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?