Add `ZeroSumNormal` support

[AlexAndorra]

Currently, Bambi uses reference-encoding by default when categorical predictors and / or a Categorical/Multinomial likelihood is present in the model. It'd be great to add the choice to use a zero-sum constraint, instead of a reference-encoding one, since many modeling cases involve categories without clear placebo/reference.

It shouldn't be too hard (famous last words), since PyMC already has ZeroSumNormal.

cc @jessegrabowski @canyon289

[tomicapretto]

There's a hack to do it, which is to build the indicator columns yourself and then pass them to the formula and use a ZeroSumNormal prior for that term. But it's ugly and very confusing.

The problem I see with a straightforward implementation is that we would need to somehow intercept the creation of the design matrix to remove the factor with the ZeroSumNormal prior. I think it would be better to modify formulae so it supports something like ensure_full_rank in here https://matthewwardrop.github.io/formulaic/latest/guides/model_specs/

[Chirag3841]

@AlexAndorra I guess here we can add a sum encoding option: use Formulaic sum-to-zero contrasts, then assign pm.ZeroSumNormal to the categorical coefficients instead of reference (treatment) dummies.

[AlexAndorra]

What would the API look like for the user @Chirag3841 ?

[Chirag3841]

@AlexAndorra model = bmb.Model(
"y ~ x + cat",
data,
categorical_encoding="sum"
)
Like that
where we are assigning categorical_encoding in init part of model.py and we can add zero-sum encoding for categorical predictors in else part.

[AlexAndorra]

That's be great @Chirag3841 ! Something like categorical_encoding="zero-sum" and categorical_encoding="reference" would be even clearer, if possible

[Chirag3841]

@AlexAndorra I would like to solve this issue too if anyone had not taken it yet.

[AlexAndorra]

That'd be great @Chirag3841 ! I think it's up for grabs (cc @tomicapretto )