# Mass near edges in transformed distribution

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?

logit((1-2*alpha) * x[i] + alpha) ~ normal(mu_x, sigma_x)

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).