Understanding multilevel model coefficients

Questions version agnostic
2

  1. a[0] is the parameter associated with the first actor. a_bar is a separate parameter that is used to specify the prior on the mean of a[0] (and a[1], etc.). Parameters like a_bar (and sigma_a, etc.) are sometimes referred to as hyperparameters. So the influence of a_bar on a[0] is already taken care of during model specification and the posterior samples you see of a[0] can be interpreted without adding a_bar or anything like that.

  2. Creating a pm.Deterministic saving the values into the trace. If you don’t want to save them, then you just do:

pulled_left = pm.Binomial("pulled_left",
                          1,
                          pm.math.invlogit(a[actor_] + 
                                           g[block_] + 
                                           b[treatment_]
                          ), 
                          observed=d.pulled_left.values
)
  1. If you are unfamiliar with interpreting coefficients in GLMs, I would poke around for something like this or this until you find one that makes sense to you.