Add Support for (in-memory) Regression compression a la duckreg

[s3alfisc]

Supersedes #574 .

• Adds a class for compressed regression, FeolsCompressed.
• Adds use_compression argument to pf.feols() that supports up to two-way fixed effects via the Mundlak transform, which is run automatically when users opt into fixed effects syntax.
• Supported inference: iid, hetero. When Mundlak is used, only wild cluster bootstrap inference is supported. Cluster variables need to be part of the model.
• No prediction method is supported yet.

%load_ext autoreload
%autoreload 2

import pyfixest as pf
from pyfixest.estimation.estimation import feols
import pytest
import pandas as pd
import numpy as np

data = pf.get_data()

fit = pf.feols("Y ~ X1 + X2| f1", data=data, vcov = "hetero", ssc = pf.ssc(adj = False, cluster_adj = False))
fit_c = pf.feols("Y ~ X1 + X2 + C(f1)", data = data, use_compression=True, vcov = "hetero", ssc = pf.ssc(adj = False, cluster_adj = False))

pf.etable([fit, fit_c], keep = ["X1", "X2"], digits = 6)

FYI @apoorvalal

[s3alfisc]

Implementation / Status:

For compressed estimation, fixed effects are always handled via the Mundlak transform. Up to two-way fixed effects are supported. There are no checks if the input data is a panel when using two fixed effects. Maybe we should have one?

Unit tests are implemented and pass.

Currently not supported: if a cluster variable is not part of the model formula.

[s3alfisc]

@pre-commit.ci autofix

[s3alfisc]

Something appears off with Mundlak transform iid & hetero SEs. Coefs are matching though.

[s3alfisc]

pre-commit.ci autofix

[codecov]

Codecov Report

Attention: Patch coverage is 86.13861% with 28 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
pyfixest/estimation/feols_compressed_.py	83.33%	26 Missing ⚠️
pyfixest/estimation/estimation.py	91.66%	1 Missing ⚠️
pyfixest/report/summarize.py	75.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
pyfixest/estimation/FixestMulti_.py	81.72% <100.00%> (+1.14%)	⬆️
pyfixest/estimation/feols_.py	82.12% <100.00%> (-1.83%)	⬇️
pyfixest/estimation/model_matrix_fixest_.py	85.08% <100.00%> (+0.16%)	⬆️
pyfixest/estimation/estimation.py	95.12% <91.66%> (+19.40%)	⬆️
pyfixest/report/summarize.py	90.09% <75.00%> (-0.25%)	⬇️
pyfixest/estimation/feols_compressed_.py	83.33% <83.33%> (ø)

... and 1 file with indirect coverage changes