A coauthor and I are thinking about an 8schools like case in which there are multiple experiments and you only have the mean and the standard deviation of the effect. The question is how to adjust for correlation between the schools whereby you have prior information on the correlation parameters but are not able to fold that information into a multilevel structure. Would the implementation below be appropriate?

```
data {
int<lower=0> J; // number of schools
vector[J] y; // estimated treatment effects
vector<lower=0>[J] sigma; // standard error of effect estimates
}
parameters {
real mu; // population treatment effect
real<lower=0> tau; // standard deviation in treatment effects
vector[J] eta; // unscaled deviation from mu by school
cholesky_factor_corr[J] L_Omega;
}
transformed parameters {
matrix[J, J] L_Sigma;
vector[J] theta = mu + tau * eta; // school treatment effects
L_Sigma = diag_pre_multiply(sigma, L_Omega);
}
model {
L_Omega ~ lkj_corr_cholesky(4);
target += normal_lpdf(eta | 0, 1); // prior log-density
target += multi_normal_cholesky_lpdf(y | theta, L_Sigma); // log-likelihood
}
```