diff-diff/diff_diff/triple_diff.py at main · UtilityTools/diff-diff · GitHub

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"""

Triple Difference (DDD) estimators.

Implements the methodology from Ortiz-Villavicencio & Sant'Anna (2025)

"Better Understanding Triple Differences Estimators" for causal inference

when treatment requires satisfying two criteria:

1. Belonging to a treated group (e.g., a state with a policy)

2. Being in an eligible partition (e.g., women, low-income, etc.)

This module provides regression adjustment, inverse probability weighting,

and doubly robust estimators that correctly handle covariate adjustment,

unlike naive implementations. Standard errors use the efficient influence

function: SE = std(IF) / sqrt(n), which is inherently heteroskedasticity-

robust. Cluster-robust SEs are available via the ``cluster`` parameter.

The DDD is computed via three pairwise DiD comparisons matching R's

``triplediff::ddd()`` package (panel=FALSE mode).

Reference:

Ortiz-Villavicencio, M., & Sant'Anna, P. H. C. (2025).

Better Understanding Triple Differences Estimators.

arXiv:2505.09942.

"""

import warnings

from dataclasses import dataclass, field

from typing import Any, Dict, List, Optional, Tuple

import numpy as np

import pandas as pd

from diff_diff.linalg import solve_logit, solve_ols

from diff_diff.results import _format_survey_block, _get_significance_stars

from diff_diff.utils import safe_inference

_MIN_CELL_SIZE = 10

# =============================================================================

# Results Classes

# =============================================================================

@dataclass

class TripleDifferenceResults:

"""

Results from Triple Difference (DDD) estimation.

Provides access to the estimated average treatment effect on the treated

(ATT), standard errors, confidence intervals, and diagnostic information.

Attributes

----------

att : float

Average Treatment effect on the Treated (ATT).

This is the effect on units in the treated group (G=1) and eligible

partition (P=1) after treatment (T=1).

se : float

Standard error of the ATT estimate.

t_stat : float

T-statistic for the ATT estimate.

p_value : float

P-value for the null hypothesis that ATT = 0.

conf_int : tuple[float, float]

Confidence interval for the ATT.

n_obs : int

Total number of observations used in estimation.

n_treated_eligible : int

Number of observations in treated group and eligible partition.

n_treated_ineligible : int

Number of observations in treated group and ineligible partition.

n_control_eligible : int

Number of observations in control group and eligible partition.

n_control_ineligible : int

Number of observations in control group and ineligible partition.

estimation_method : str

Estimation method used: "dr" (doubly robust), "reg" (regression

adjustment), or "ipw" (inverse probability weighting).

alpha : float

Significance level used for confidence intervals.

"""

att: float

se: float

t_stat: float

p_value: float

conf_int: Tuple[float, float]

n_obs: int

n_treated_eligible: int

n_treated_ineligible: int

n_control_eligible: int

n_control_ineligible: int

estimation_method: str

alpha: float = 0.05

# Group means for diagnostics

group_means: Optional[Dict[str, float]] = field(default=None)

# Propensity score diagnostics (for IPW/DR)

pscore_stats: Optional[Dict[str, float]] = field(default=None)

# Regression diagnostics

r_squared: Optional[float] = field(default=None)

# Covariate balance statistics

covariate_balance: Optional[pd.DataFrame] = field(default=None, repr=False)

# Inference details

inference_method: str = field(default="analytical")

n_bootstrap: Optional[int] = field(default=None)

n_clusters: Optional[int] = field(default=None)

# Survey design metadata (SurveyMetadata instance from diff_diff.survey)

survey_metadata: Optional[Any] = field(default=None)

# EPV diagnostics per subgroup comparison

epv_diagnostics: Optional[Dict[int, Dict[str, Any]]] = field(

default=None, repr=False

)

epv_threshold: float = 10

pscore_fallback: str = "error"

def __repr__(self) -> str:

"""Concise string representation."""

return (

f"TripleDifferenceResults(ATT={self.att:.4f}{self.significance_stars}, "

f"SE={self.se:.4f}, p={self.p_value:.4f}, method={self.estimation_method})"

)

def summary(self, alpha: Optional[float] = None) -> str:

"""

Generate a formatted summary of the estimation results.

Parameters

----------

alpha : float, optional

Significance level for confidence intervals. Defaults to the

alpha used during estimation.

Returns

-------

str

Formatted summary table.

"""

alpha = alpha or self.alpha

conf_level = int((1 - alpha) * 100)

lines = [

"=" * 75,

"Triple Difference (DDD) Estimation Results".center(75),

"=" * 75,

"",

f"{'Estimation method:':<30} {self.estimation_method:>15}",

f"{'Total observations:':<30} {self.n_obs:>15}",

"",

"Sample Composition by Cell:",

f" {'Treated group, Eligible:':<28} {self.n_treated_eligible:>15}",

f" {'Treated group, Ineligible:':<28} {self.n_treated_ineligible:>15}",

f" {'Control group, Eligible:':<28} {self.n_control_eligible:>15}",

f" {'Control group, Ineligible:':<28} {self.n_control_ineligible:>15}",

]

if self.r_squared is not None:

lines.append(f"{'R-squared:':<30} {self.r_squared:>15.4f}")

# Add survey design info

if self.survey_metadata is not None:

sm = self.survey_metadata

lines.extend(_format_survey_block(sm, 75))

if self.inference_method != "analytical":

lines.append(f"{'Inference method:':<30} {self.inference_method:>15}")

if self.n_bootstrap is not None:

lines.append(f"{'Bootstrap replications:':<30} {self.n_bootstrap:>15}")

if self.n_clusters is not None:

lines.append(f"{'Number of clusters:':<30} {self.n_clusters:>15}")

lines.extend(

[

"",

"-" * 75,

f"{'Parameter':<15} {'Estimate':>12} {'Std. Err.':>12} {'t-stat':>10} {'P>|t|':>10} {'':>5}",

"-" * 75,

f"{'ATT':<15} {self.att:>12.4f} {self.se:>12.4f} {self.t_stat:>10.3f} {self.p_value:>10.4f} {self.significance_stars:>5}",

"-" * 75,

"",

f"{conf_level}% Confidence Interval: [{self.conf_int[0]:.4f}, {self.conf_int[1]:.4f}]",

]

)

# EPV diagnostics block (if any subgroup has low EPV)

if self.epv_diagnostics:

low_epv = {k: v for k, v in self.epv_diagnostics.items() if v.get("is_low")}

if low_epv:

n_affected = len(low_epv)

n_total = len(self.epv_diagnostics)

min_entry = min(low_epv.values(), key=lambda v: v["epv"])

lines.extend(

[

"",

"-" * 75,

"EPV Diagnostics".center(75),

"-" * 75,

f"WARNING: Low Events Per Variable (EPV) in "

f"{n_affected} of {n_total} subgroup comparison(s).",

f"Minimum EPV: {min_entry['epv']:.1f}. "

f"Threshold: {self.epv_threshold:.0f}.",

"Consider: estimation_method='reg' or fewer covariates.",

"Call results.epv_summary() for details.",

"-" * 75,

]

)

# Show group means if available

if self.group_means:

lines.extend(

[

"",

"-" * 75,

"Cell Means (Y):",

"-" * 75,

]

)

for cell, mean in self.group_means.items():

lines.append(f" {cell:<35} {mean:>12.4f}")

# Show propensity score diagnostics if available

if self.pscore_stats:

lines.extend(

[

"",

"-" * 75,

"Propensity Score Diagnostics:",

"-" * 75,

]

)

for stat, value in self.pscore_stats.items():

lines.append(f" {stat:<35} {value:>12.4f}")

lines.extend(

[

"",

"Signif. codes: '***' 0.001, '**' 0.01, '*' 0.05, '.' 0.1",

"=" * 75,

]

)

return "\n".join(lines)

def print_summary(self, alpha: Optional[float] = None) -> None:

"""Print the summary to stdout."""

print(self.summary(alpha))

def to_dict(self) -> Dict[str, Any]:

"""

Convert results to a dictionary.

Returns

-------

Dict[str, Any]

Dictionary containing all estimation results.

"""

result = {

"att": self.att,

"se": self.se,

"t_stat": self.t_stat,

"p_value": self.p_value,

"conf_int_lower": self.conf_int[0],

"conf_int_upper": self.conf_int[1],

"n_obs": self.n_obs,

"n_treated_eligible": self.n_treated_eligible,

"n_treated_ineligible": self.n_treated_ineligible,

"n_control_eligible": self.n_control_eligible,

"n_control_ineligible": self.n_control_ineligible,

"estimation_method": self.estimation_method,

"inference_method": self.inference_method,

}

if self.r_squared is not None:

result["r_squared"] = self.r_squared

if self.n_bootstrap is not None:

result["n_bootstrap"] = self.n_bootstrap

if self.n_clusters is not None:

result["n_clusters"] = self.n_clusters

if self.survey_metadata is not None:

sm = self.survey_metadata

result["weight_type"] = sm.weight_type

result["effective_n"] = sm.effective_n

result["design_effect"] = sm.design_effect

result["sum_weights"] = sm.sum_weights

result["n_strata"] = sm.n_strata

result["n_psu"] = sm.n_psu

result["df_survey"] = sm.df_survey

return result

def to_dataframe(self) -> pd.DataFrame:

"""

Convert results to a pandas DataFrame.

Returns

-------

pd.DataFrame

DataFrame with estimation results.

"""

return pd.DataFrame([self.to_dict()])

@property

def is_significant(self) -> bool:

"""Check if the ATT is statistically significant at the alpha level."""

return bool(self.p_value < self.alpha)

@property

def significance_stars(self) -> str:

"""Return significance stars based on p-value."""

return _get_significance_stars(self.p_value)

def epv_summary(self, show_all: bool = False) -> pd.DataFrame:

"""

Return per-subgroup EPV diagnostics as a DataFrame.

Parameters

----------

show_all : bool, default False

If False, only show subgroups with low EPV. If True, show all.

Returns

-------

pd.DataFrame

Columns: subgroup, epv, n_events, n_params, is_low.

"""

if not self.epv_diagnostics:

return pd.DataFrame(

columns=["subgroup", "epv", "n_events", "n_params", "is_low"]

)

rows = []

for sg, diag in sorted(self.epv_diagnostics.items()):

if show_all or diag.get("is_low", False):

rows.append(

{

"subgroup": sg,

"epv": diag.get("epv"),

"n_events": diag.get("n_events"),

"n_params": diag.get("k"),

"is_low": diag.get("is_low", False),

}

)

cols = ["subgroup", "epv", "n_events", "n_params", "is_low"]

return pd.DataFrame(rows, columns=cols) if rows else pd.DataFrame(columns=cols)

# =============================================================================

# Helper Functions

# =============================================================================

# Main Estimator Class

# =============================================================================

class TripleDifference:

"""

Triple Difference (DDD) estimator.

Estimates the Average Treatment effect on the Treated (ATT) when treatment

requires satisfying two criteria: belonging to a treated group AND being

in an eligible partition of the population. The DDD design was popularized

by Gruber (1994) [2]_.

This implementation follows Ortiz-Villavicencio & Sant'Anna (2025) [1]_,

which shows that naive DDD implementations (difference of two DiDs,

three-way fixed effects) are invalid when covariates are needed for

identification.

Parameters

----------

estimation_method : str, default="dr"

Estimation method to use:

- "dr": Doubly robust (recommended). Consistent if either the outcome

model or propensity score model is correctly specified.

- "reg": Regression adjustment (outcome regression).

- "ipw": Inverse probability weighting.

robust : bool, default=True

Whether to use heteroskedasticity-robust standard errors.

Note: influence function-based SEs are inherently robust to

heteroskedasticity, so this parameter has no effect. Retained

for API compatibility.

cluster : str, optional

Column name for cluster-robust standard errors. When provided,

SEs are computed using the Liang-Zeger cluster-robust variance

estimator on the influence function.

alpha : float, default=0.05

Significance level for confidence intervals.

pscore_trim : float, default=0.01

Trimming threshold for propensity scores. Scores below this value

or above (1 - pscore_trim) are clipped to avoid extreme weights.

rank_deficient_action : str, default="warn"

Action when design matrix is rank-deficient (linearly dependent columns):

- "warn": Issue warning and drop linearly dependent columns (default)

- "error": Raise ValueError

- "silent": Drop columns silently without warning

epv_threshold : float, default=10

Events Per Variable threshold for propensity score logit.

When the ratio of minority-class observations to predictor

variables (excluding intercept) falls below this value, a

warning is emitted (or ``ValueError`` raised if

``rank_deficient_action="error"``). Based on Peduzzi et al.

(1996). Only applies to IPW and DR estimation methods.

pscore_fallback : str, default="error"

Action when propensity score estimation fails:

- "error": Raise the exception (default)

- "unconditional": Fall back to unconditional propensity with

a warning. For IPW, drops all covariates. For DR, the

propensity model becomes unconditional but outcome regression

still uses covariates.

When ``rank_deficient_action="error"``, errors are always

re-raised regardless of this setting.

Attributes

----------

results_ : TripleDifferenceResults

Estimation results after calling fit().

is_fitted_ : bool

Whether the model has been fitted.

Examples

--------

Basic usage with a DataFrame:

>>> import pandas as pd

>>> from diff_diff import TripleDifference

>>>

>>> # Data where treatment affects women (partition=1) in states

>>> # that enacted a policy (group=1)

>>> data = pd.DataFrame({

... 'outcome': [...],

... 'group': [1, 1, 0, 0, ...], # 1=policy state, 0=control state

... 'partition': [1, 0, 1, 0, ...], # 1=women, 0=men

... 'post': [0, 0, 1, 1, ...], # 1=post-treatment period

... })

>>>

>>> # Fit using doubly robust estimation

>>> ddd = TripleDifference(estimation_method="dr")

>>> results = ddd.fit(

... data,

... outcome='outcome',

... group='group',

... partition='partition',

... time='post'

... )

>>> print(results.att) # ATT estimate

With covariates (properly handled unlike naive DDD):

>>> results = ddd.fit(

... data,

... outcome='outcome',

... group='group',

... partition='partition',

... time='post',

... covariates=['age', 'income']

... )

Notes

-----

The DDD estimator is appropriate when:

1. Treatment affects only units satisfying BOTH criteria:

- Belonging to a treated group (G=1), e.g., states with a policy

- Being in an eligible partition (P=1), e.g., women, low-income

2. The DDD parallel trends assumption holds: the differential trend

between eligible and ineligible partitions would have been the same

across treated and control groups, absent treatment.

This is weaker than requiring separate parallel trends for two DiDs,

as biases can cancel out in the differencing.

References

----------

.. [1] Ortiz-Villavicencio, M., & Sant'Anna, P. H. C. (2025).

Better Understanding Triple Differences Estimators.

arXiv:2505.09942.

.. [2] Gruber, J. (1994). The incidence of mandated maternity benefits.

American Economic Review, 84(3), 622-641.

"""

def __init__(

self,

estimation_method: str = "dr",

robust: bool = True,

cluster: Optional[str] = None,

alpha: float = 0.05,

pscore_trim: float = 0.01,

rank_deficient_action: str = "warn",

epv_threshold: float = 10,

pscore_fallback: str = "error",

if estimation_method not in ("dr", "reg", "ipw"):

raise ValueError(

f"estimation_method must be 'dr', 'reg', or 'ipw', " f"got '{estimation_method}'"

)

if rank_deficient_action not in ["warn", "error", "silent"]:

raise ValueError(

f"rank_deficient_action must be 'warn', 'error', or 'silent', "

f"got '{rank_deficient_action}'"

)

if epv_threshold <= 0:

raise ValueError(

f"epv_threshold must be > 0, got {epv_threshold}"

)

if pscore_fallback not in {"error", "unconditional"}:

raise ValueError(

f"pscore_fallback must be 'error' or 'unconditional', "

f"got '{pscore_fallback}'"

)

self.estimation_method = estimation_method

self.robust = robust

self.cluster = cluster

self.alpha = alpha

self.pscore_trim = pscore_trim

self.rank_deficient_action = rank_deficient_action

self.epv_threshold = epv_threshold

self.pscore_fallback = pscore_fallback

self.is_fitted_ = False

self.results_: Optional[TripleDifferenceResults] = None

def fit(

self,

data: pd.DataFrame,

outcome: str,

group: str,

partition: str,

time: str,

covariates: Optional[List[str]] = None,

survey_design=None,

) -> TripleDifferenceResults:

"""

Fit the Triple Difference model.

Parameters

----------

data : pd.DataFrame

DataFrame containing all variables.

outcome : str

Name of the outcome variable column.

group : str

Name of the group indicator column (0/1).

1 = treated group (e.g., states that enacted policy).

0 = control group.

partition : str

Name of the partition/eligibility indicator column (0/1).

1 = eligible partition (e.g., women, targeted demographic).

0 = ineligible partition.

time : str

Name of the time period indicator column (0/1).

1 = post-treatment period.

0 = pre-treatment period.

covariates : list of str, optional

List of covariate column names to adjust for.

These are properly incorporated using the selected estimation

method (unlike naive DDD implementations).

survey_design : SurveyDesign, optional

Survey design specification for complex survey data. When

provided, uses survey weights for estimation and Taylor Series

Linearization (TSL) for variance estimation. Supported with

all estimation methods ("reg", "ipw", "dr").

Returns

-------

TripleDifferenceResults

Object containing estimation results.

Raises

------

ValueError

If required columns are missing or data validation fails.

NotImplementedError

If survey_design is used with wild_bootstrap inference.

"""

# Reset replicate state from any previous fit

self._replicate_n_valid = None

# Resolve survey design if provided

from diff_diff.survey import (

_inject_cluster_as_psu,

_resolve_effective_cluster,

_resolve_survey_for_fit,

compute_survey_metadata,

)

resolved_survey, survey_weights, survey_weight_type, survey_metadata = (

_resolve_survey_for_fit(survey_design, data, "analytical")

)

if resolved_survey is not None and resolved_survey.weight_type != "pweight":

raise ValueError(

f"TripleDifference survey support requires weight_type='pweight', "

f"got '{resolved_survey.weight_type}'. The survey variance math "

f"assumes probability weights (pweight)."

)

# Validate inputs

self._validate_data(data, outcome, group, partition, time, covariates)

# Extract data

y = data[outcome].values.astype(float)

G = data[group].values.astype(float)

P = data[partition].values.astype(float)

T = data[time].values.astype(float)

# Store cluster IDs for SE computation

self._cluster_ids = data[self.cluster].values if self.cluster is not None else None

if self._cluster_ids is not None and np.any(pd.isna(data[self.cluster])):

raise ValueError(f"Cluster column '{self.cluster}' contains missing values")

# Resolve effective cluster and inject cluster-as-PSU for survey variance

if resolved_survey is not None:

effective_cluster_ids = _resolve_effective_cluster(

resolved_survey, self._cluster_ids, self.cluster

)

if effective_cluster_ids is not None:

resolved_survey = _inject_cluster_as_psu(resolved_survey, effective_cluster_ids)

if resolved_survey.psu is not None and survey_metadata is not None:

raw_w = (

data[survey_design.weights].values.astype(np.float64)

if survey_design.weights

else np.ones(len(data), dtype=np.float64)

)

survey_metadata = compute_survey_metadata(resolved_survey, raw_w)

# Get covariates if specified

X = None

if covariates:

X = data[covariates].values.astype(float)

if np.any(np.isnan(X)):

raise ValueError("Covariates contain missing values")

# Count observations in each cell

n_obs = len(y)

n_treated_eligible = int(np.sum((G == 1) & (P == 1)))

n_treated_ineligible = int(np.sum((G == 1) & (P == 0)))

n_control_eligible = int(np.sum((G == 0) & (P == 1)))

n_control_ineligible = int(np.sum((G == 0) & (P == 0)))

# Compute cell means for diagnostics

group_means = self._compute_cell_means(y, G, P, T, weights=survey_weights)

# Estimate ATT based on method

if self.estimation_method == "reg":

att, se, r_squared, pscore_stats, epv_diag = self._regression_adjustment(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

elif self.estimation_method == "ipw":

att, se, r_squared, pscore_stats, epv_diag = self._ipw_estimation(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

else: # doubly robust

att, se, r_squared, pscore_stats, epv_diag = self._doubly_robust(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

# Compute inference

# When survey design is active, use survey df (n_PSU - n_strata)

if survey_metadata is not None and survey_metadata.df_survey is not None:

df = survey_metadata.df_survey

# Override with effective replicate df only when replicates were dropped

if (hasattr(self, '_replicate_n_valid') and self._replicate_n_valid is not None

and resolved_survey is not None

and self._replicate_n_valid < resolved_survey.n_replicates):

df = self._replicate_n_valid - 1

survey_metadata.df_survey = self._replicate_n_valid - 1

# df <= 0 means insufficient rank for t-based inference

if df is not None and df <= 0:

df = 0 # Forces NaN from t-distribution

elif (resolved_survey is not None

and hasattr(resolved_survey, 'uses_replicate_variance')

and resolved_survey.uses_replicate_variance):

# Replicate design with undefined df (rank <= 1) — NaN inference

df = 0 # Forces NaN from t-distribution

else:

df = n_obs - 8 # Approximate df (8 cell means)

if covariates:

df -= len(covariates)

df = max(df, 1)

t_stat, p_value, conf_int = safe_inference(att, se, alpha=self.alpha, df=df)

# Get number of clusters if clustering

n_clusters = None

if self.cluster is not None:

n_clusters = data[self.cluster].nunique()

# Create results object

self.results_ = TripleDifferenceResults(

att=att,

se=se,

t_stat=t_stat,

p_value=p_value,

conf_int=conf_int,

n_obs=n_obs,

n_treated_eligible=n_treated_eligible,

n_treated_ineligible=n_treated_ineligible,

n_control_eligible=n_control_eligible,

n_control_ineligible=n_control_ineligible,

estimation_method=self.estimation_method,

alpha=self.alpha,

group_means=group_means,

pscore_stats=pscore_stats,

r_squared=r_squared,

inference_method="analytical",

n_clusters=n_clusters,

survey_metadata=survey_metadata,

epv_diagnostics=epv_diag if epv_diag else None,

epv_threshold=self.epv_threshold,

pscore_fallback=self.pscore_fallback,

)

self.is_fitted_ = True

return self.results_

def _validate_data(

self,

data: pd.DataFrame,

outcome: str,

group: str,

partition: str,

time: str,

covariates: Optional[List[str]] = None,

) -> None:

"""Validate input data."""

if not isinstance(data, pd.DataFrame):

raise TypeError("data must be a pandas DataFrame")

# Check required columns exist

required_cols = [outcome, group, partition, time]

if covariates:

required_cols.extend(covariates)

if self.cluster is not None:

required_cols.append(self.cluster)

missing_cols = [col for col in required_cols if col not in data.columns]

if missing_cols:

raise ValueError(f"Missing columns in data: {missing_cols}")

# Check for missing values in required columns

for col in [outcome, group, partition, time]:

if data[col].isna().any():

raise ValueError(f"Column '{col}' contains missing values")

# Validate binary variables

for col, name in [(group, "group"), (partition, "partition"), (time, "time")]:

unique_vals = set(data[col].unique())

if not unique_vals.issubset({0, 1, 0.0, 1.0}):

raise ValueError(

f"'{name}' column must be binary (0/1), " f"got values: {sorted(unique_vals)}"

)

if len(unique_vals) < 2:

raise ValueError(f"'{name}' column must have both 0 and 1 values")

# Check we have observations in all cells

G = data[group].values

P = data[partition].values

T = data[time].values

cells = [

((G == 1) & (P == 1) & (T == 0), "treated, eligible, pre"),

((G == 1) & (P == 1) & (T == 1), "treated, eligible, post"),

((G == 1) & (P == 0) & (T == 0), "treated, ineligible, pre"),

((G == 1) & (P == 0) & (T == 1), "treated, ineligible, post"),

((G == 0) & (P == 1) & (T == 0), "control, eligible, pre"),

((G == 0) & (P == 1) & (T == 1), "control, eligible, post"),

((G == 0) & (P == 0) & (T == 0), "control, ineligible, pre"),

((G == 0) & (P == 0) & (T == 1), "control, ineligible, post"),

]

for mask, cell_name in cells:

n_cell = int(np.sum(mask))

if n_cell == 0:

raise ValueError(

f"No observations in cell: {cell_name}. "

"DDD requires observations in all 8 cells."

)

elif n_cell < _MIN_CELL_SIZE:

warnings.warn(

f"Low observation count ({n_cell}) in cell: {cell_name}. "

f"Estimates may be unreliable with fewer than "

f"{_MIN_CELL_SIZE} observations per cell.",

UserWarning,

stacklevel=2,

)

def _compute_cell_means(

self,

y: np.ndarray,

G: np.ndarray,

P: np.ndarray,

T: np.ndarray,

weights: Optional[np.ndarray] = None,

) -> Dict[str, float]:

"""Compute mean outcomes for each of the 8 DDD cells."""

means = {}

for g_val, g_name in [(1, "Treated"), (0, "Control")]:

for p_val, p_name in [(1, "Eligible"), (0, "Ineligible")]:

for t_val, t_name in [(0, "Pre"), (1, "Post")]:

mask = (G == g_val) & (P == p_val) & (T == t_val)

cell_name = f"{g_name}, {p_name}, {t_name}"

if weights is not None:

w_cell = weights[mask]

if np.sum(w_cell) <= 0:

raise ValueError(

f"Cell '{cell_name}' has zero effective survey "

f"weight. Cannot compute weighted cell mean. "

f"Check subpopulation/domain definition."

)

means[cell_name] = float(np.average(y[mask], weights=w_cell))

else:

means[cell_name] = float(np.mean(y[mask]))

return means

# =========================================================================

# Three-DiD Decomposition (matches R's triplediff::ddd())

# =========================================================================

# The DDD is decomposed into three pairwise DiD comparisons:

# DiD_3: subgroup 3 (G=1,P=0) vs subgroup 4 (G=1,P=1)

# DiD_2: subgroup 2 (G=0,P=1) vs subgroup 4 (G=1,P=1)

# DiD_1: subgroup 1 (G=0,P=0) vs subgroup 4 (G=1,P=1)

# DDD = DiD_3 + DiD_2 - DiD_1

# Each DiD uses the selected estimation method (DR, IPW, or RA).

# SE is computed from the combined influence function:

# inf = w3*inf_3 + w2*inf_2 - w1*inf_1

# SE = std(inf, ddof=1) / sqrt(n)

# Reference: Ortiz-Villavicencio & Sant'Anna (2025), implemented in

# R's triplediff::ddd() with panel=FALSE (repeated cross-section).

# =========================================================================

def _regression_adjustment(

self,

y: np.ndarray,

G: np.ndarray,

P: np.ndarray,

T: np.ndarray,

X: Optional[np.ndarray],

survey_weights: Optional[np.ndarray] = None,

resolved_survey=None,

) -> Tuple[float, float, Optional[float], Optional[Dict[str, float]], Dict[int, Dict[str, Any]]]:

"""

Estimate ATT using regression adjustment via three-DiD decomposition.

For each pairwise comparison (subgroup j vs subgroup 4), fits

separate outcome models per subgroup-time cell and computes

imputed counterfactual means. Matches R's triplediff::ddd()

with est_method="reg".

"""

return self._estimate_ddd_decomposition(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

def _ipw_estimation(

self,

y: np.ndarray,

G: np.ndarray,

P: np.ndarray,

T: np.ndarray,

X: Optional[np.ndarray],

survey_weights: Optional[np.ndarray] = None,

resolved_survey=None,

) -> Tuple[float, float, Optional[float], Optional[Dict[str, float]], Dict[int, Dict[str, Any]]]:

"""

Estimate ATT using inverse probability weighting via three-DiD

decomposition.

For each pairwise comparison, estimates propensity scores for

subgroup membership P(subgroup=4|X) within {j, 4} subset.

Matches R's triplediff::ddd() with est_method="ipw".

"""

return self._estimate_ddd_decomposition(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

def _doubly_robust(

self,

y: np.ndarray,

G: np.ndarray,

P: np.ndarray,

T: np.ndarray,

X: Optional[np.ndarray],

survey_weights: Optional[np.ndarray] = None,

resolved_survey=None,

) -> Tuple[float, float, Optional[float], Optional[Dict[str, float]], Dict[int, Dict[str, Any]]]:

"""

Estimate ATT using doubly robust estimation via three-DiD

decomposition.

Combines outcome regression and IPW for robustness: consistent

if either the outcome model or propensity score model is

correctly specified. Matches R's triplediff::ddd() with

est_method="dr".

"""

return self._estimate_ddd_decomposition(

survey_weights=survey_weights,

resolved_survey=resolved_survey,

)

def _estimate_ddd_decomposition(

self,

y: np.ndarray,

G: np.ndarray,

P: np.ndarray,

T: np.ndarray,

X: Optional[np.ndarray],

survey_weights: Optional[np.ndarray] = None,

resolved_survey=None,

) -> Tuple[float, float, Optional[float], Optional[Dict[str, float]], Dict[int, Dict[str, Any]]]:

"""

Core DDD estimation via three-DiD decomposition.

Implements the methodology from Ortiz-Villavicencio & Sant'Anna

(2025), matching R's triplediff::ddd() for repeated cross-section

data (panel=FALSE).

The DDD is decomposed into three pairwise DiD comparisons,

each using the selected estimation method (DR, IPW, or RA):

DDD = DiD_3 + DiD_2 - DiD_1

Standard errors use the efficient influence function:

SE = std(w3*IF_3 + w2*IF_2 - w1*IF_1) / sqrt(n)

When resolved_survey is provided, survey-weighted SE is computed

using TSL on the combined influence function.

"""

n = len(y)

est_method = self.estimation_method

# Assign subgroups following R convention:

# 4: G=1, P=1 (treated, eligible - reference/"treated")

# 3: G=1, P=0 (treated, ineligible)

# 2: G=0, P=1 (control, eligible)

# 1: G=0, P=0 (control, ineligible)

subgroup = np.zeros(n, dtype=int)

subgroup[(G == 1) & (P == 1)] = 4

subgroup[(G == 1) & (P == 0)] = 3

subgroup[(G == 0) & (P == 1)] = 2

subgroup[(G == 0) & (P == 0)] = 1

post = T.astype(float)

# Covariate matrix (always includes intercept)

if X is not None and X.shape[1] > 0:

covX = np.column_stack([np.ones(n), X])

has_covariates = True

else:

covX = np.ones((n, 1))

has_covariates = False

# Three DiD comparisons: j vs 4 for j in {3, 2, 1}

did_results = {}

pscore_stats = None

all_pscores = {} # Collect pscores for diagnostics

overlap_issues = [] # Collect overlap diagnostics across comparisons

any_nonfinite_if = False

epv_all = {} # Collect EPV diagnostics per subgroup comparison

with np.errstate(divide="ignore", invalid="ignore", over="ignore"):

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