AverageDerivative

Average derivative estimator for continuous treatments

from _api_doc_utils import *

1 Where it fits

Group: Causal inference

AverageDerivative targets an average marginal effect of a scalar continuous treatment. The class exposes three related estimating equations through method='ob', 'ipw', or 'dr'.

The doubly robust option combines outcome-bridge and weighting components, while the other options expose the individual pieces.

2 Python API

Constructor: cm.AverageDerivative

Call fit(y, d, w). The summary reports method, coef, se, and vcov. There is no predict() method because the object is a semiparametric target rather than a full conditional mean model.

print(inspect.signature(cm.AverageDerivative))
(method='dr', fd_eps=1e-06)
cls = cm.AverageDerivative
display(HTML(html_table(["Public method"], public_methods(cls))))
Public method
fit(self, /, y, d, w)
summary(self, /, vcov=None, lags=None, clusters=None)

3 Minimal example

rng=np.random.default_rng(12)
w=rng.normal(size=(320,2)); d=.2+w@np.array([.5,-.3])+rng.normal(scale=.7,size=320); y=.8*d+w@np.array([.2,-.1])+rng.normal(scale=.5,size=320)
model=cm.AverageDerivative(method="dr"); model.fit(y,d,w)
print(model.summary())
{'method': 'dr', 'coef': 0.775623613574262, 'se': 0.04377879620928101, 'vcov': array([[0.00191658]])}

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(112); w=rng.normal(size=(120,2)); d=.2+w@np.array([.5,-.3])+rng.normal(size=120)*.7; y=.8*d+w@np.array([.2,-.1])+rng.normal(size=120)*.5
model=cm.AverageDerivative(method='dr'); model.fit(y,d,w)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))
summary() key shape
method ()
coef ()
se ()
vcov (1, 1)