if you’re looking to reparameterise because the model runs slow or doesn’t converge then @avehtari advise RE priors might apply here too since none of the parameters seem to have priors in your model unless I’ve misunderstood something.

Just IMHO, and assuming your objective is performance, I would tend to think about it in terms of (1) Am I performing any operations that I don’t need to? (2) Have I vectorised as much as possible?

According to this, the exp function is vectorised. so you can write :

mu_index=exp(mu_index);

instead of:

for (n in 1:N){
mu_index[n]=exp(mu_index[n]);
}

Similarly, this says that normal_rng is vectorised so you can write this:

yrep=normal_rng(mu_index, sigma_cps_index);

instead of this:

for (i in 1:N)
yrep[i]= normal_rng(mu_index[i], sigma_cps_index[i]);

Except for that, I don’t see anything else personally, but others might.

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Variable definition base type mismatch, variable declared as base type vector variable definition has base type real[ ] error in ‘model49c4729690b_stan_CPS_11’ at line 50, column 54