PartiallyLinearDML

Cross-fit partially linear Double ML

from _api_doc_utils import *

1 Where it fits

Group: Causal inference

PartiallyLinearDML estimates the treatment coefficient in

\[ y = \theta d + g(x) + u, \qquad d = m(x) + v, \]

using cross-fitted ridge nuisance regressions. The final coefficient is estimated from the orthogonalized residual-on-residual score. Fold membership is a deterministic seeded shuffle, so equal seeds reproduce assignments and different seeds change them.

2 Python API

Constructor: cm.PartiallyLinearDML

Use PartiallyLinearDML(penalty=None, cv=5, n_folds=5, seed=42), then fit(y, d, x). summary() reports the coefficient, robust standard error, covariance, and selected nuisance penalties by fold.

print(inspect.signature(cm.PartiallyLinearDML))

(penalty=None, cv=5, n_folds=5, seed=42)

cls = cm.PartiallyLinearDML
display(HTML(html_table(["Public method"], public_methods(cls))))

Public method
fit(self, /, y, d, x)
summary(self, /, vcov=None, lags=None, clusters=None)

3 Minimal example

rng = np.random.default_rng(13)
x = rng.normal(size=(400, 4))
d = 0.3 + x @ np.array([0.5, -0.4, 0.2, 0.1]) + rng.normal(scale=0.8, size=400)
y = 1.3 * d + x @ np.array([0.4, -0.2, 0.1, 0.3]) + rng.normal(scale=0.6, size=400)
model = cm.PartiallyLinearDML(penalty=np.logspace(-4, 1, 10), cv=3, n_folds=4, seed=1)
model.fit(y, d, x)
print(model.summary()['coef'])
print(model.summary()['outcome_penalties'][:2])

1.357518301172487
[2.7825594e+00 1.0000000e-04]

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

rng = np.random.default_rng(113)
x = rng.normal(size=(160, 4))
d = 0.3 + x @ np.array([0.5, -0.4, 0.2, 0.1]) + rng.normal(size=160) * 0.8
y = 1.3 * d + x @ np.array([0.4, -0.2, 0.1, 0.3]) + rng.normal(size=160) * 0.6
model = cm.PartiallyLinearDML(penalty=np.logspace(-4, 1, 6), cv=3, n_folds=4, seed=1)
model.fit(y, d, x)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))

summary() key	shape
coef	()
se	()
vcov	(1, 1)
outcome_penalties	(4,)
treatment_penalties	(4,)