In the ‘2PL Tutorial’ case study, the following model is presented as `reg_centered.stan`

:

```
data {
int<lower=1> I; // # questions
int<lower=1> J; // # persons
int<lower=1> N; // # observations
int<lower=1, upper=I> ii[N]; // question for n
int<lower=1, upper=J> jj[N]; // person for n
int<lower=0, upper=1> y[N]; // correctness for n
real x[J]; // covariate for person j
}
parameters {
vector<lower=0>[I] alpha; // discrimination for item i
vector[I] beta; // difficulty for item i
vector[J] theta; // ability for person j
real gamma; // regression coefficient of x
}
model {
vector[N] eta;
alpha ~ lognormal(0.5,1);
beta ~ normal(0,10);
for (j in 1:J)
theta[j] ~ normal(gamma * x[j],1);
for (n in 1:N)
eta[n] <- alpha[ii[n]] * (theta[jj[n]] - beta[ii[n]]);
y ~ bernoulli_logit(eta);
}
```

This represents the 2PL model with latent regression, for a single covariate. The regression coefficient is denoted by the parameter `gamma`

.

After reading through the model, I am still unsure why there is no prior given for `gamma`

.

Can anyone explain to me what is going on here?

Thanks,

Michael