Enhance formula parsing

[leostimpfle]

• Enable formulaic's MULTISTAGE syntax Implement formulaic's multistage syntax #1125
• Enable formulaic's MULTIPART syntax Use formulaic's MULTIPART syntax #1213
• Use stateful_transform for fixed effects encoding Implement fixed effects encoding as formulaic transformation #1218

To do

• The ^ operator is currently reserved for interactions of fixed effects (see here). This is necessary only because the operator expects a number on the right side (e.g., X^2). We could avoid this if we decided to use a different symbol for fixed effect interactions (e.g., f1:f2).
• Validate that the stateful_transform works correctly on the captured context (see here and related to Enable formulaic to parse custom data transforms from context #769).
• Set transforms consistently across project to address Bug: predict() method fails with new data and pyfixest special syntax - i(), C(), var1^var2 operators #684
• Clean up tests to remove deprecated syntax (Y+Y2 ~X1 should be replaced with sw(Y, Y2) ~ X1; Y ~ X1 | X2 ~ Z2 with Y ~ X1 + [X2 ~ Z2])
• formulaic.formula.Formula.required_variables calls ast.parse(factor.expr, mode="eval") which might fail if variable names are not valid Python expressions (e.g., 0_X2_1). This, however, is necessary to account for transformed variables (e.g., Y ~ C(X2) + [X2 ~ Z2]).
• Guard against specification of multiple multistage parts. For example, we do not support Y ~ [X1 ~ Z1] + [X2 ~ Z2].
• Guard against specification of more than two formula parts (we only allow a single second part for fixed effects).

[codecov]

Codecov Report

❌ Patch coverage is 96.17225% with 8 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
pyfixest/estimation/formula/parse.py	91.57%	8 Missing ⚠️

Flag	Coverage Δ
core-tests	71.25% <91.34%> (+0.24%)	⬆️
test-r-core	52.74% <91.86%> (+0.14%)	⬆️
test-r-extended	19.27% <32.53%> (+0.52%)	⬆️
test-r-fixest	40.01% <91.38%> (+0.17%)	⬆️
tests-extended	?

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
pyfixest/did/did2s.py	89.42% <100.00%> (+0.10%)	⬆️
pyfixest/estimation/FixestMulti_.py	82.01% <ø> (ø)
pyfixest/estimation/formula/__init__.py	100.00% <100.00%> (ø)
pyfixest/estimation/formula/model_matrix.py	95.23% <100.00%> (-0.08%)	⬇️
...stimation/formula/transforms/factor_interaction.py	95.83% <100.00%> (ø)
...ation/formula/transforms/fixed_effects_encoding.py	100.00% <100.00%> (ø)
pyfixest/estimation/formula/transforms/misc.py	100.00% <100.00%> (ø)
pyfixest/estimation/formula/utils.py	97.50% <100.00%> (+0.20%)	⬆️
pyfixest/estimation/models/feols_.py	87.44% <100.00%> (-4.77%)	⬇️
pyfixest/estimation/models/feols_compressed_.py	80.23% <100.00%> (ø)
... and 3 more

... and 4 files with indirect coverage changes

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[leostimpfle]

@s3alfisc The core changes to formula parsing are now ready. Feel free to have a look and let me know any comments. I'll continue to work through the to-dos listed above.

[s3alfisc]

Just took a quick look and was thinking - maybe it would be best if we'd do a pair review for this through a call? I would make sure to spent some time with it before to come prepared 😃

[leostimpfle]

Very happy to jump on a call!