJ = max(J); // Number of total subjects
int NK = max(K); // Number of total bandits
}
parameters {
// Participant parameters
vector[2] theta_mu; //subject means ;
matrix[2,NJ] theta_pr_minus2;
vector<lower=0>[2] sigma;
cholesky_factor_corr[3] L;
}
transformed parameters {
matrix[3,NJ] theta_pr;
vector<lower=0>[3] sigma_pr;
sigma_pr[3]=1;
sigma_pr[1:2]=sigma;
theta_pr[1:2,]=theta_pr_minus2;
theta_pr[3,] = to_row_vector(age_zscored);
vector[NJ] b1; // Inverse temperature
vector[NJ] a1; // Learning rate (pos)
// Construction block
{
// Rotate random effects
matrix[NJ,3] theta = transpose(diag_pre_multiply(sigma_pr, L) * theta_pr);
// Construct random effects
b1 = (theta_mu[1] + theta[,1]) * 10;
a1 = Phi_approx(theta_mu[2] + theta[,2]);
}
}
model {
// Initialize Q-values
array[NJ, NK] real Q = rep_array(0.5, NJ, NK);
// Construct linear predictor
vector[N] mu;
for (n in 1:N) {
// Compute (scaled) difference in expected values
mu[n] = b1[J[n]] * (Q[J[n],K[n]] - 0.5);
// Compute prediction error
real delta = R[n] - Q[J[n],K[n]];
// Assign learning rate
real eta = a1[J[n]];
// Update state-action values
Q[J[n],K[n]] += eta * delta;
}
// Likelihood
target += bernoulli_logit_lpmf(Y | mu);
// Priors
target += normal_lpdf(theta_mu | 0, 2);
// target += std_normal_lpdf(to_vector(theta_pr_minus2));
target += std_normal_lpdf(to_vector(theta_pr_minus2));
target += student_t_lpdf(sigma | 3, 0, 1);
// age_zscored ~ normal(predicted_age,.05);
// age_squared_zscored ~ normal(predicted_age_squared,.05);
target += lkj_corr_cholesky_lpdf(L | 23);
// L[2,1] ~ beta(9,1);
L[3,2] ~ beta(9,1);
// prior correlation
}
generated quantities {
matrix[3,3] Omega = multiply_lower_tri_self_transpose(L);
}
```