I am trying to model a percentage response variable. Looked at bounded distributions but you can’t specify observed variables. I also tried using a Beta distribution to constraint my observed data from 0 to 1 but I had some exceptions with PyMC3. I would prefer using Normal distributions. Maybe there’s something I could do with the logistic function?

I am doing a multi-level model:

```
# Intercept for each store, distributed around group mean mu_a
a = pm.Normal('alpha', mu=mu_a, sd=sigma_a, shape=len(uniqueStores))
# Intercept for each store, distributed around group mean mu_a
b = pm.Normal('Shift1Score', mu=mu_b, sd=sigma_b, shape=len(uniqueStores))
score_est = pm.math.sigmoid(a[storeIDX] + (b[storeIDX] * audits.Shift1Score.values))
# Data likelihood
y_like = pm.Normal('y_like', mu=score_est, sd=eps, observed=audits.FinalScore)
```

Even with the sigmoid here I still get a posterior where the HPC contains values greater than 1.

Help would be greatly appreciated! Thanks!