Trying to use ZeroSUMNormal and not understanding results

Questions v5
7

Sorry, totally my fault, I didn’t think about the number at all…
The priors in the model really don’t fit at all, I get what I think is reasonable parameters if I fix those up a bit (also switched to measuring mass in kg, to make the numbers a bit more managable):

species_idx, species = penguins['species'].factorize(sort=True)
COORDS = {"species": species}

with pm.Model(coords=COORDS) as model_zsn:

    intercept = pm.Normal("intercept", sigma=10)
    species_sigma = pm.HalfNormal("species_sigma", sigma=1)
    α_species = pm.ZeroSumNormal("α_species", sigma=species_sigma, dims="species")

    species_id = pm.ConstantData("species_id", species_idx)
    mu = intercept + α_species[species_id]

    σ = pm.HalfNormal("σ", 0.5)
    mass = pm.Normal("mass", mu, σ, observed=penguins["body_mass_g"] / 1000)

    trace_zsn = pm.sample()

az.summary(trace_zsn, round_to=2)

It might also be a good idea to check if modeling the mass on log scale fits the data better.