IRT model with random items

[martinmodrak]

@Jose_Kaire

I need to constrain a vector so it sums to zero for each group in the dataset

Well you can always have N_total - N_groups raw variables and store the position last elements of each group and then copy the raw variables directly to “actual” variables, skipping the last elements and then compute the last elements. This would require a bunch of for loops and it would be easy to do some of-by-one errors, but you should be able to get it going relatively easily.

Further, this simple trick is not always well-behaved, but there are some more complex solutions. One is to have a soft constraint, something like:

for(group in 1:N_groups) {
   sum(b[group]) ~ normal(0, 0.01 * N_group_members[group]); 
}

Or, even better, but more complex is described here:

Test: Soft vs Hard sum-to-zero constrain + choosing the right prior for soft constrain

vector Q_sum_to_zero_QR(int N) { vector [2*N] Q_r; for(i in 1:N) { Q_r[i] = -sqrt((N-i)/(N-i+1.0)); Q_r[i+N] = inv_sqrt((N-i) * (N-i+1)); } return Q_r; } vector sum_to_zero_QR(vector x_raw, vector Q_r) { int N = num_elements(x_raw) + 1; vector [N] x; real x_aux = 0; for(i in 1:N-1){ x[i] = x_aux + x_raw[i] * Q_r[i]; x_aux = x_aux + x_raw[i] * Q_r[i+N]; } x[N] = x_aux; return x; } To whom to use this in the future. N…