I am fitting a model in Stan where an individual-specific parameter x_i \in [0,1] is modeled as

```
logit(x[i]) ~ normal(mu_x, sigma_x)
# Jacobian adjustment omitted from example for brevity
```

where `mu_x`

and `sigma_x`

are hyperparameters.

During PPC I found that the model would really like to have mass near `0`

for some `x[i]`

. What’s the recommended way to deal with this?

I can think of an ad-hoc adjustment like

```
logit((1-2*alpha) * x[i] + alpha) ~ normal(mu_x, sigma_x)
# Jacobian adjustment omitted from example for brevity
```

which would “shrink” the edges and allow mass there, with either `alpha=0.1`

or something like that as data, or estimated (if identified, about which I am concerned, for numerical reasons).

Is there anything more disciplined?