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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.
This implementation follows Ortiz-Villavicencio & Sant'Anna (2025), 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(
y,
G,
P,
T,
X,
survey_weights=survey_weights,
resolved_survey=resolved_survey,
)
elif self.estimation_method == "ipw":
att, se, r_squared, pscore_stats, epv_diag = self._ipw_estimation(
y,
G,
P,
T,
X,
survey_weights=survey_weights,
resolved_survey=resolved_survey,
)
else: # doubly robust
att, se, r_squared, pscore_stats, epv_diag = self._doubly_robust(
y,
G,
P,
T,
X,
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(
y,
G,
P,
T,
X,
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(
y,
G,
P,
T,
X,
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(
y,
G,
P,
T,
X,
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"):
for j in [3, 2, 1]:
mask = (subgroup == j) | (subgroup == 4)
y_sub = y[mask]
post_sub = post[mask]
sg_sub = subgroup[mask]
covX_sub = covX[mask]