Sampling issues: Ordinal probit model with fixed threshold extremes

Modeling
2

Here’s how to properly construct an ordered vector with fixed upper and lower bounds

parameters {
  ...
  simplex[K-2] c_;
}
transformed parameters {
  ordered[K-1] c;  // thresholds
  c[1] = c_lower;
  for (i in 2:(K-1)) {
    c[i] = c[i-1] + c_[i-1]*(c_upper-c_lower);
  }
  ...
}

Second, that uniform prior on sigma is going to cause problems. I’d say try normal(0, K) instead (it is automatically truncated to positive only).

And finally, don’t compute theta manually. Stan has a builtin ordered probit distribution.