# Syntax question: Constrain parameters by groups

Hello,

I am trying to fit an IRT model where the item parameters vary by group. I am following this post as a guide for my syntax. My goal is to restrict the betas (difficulty parameters) so that they sum to 0 for each group. This is my code at the moment:

``````data {
int<lower=1> K;                // number of items
int<lower=1> I;                // number of students
int<lower=1> N;                // total number of observations (student x items)
int<lower=1> J;                // number of groups
int<lower=1, upper=K> kk[N];   // variable indexing the items
int<lower=1, upper=I> ii[N];   // variable indexing the students
int<lower=0, upper=1> y[N];    // binary variable outcome
int<lower=0, upper=J> jj[I];   // variable indexing the group membership
}

parameters {
vector[J] beta_raw[K-1];         // difficulty of item
vector[I] theta_norm;             // student ability
vector[J] mu;                    // mean theta of every group
real<lower=0> sigma;             // hyperprior theta
}
transformed parameters {
vector[I] theta;
vector[K] beta[J];

theta = mu[jj] + theta_norm * sigma;
for (j in 1:J) {
beta[j] = append_row(beta_raw[j], -sum(beta_raw[j]));
}
}

model {
for (k in 1:J) {
beta[k] ~ normal(0, 1);  // prior on the beta
}

mu ~ std_normal();
theta_norm ~ std_normal();
sigma ~ exponential(.1);         // hyperprior theta

for (n in 1:N) {
y[n] ~ bernoulli_logit(theta[ii[n]] - beta[jj[ii[n]], kk[n]]);
}
}

}
``````

The code works well as long as the number of groups (K) is 1 less than the number of items (I). However, under other configurations, for example, K>I, the indices do not quite work out. I would get an error stating that my index is out of range.

Any pointers on how to make the code above more general so that it can work with more configurations of K and I?

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In the code above, it looks like you may be swapping K and J when you define `beta`. I’m guessing that’s the source of the error.

Also, it looks like you could vectorize the `bernoulli_logit` sampling statement, which could help with performance.

2 Likes