likert_comparison.py

import cmdstanpy

MODEL_FILE = "likert_comparison.stan"
DATA = {
    "K": 3,
    "N_pre": 30,
    "N_post": 29,
    "pre": [1] * 14 + [2] * 12 + [3] * 4,
    "post": [1] * 6 + [2] * 13 + [3] * 10
}

if __name__ == "__main__":
    model = cmdstanpy.CmdStanModel(stan_file=MODEL_FILE)
    fit = model.sample(data=DATA)
    print(fit.diagnose())
    print(fit.summary())

likert_comparison.stan

data {
  int N_pre;
  int N_post;
  int K;
  int<lower=1,upper=K> pre[N_pre];
  int<lower=1,upper=K> post[N_post];
}
parameters {
  ordered[K-1] cutpoints;
  vector[2] eta;
}
model {
  eta ~ normal(0, 3);
  cutpoints[1] ~ normal(0, 3);
  cutpoints[2] - cutpoints[1] ~ normal(0, 3);
  for (n in 1:N_pre)
    pre[n] ~ ordered_logistic(eta[1], cutpoints);
  for (n in 1:N_post)
    post[n] ~ ordered_logistic(eta[2], cutpoints);
}
generated quantities {
  int<lower=0,upper=1> post_greater_than_pre = eta[2] > eta[1] ? 1 : 0;
}