Hello,

I have a hierarchical model to fit an inverse logit function into data (example bellow) and I would like to add the `generate quantities`

block to be able to compare with other models using WAIC, LOO-IC. I have tried this:

```
generated quantities {
// For log likelihood calculation
real log_lik[N];
for (n in 1:J) {
log_lik[n] += normal_lpdf(y[n] | PSE[n]-inv_logit(steepness[n]*(GS-inflection[n])), sigma);
}
}
```

which gives me the following problem:

```
C:\Users\AppData\Local\Continuum\anaconda3\lib\site-packages\arviz\stats\stats.py:839: RuntimeWarning: invalid value encountered in greater
(tailinds,) = np.where(x > xcutoff) # pylint: disable=unbalanced-tuple-unpacking
C:\Users\AppData\Local\Continuum\anaconda3\lib\site-packages\arviz\stats\stats.py:683: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.
"Estimated shape parameter of Pareto distribution is greater than 0.7 for "
```

What is the problem?

Also, what is the difference between `normal_log`

and `normal_lpdf`

? (the `normal_log`

is used here)

The entire code goes like this:

```
data{
int<lower=0> N; // number of all datapoints
int<lower=0> J; // number of subjects
vector[N] y;
vector[N] GS;
int subject[N]; // labels for subjects
}
parameters{
// all parameters vary by subject
vector[J] PSE;
vector[J] steepness;
vector[J] inflection;
real mu_pse;
real mu_steepness;
real mu_inflection;
real<lower=0> sigma; // residual error of the observations, need to be positive
real<lower=0> sigma_pse;
real<lower=0> sigma_steepness;
real<lower=0> sigma_inflection;
}
model{
mu_pse ~ normal(0.5, 1);
//mu_steepness ~ exponential(0.2); // gamma(7, 0.3) this is on a much tighter scale than your guess in the first post
//mu_inflection ~ gamma(7, 0.15);
mu_steepness ~ normal(2,1);
mu_inflection ~ normal(0.5,1);
PSE ~ normal(mu_pse, sigma_pse);
steepness ~ normal(mu_steepness, sigma_steepness);
inflection ~ normal(mu_inflection, sigma_inflection);
y ~ normal(PSE[subject]-inv_logit(steepness[subject].*(GS-inflection[subject])), sigma);
}
generated quantities {
// For log likelihood calculation
real log_lik[N];
for (n in 1:J) {
log_lik[n] += normal_lpdf(y[n] | PSE[n]-inv_logit(steepness[n]*(GS-inflection[n])), sigma);
}
}
```

## Data:

```
GS = np.array([0. , 0.33, 0.6 , 0.8 , 1. , 1.33])
y = np.array([[0.4 , 0. , 0.2 , 0.6 , 0.2 , 0.2 ],
[0.5 , 0.5 , 0.5 , 0.6 , 0.4 , 0.25],
[0.6 , 0. , 0. , 0.2 , 0. , 0. ],
[0.2 , 0.2 , 1. , 0.6 , 0.2 , 0.2 ],
[0.6 , 0. , 0. , 0. , 0. , 0. ],
[1. , 0.6 , 0.2 , 0.4 , 0.4 , 0. ],
[0.2 , 0.4 , 0. , 0.2 , 0.2 , 0. ],
[0. , 0. , 0. , 0. , 0. , 0.4 ],
[0.8 , 0.2 , 0.8 , 0.2 , 0.4 , 0.6 ],
[0.2 , 0.2 , 0. , 0.2 , 0. , 0. ],
[0.4 , 0.2 , 0.2 , 0.2 , 0. , 0. ],
[0. , 0. , 0.4 , 0.4 , 0.2 , 0. ],
[1. , 0. , 0. , 0. , 0. , 0. ],
[0.6 , 0. , 0.4 , 0. , 0.2 , 0. ],
[0.6 , 0.6 , 0.2 , 0.2 , 0.4 , 0.6 ],
[0.8 , 0.2 , 0.2 , 0.2 , 0. , 0.4 ],
[0.8 , 0.4 , 0.2 , 0. , 0.6 , 0.2 ],
[0.4 , 0.2 , 0.2 , 0. , 0.2 , 0. ],
[0.5 , 0.2 , 0. , 0. , 0.2 , 0.2 ],
[0.5 , 0. , 0.4 , 0. , 0. , 0. ],
[0.8 , 0.4 , 0. , 0. , 0. , 0. ],
[0.2 , 0.2 , 0.2 , 0.2 , 0.2 , 0. ],
[0.4 , 0.6 , 0.6 , 0.2 , 0.6 , 0. ],
[0.2 , 0.6 , 0.4 , 0.4 , 0. , 0. ]])
```