Dear all,

I have a warning while executing my stan model with cmdstan, but I cannot get the reason of it.

The model is

///////////////////////// DATA /////////////////////////////////////

data {

int<lower = 0> N; // number of users

int<lower = 0> Q; // number of user covariates

int<lower = 0, upper = 1> Y[N];

matrix[Q,N] X; // design matrix of user covariates

vector[N] f; // design matrix of books

matrix[Q,Q] L0; // empirical variance-covariance matrix of beta

int<lower = 0> L1; // empirical variance of alpha

vector[Q] m0; // mean of beta

int<lower = 0> m1; // mean of alpha

}

//////////////////// PARAMETERS /////////////////////////////////

parameters {

row_vector[Q] beta; // coefficients related to users

real alpha; // coefficients related to books

real mu; // user-level random effect

real<lower = 0> tau;

real<lower = 0> eta;

}

transformed parameters {

// Probability trasformation from linear predictor

real<lower=0> odds[N];

real<lower=0, upper=1> prob[N];

for (i in 1:N)

{

odds[i] = exp(beta*X[,i] + alpha*f[i] + mu);

prob[i] = odds[i] / (odds[i] + 1.0);

}

}

////////////////// MODEL ////////////////////////

model {

```
// Likelihood
for (i in 1:N)
{
Y[i] ~ bernoulli(prob[i])
}
// Priors
mu ~ normal( 0, sqrt(100));
beta ~ multi_normal( m0, inv_sqrt(tau)*L0);
alpha ~ normal( m1, inv_sqrt(eta)*L1);
tau ~ gamma(0.01, 0.01);
eta ~ gamma(0.01, 0.01);
```

}

The warning I get is

Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

validate transformed params: prob[k0__] is -nan, but must be greater than or equal to 0

If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

Could you please help me understanding the problem?

Thank you very much!

Ilaria