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Group & conditional effects with DoubleML (GATE / CATE)

@doubleml ✓ P D · Jun 4, 2026 · 836 views

Source DoubleML — Bach, Chernozhukov, Kurz & Spindler

@misc{doubleml,
  title        = {DoubleML},
  author       = {Bach and Chernozhukov and Kurz and Spindler},
  howpublished = {\url{https://docs.doubleml.org/}},
  note         = {Software / documentation}
}

Summary by StatsDoge

Slice the average effect: Group Average Treatment Effects and a CATE surface from a debiased IRM, with simultaneous confidence bands.

Input · what goes in

Outcome Y, binary treatment D, covariates X — plus the grouping variable(s) you want effects for.

Show data format & exampleHide example

Format — one row per unit: y, d ∈ {0,1}, covariates X.

  y     d   age  inc   educ
 1.2    1   41   38k   13
-0.3    0   53   21k   11

Pipeline · the recipe ⑂ has parallel branches

↑ Click any step in the diagram to read its logic, code, assumptions & discussion.

Data prep

Build DoubleMLData (y, d, X)

Data preparation — shapes the raw inputs into what the estimator expects.

What happens here

Declare outcome, binary treatment and covariates.

Reads from the input data Feeds into the final output

Key code

dml_data = dml.DoubleMLData(df, y_col='y', d_cols='d', x_cols=X)

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Estimation

Fit an Interactive Regression Model (IRM)

The core estimate — where the causal quantity itself is computed.

What happens here

Cross-fitted, Neyman-orthogonal IRM with ML nuisances — the per-unit signal for heterogeneity.

Formula

\psi(W; heta,\eta)=g_1(X)-g_0(X)+\dfrac{D\,(Y-g_1(X))}{m(X)}-\dfrac{(1-D)(Y-g_0(X))}{1-m(X)}- heta

Reads from the input data Feeds into the final output

Key code

dml_irm = dml.DoubleMLIRM(dml_data, ml_g, ml_m).fit()

Reference / docs ↗

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Heterogeneity

Group Average Treatment Effects

Heterogeneity — who is affected, and by how much, not just on average.

What happens here

Average the orthogonal signal within each group to get a GATE per subgroup.

Formula

heta_g=\mathbb{E}\!\left[\, heta(X)\mid G=g\, ight]

Reads from the input data Feeds into the final output

Key code

gate = dml_irm.gate(groups=groups); gate.confint(joint=True)

Reference / docs ↗

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Heterogeneity

CATE via a basis expansion

Heterogeneity — who is affected, and by how much, not just on average.

What happens here

Project the signal onto a spline basis to trace a smooth CATE in a covariate.

Formula

heta(x)\approx \phi(x)^ opeta,\qquad heta(x)=\mathbb{E}\!\left[\,Y(1)-Y(0)\mid X=x\, ight]

Reads from the input data Feeds into the final output

Key code

cate = dml_irm.cate(basis); cate.confint(X_grid, joint=True)

Reference / docs ↗

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Reporting

Plot with simultaneous bands

Reporting — turn the numbers into a figure or table a reader can act on.

What happens here

Show GATE bars and the CATE curve with joint (not pointwise) confidence bands.

Reads from the input data Feeds into the final output

Key code

# matplotlib: GATE bars + CATE curve with joint CIs

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Output · what you get 3 figures

Fig 1Group Average Treatment Effects — the effect within each subgroup, with joint confidence bands.

Fig 2CATE estimated along a continuous covariate, with simultaneous bands.

Fig 3A smooth CATE surface from a spline basis projection of the orthogonal signal.

Figures reproduced from DoubleML — Bach, Chernozhukov, Kurz & Spindler — unofficial community showcase; all credit to the original authors.

⚠️ Unofficial community showcase of a DoubleML example. Not affiliated with the authors; figures are from the public documentation. All credit to Bach, Chernozhukov, Kurz & Spindler.

Slice the average effect: Group Average Treatment Effects and a CATE surface from a debiased IRM, with simultaneous confidence bands.

Group & conditional effects with DoubleML (GATE / CATE)

Input · what goes in

Pipeline · the recipe ⑂ has parallel branches

Output · what you get 3 figures

Discussion (0)