PartiallyLinearDML

Cross-fit partially linear Double ML

Code 
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.

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

3 Minimal example

Code 
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])

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.

Code 
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))))