Jacobian determinant adjustment for Rstanarm's implementation of the induced dirichlet prior in stan_polr

Developers
5

Is this an empirical observation, or an intuition?

I’ve tried both with simulated data and the code from rstanarm is typically much faster. However, the comparison isn’t exactly fair because the stan_polr also implements the R2D2 prior on \boldsymbol{\beta} (although it does in a weird way, using a unit_vector instead of a simplex). I would like to experiment with the R2D2 prior myself but I don’t exactly understand how to implement it with ordered logistic regression. I discuss this in my last reply from this thread if you’d like to take a look.

If you’re interested in digging here, you might check whether the two approaches are literally the same underlying parameterization, with one writing out in Stan code what the other hides behind the relatively more complicated simplex constraint.

By “writing out the simplex constraint”, do you mean doing something similar to what’s described in this “change of variable” example where the lognormal distribution is coded as the logarithm of y > 0 is assigned a normal distribution? So something like this :

parameters {
  real<lower=0> y;
}
model {
  log(y) ~ normal(mu, sigma);
  target += -log(y);
}

The stan manual chapter you linked doesn’t really give code examples so I’m not sure how I would write them out.