[re-inserted OP in BCC]
We have to put this all in context. Let's assume
we're talking about parameters for an IRT model.
If the goal is to identify the model by using
> alpha_adj <- alpha - mean(alpha)
and then using alpha_adj in the likelihood rather than alpha,
it just won't work in Stan. Read the problematic posteriors
chapter of the manual for both examples and theory. The synopsis
is that NUTS will run off forever and never turn around if
the parameter alpha isn't identified in the model. It's
not enough for the transformed parameter to be identified.
As Andrew says, using a centered prior on alpha with a constrained
scale relative to beta will only roughly center each posterior draw.
But it will identify the model in the sense Andrew describes in
his regression book with Jennifer.
Also, if you do a penalized MLE, you should get the alpha properly
centered if beta gets an uninformative prior.
alpha ~ normal(0,1)
beta ~ uniform(-inf,inf)
This lets the alpha identify the scale and location (in the sense
of "identify" Andrew talks about in his regression book with Jennifer),
while letting beta float. This is the direction Sophia Rabe-Hesketh
recommended because in IRT models the focus is usually on the test
questions (beta), not the students (alpha). Of course, we'd more usually
put a hierarchical prior on beta in Bayesian models:
beta ~ normal(mu_beta, sigma_beta);
- Bob