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data {
int N; // Examinees
int n; // Items
int C; // Grades
int<lower=1, upper=C - 1> delta[N, n];
real D; // Constant
}

parameters {
real a[n];
ordered[C] b[n];
real theta[N];
real<lower=0> aSigma;
real<lower=0> bSigma;
real<lower=0> thetaSigma;
}

transformed parameters {
vector[C] pa[N, n];
simplex[C] p[N, n];
for (i in 1:N) {
for (j in 1:n) {
for (c in 1:C) {
pa[i][j][c] = 1 / (1 + exp(-D * a[j] * (theta[i] - b[j][c])));
if (c == 1) {
p[i][j][c] = 1 - pa[i][j][c];
} else if (c == C) {
p[i][j][c] = pa[i][j][c - 1] - 0;
} else {
p[i][j][c] = pa[i][j][c - 1] - pa[i][j][c];
}
}
}
}
}

model {
aSigma ~ cauchy(0, 5);
bSigma ~ cauchy(0, 5);
thetaSigma ~ cauchy(0, 5);

for (i in 1:N) {
theta[N] ~ normal(0, thetaSigma);
}

for (j in 1:n) {
a[j] ~ lognormal(0, aSigma);
b[j] ~ normal(0, bSigma);
}

for (i in 1:N) {
for (j in 1:n) {
delta[i][j] ~ categolical(p[i][j]);
}
}
}

PyStan で IRT 走らせることはできるようになったが遅い。
5000 人 × 20 項目で使い物にならないレベルになったのでもう項目の値は不定期にエグザメトリカあたりで推論させて手で入れるプランで暫定としよ
受験者パラメータは項目パラメータから最尤法で結構な速度で出せるのでこっちは定期的およびリクエスト飛んだときに計算する #SIISI