Hi,

In line with what @Bob_Carpenter suggested: how would I go about setting up my code if I want to compare the predicted latent trait of respondents with the same response behavior across different item parameter values (for example stemming from models with different identifying constraints) while accomodating the uncertainty in the parameters from previous estimation?

If I had new observed data, then I’d probably run the script below to update the posterior distributions of the item parameters (discrimination, difficulty, and cutpoint) and obtain the distributions of the latent trait (theta).

But if I manually generated new response data where my only interest is to obtain the latent trait and not update the distribution of the items, then the script below will not get that job done.

Do you have suggestions as to how to proceed or examples I could look at?

Thanks!

```
data {
int<lower=1> J; // total number of respondents
int<lower=1> K; // total number of items
int<lower=1> N; // total number of responses
int<lower=0> jj[N]; // respondent for observation n
int<lower=0> kk[N]; // item for observation n
int<lower=1,upper=C> z[N]; // response for observation n; z in {1 ... C}
int<lower=1> C; // max categories of items
int<lower=1> D; // dimensions
matrix[K, 2] beta_prior; // priors for discrimination parameters, mu and sd
matrix[K, 2] alpha_prior; // priors for difficulty parameters
matrix[K*(C-1), 2] tau_prior; // priors for cutpoint parameters
int tau_pl[K,C-1]; // match the format of tau_prior to tau
}
parameters {
ordered[C-1] tau[K]; // threshold parameters
matrix[J,D] theta; // theta in of person j
vector[K] alpha;
matrix[K,D] beta;
}
model {
vector[C] prob; // probabilities
real eta; // linear predictor
for (k in 1:K){
beta[k,1] ~ normal(beta_prior[k,1], beta_prior[k,2]);
alpha[k] ~ normal(alpha_prior[k,1], alpha_prior[k,2]);
for (i in 1:(C-1)){
tau[k,i] ~ normal(tau_prior[tau_pl[k,i],1], tau_prior[tau_pl[k,i],2]);
}
}
for (n in 1:N){
eta = beta[kk[n],1]* theta[jj[n],1] + alpha[kk[n]];
prob[1] = Phi_approx((tau[kk[n],1] - eta));
for (c in 2:(C-1)){
prob[c] = Phi_approx((tau[kk[n],c] - eta)) - Phi_approx((tau[kk[n],c-1] - eta));
}
prob[C] = 1 - Phi_approx((tau[kk[n],C-1] - eta));
z[n] ~ categorical(prob);
}
}
```