```
data {
//int<lower = 0> N;
int<lower=0> n_examinee; // Number of examinees
int<lower=0> n_item; // Number of items
//int<lower = 0> y[N];
int<lower=0> Y[n_examinee, n_item]; //The data matrix (count)
}
parameters {
vector [n_examinee] theta; //
vector <lower = 0> [n_item] easiness; //
//real <lower = 0> sdt;
//real <lower = 0> alpha;
//real <lower = 0> beta;
}
transformed parameters {
matrix [n_examinee, n_item] lambdas;
for(i in 1:n_examinee){
for (j in 1:n_item){
lambdas[i,j] = exp(theta[i] + easiness[j]) ;
}
}
}
model {
theta ~ normal(0, .3);
///sdt ~ gamma(1,30);
easiness ~ uniform(0,3);
for(i in 1:n_examinee){
for (j in 1:n_item){
Y[i,j] ~ poisson(lambdas[i,j]);
}
}
}
```

For a few weeks I have been trying to get this model to work in stan, specifically the RPCM(Rasch Poisson counts model), but for some reason havenâ€™t been able to get it to accurately run. This is how I am generating the data in R:

```
n <- 200
n_item <- 20
easiness <- log(seq(5, 40, length.out = n_item))
theta <- rnorm(n, 0, .3)
gen_test_data <- function(true_deltas, true_abilities, n_persons) {
out <- data.frame(
item1 = numeric(n_persons)
)
for (j in 1:length(true_deltas)) {
lambdas <- exp(true_abilities + true_deltas[j])
out[[paste0("item", j)]] <- rpois(n_persons, lambdas)
}
return(out)
}
df <- gen_test_data(easiness, theta, length(theta))
rpcsm <- stan(file = "rpcm.stan", data = list(n_examinee = n,
n_item = n_item,
Y = df), iter = 4000)
```

Could anyone point to any clear problems? I have tried different variations but the rhats are never good.