"""
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
# =============================================================================
[docs]
@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"
[docs]
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})"
)
[docs]
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)
[docs]
def print_summary(self, alpha: Optional[float] = None) -> None:
"""Print the summary to stdout."""
print(self.summary(alpha))
[docs]
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
[docs]
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)
[docs]
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
# =============================================================================
[docs]
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.
"""
[docs]
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
[docs]
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]
n_sub = len(y_sub)
PA4 = (sg_sub == 4).astype(float)
PAa = (sg_sub == j).astype(float)
# Subset survey weights for this comparison (needed for logit)
w_sub = survey_weights[mask] if survey_weights is not None else None
# --- Propensity scores ---
if est_method == "reg":
# RA: no propensity scores needed
pscore_sub = np.ones(n_sub)
hessian = None
elif has_covariates:
# Logistic regression: P(subgroup=4 | X) within {j, 4}
ps_estimated = True
diag = {}
try:
_, pscore_sub = solve_logit(
covX_sub[:, 1:],
PA4,
rank_deficient_action=self.rank_deficient_action,
weights=w_sub,
epv_threshold=self.epv_threshold,
context_label=f"subgroup {j} vs 4",
diagnostics_out=diag,
)
except Exception:
if (
self.pscore_fallback == "error"
or self.rank_deficient_action == "error"
):
raise
if w_sub is not None:
pos = w_sub > 0
if np.any(pos):
p_uc = float(np.average(PA4[pos], weights=w_sub[pos]))
else:
p_uc = float(np.mean(PA4))
else:
p_uc = float(np.mean(PA4))
pscore_sub = np.full(n_sub, p_uc)
ps_estimated = False
warnings.warn(
f"Propensity score estimation failed for subgroup "
f"{j} vs 4; using unconditional probability. "
f"For DR, outcome regression still uses covariates. "
f"Consider estimation_method='reg' to avoid propensity "
f"scores entirely.",
UserWarning,
stacklevel=3,
)
if diag:
epv_all[j] = diag
pscore_sub = np.clip(pscore_sub, self.pscore_trim, 1 - self.pscore_trim)
all_pscores[j] = pscore_sub
# Check overlap: count obs at trim bounds
# (1e-10 tolerance for floating-point after np.clip)
n_trimmed = int(
np.sum(
(pscore_sub <= self.pscore_trim + 1e-10)
| (pscore_sub >= 1 - self.pscore_trim - 1e-10)
)
)
frac_trimmed = n_trimmed / len(pscore_sub)
if frac_trimmed > 0.05:
overlap_issues.append((j, frac_trimmed))
# Hessian only when PS was actually estimated
if ps_estimated:
W_ps = pscore_sub * (1 - pscore_sub)
if w_sub is not None:
W_ps = W_ps * w_sub
try:
XWX = covX_sub.T @ (W_ps[:, None] * covX_sub)
hessian = np.linalg.inv(XWX) * n_sub
except np.linalg.LinAlgError:
hessian = np.linalg.pinv(XWX) * n_sub
else:
hessian = None
else:
# No covariates: unconditional probability
pscore_sub = np.full(n_sub, np.mean(PA4))
pscore_sub = np.clip(pscore_sub, self.pscore_trim, 1 - self.pscore_trim)
# Check overlap (same logic as covariate branch)
n_trimmed = int(
np.sum(
(pscore_sub <= self.pscore_trim + 1e-10)
| (pscore_sub >= 1 - self.pscore_trim - 1e-10)
)
)
frac_trimmed = n_trimmed / len(pscore_sub)
if frac_trimmed > 0.05:
overlap_issues.append((j, frac_trimmed))
hessian = None
# --- Outcome regression ---
if est_method == "ipw":
# IPW: no outcome regression
or_ctrl_pre = np.zeros(n_sub)
or_ctrl_post = np.zeros(n_sub)
or_trt_pre = np.zeros(n_sub)
or_trt_post = np.zeros(n_sub)
else:
# Fit separate OLS per subgroup-time cell, predict for all
or_ctrl_pre = self._fit_predict_mu(
y_sub,
covX_sub,
sg_sub == j,
post_sub == 0,
n_sub,
weights=w_sub,
)
or_ctrl_post = self._fit_predict_mu(
y_sub,
covX_sub,
sg_sub == j,
post_sub == 1,
n_sub,
weights=w_sub,
)
or_trt_pre = self._fit_predict_mu(
y_sub,
covX_sub,
sg_sub == 4,
post_sub == 0,
n_sub,
weights=w_sub,
)
or_trt_post = self._fit_predict_mu(
y_sub,
covX_sub,
sg_sub == 4,
post_sub == 1,
n_sub,
weights=w_sub,
)
# --- Compute DiD ATT and influence function ---
att_j, inf_j = self._compute_did_rc(
y_sub,
post_sub,
PA4,
PAa,
pscore_sub,
covX_sub,
or_ctrl_pre,
or_ctrl_post,
or_trt_pre,
or_trt_post,
hessian,
est_method,
n_sub,
weights=w_sub,
)
# Track non-finite IF values (flag for NaN SE later)
if not np.all(np.isfinite(inf_j)):
any_nonfinite_if = True
inf_j = np.where(np.isfinite(inf_j), inf_j, 0.0)
# Pad influence function to full length
inf_full = np.zeros(n)
inf_full[mask] = inf_j
did_results[j] = {"att": att_j, "inf": inf_full}
# Emit overlap warning if >5% of observations trimmed in any comparison
if overlap_issues:
details = ", ".join(f"subgroup {j} vs 4: {frac:.0%}" for j, frac in overlap_issues)
warnings.warn(
f"Poor propensity score overlap ({details} of observations "
f"trimmed at bounds). IPW/DR estimates may be unreliable.",
UserWarning,
stacklevel=3,
)
# --- Combine three DiDs ---
att = (
float(did_results[3]["att"])
+ float(did_results[2]["att"])
- float(did_results[1]["att"])
)
# Influence function weights (matching R's att_dr_rc)
if survey_weights is not None:
n3 = np.sum(survey_weights[(subgroup == 3) | (subgroup == 4)])
n2 = np.sum(survey_weights[(subgroup == 2) | (subgroup == 4)])
n1 = np.sum(survey_weights[(subgroup == 1) | (subgroup == 4)])
n_total = np.sum(survey_weights)
else:
n3 = np.sum((subgroup == 3) | (subgroup == 4))
n2 = np.sum((subgroup == 2) | (subgroup == 4))
n1 = np.sum((subgroup == 1) | (subgroup == 4))
n_total = n
w3 = n_total / n3
w2 = n_total / n2
w1 = n_total / n1
inf_func = (
w3 * did_results[3]["inf"] + w2 * did_results[2]["inf"] - w1 * did_results[1]["inf"]
)
if resolved_survey is not None:
# Survey-weighted SE via TSL on the combined influence function.
# For IPW/DR: pairwise IFs include survey weights via weighted Riesz
# representers, so divide out to avoid double-weighting by TSL.
# For reg: pairwise IFs are already on the unweighted scale (WLS
# fits use weights but the IF is residual-based, not Riesz-weighted),
# so pass directly to TSL without de-weighting.
inf_for_tsl = inf_func.copy()
if est_method in ("ipw", "dr") and survey_weights is not None:
sw = survey_weights
nz = sw > 0
inf_for_tsl[nz] = inf_for_tsl[nz] / sw[nz]
if resolved_survey.uses_replicate_variance:
from diff_diff.survey import compute_replicate_if_variance
# Score-scale to match TSL bread (1/sum(w)^2):
# reg: psi = w * inf_func / sum(w)
# ipw/dr: psi = inf_func / sum(w) (survey weights cancel)
w_sum = float(resolved_survey.weights.sum())
if est_method in ("ipw", "dr") and survey_weights is not None:
psi_rep = inf_func / w_sum
else:
psi_rep = resolved_survey.weights * inf_func / w_sum
variance, n_valid_rep = compute_replicate_if_variance(psi_rep, resolved_survey)
se = float(np.sqrt(max(variance, 0.0))) if np.isfinite(variance) else np.nan
# Store effective replicate count for df update in fit()
self._replicate_n_valid = n_valid_rep
else:
from diff_diff.survey import compute_survey_vcov
vcov_survey = compute_survey_vcov(np.ones((n, 1)), inf_for_tsl, resolved_survey)
se = float(np.sqrt(vcov_survey[0, 0]))
elif self._cluster_ids is not None:
# Cluster-robust SE: sum IF within clusters, then Liang-Zeger variance
unique_clusters = np.unique(self._cluster_ids)
n_clusters_val = len(unique_clusters)
if n_clusters_val < 2:
raise ValueError(
f"Need at least 2 clusters for cluster-robust SEs, " f"got {n_clusters_val}"
)
cluster_sums = np.array(
[np.sum(inf_func[self._cluster_ids == c]) for c in unique_clusters]
)
# V = (G/(G-1)) * (1/n^2) * sum(psi_c^2)
se = float(
np.sqrt((n_clusters_val / (n_clusters_val - 1)) * np.sum(cluster_sums**2) / n**2)
)
else:
se = float(np.std(inf_func, ddof=1) / np.sqrt(n))
# Non-finite IF values make SE undefined
if any_nonfinite_if:
warnings.warn(
"Non-finite values in influence function (likely due to "
"extreme propensity scores or near-singular design). "
"SE set to NaN.",
UserWarning,
stacklevel=3,
)
se = np.nan
# Propensity score stats (for IPW/DR with covariates)
if has_covariates and est_method != "reg" and all_pscores:
all_ps = np.concatenate(list(all_pscores.values()))
pscore_stats = {
"P(subgroup=4|X) mean": float(np.mean(all_ps)),
"P(subgroup=4|X) std": float(np.std(all_ps)),
"P(subgroup=4|X) min": float(np.min(all_ps)),
"P(subgroup=4|X) max": float(np.max(all_ps)),
}
# R-squared for regression-based methods
r_squared = None
if est_method in ("reg", "dr") and has_covariates:
# Compute R-squared from fitted values on full data
mu_fitted = np.zeros(n)
for sg_val in [1, 2, 3, 4]:
for t_val in [0, 1]:
cell_mask = (subgroup == sg_val) & (post == t_val)
if np.sum(cell_mask) > 0:
X_fit = covX[cell_mask]
y_fit = y[cell_mask]
try:
beta_rs, _, _ = solve_ols(
X_fit,
y_fit,
rank_deficient_action=self.rank_deficient_action,
)
beta_rs = np.where(np.isnan(beta_rs), 0.0, beta_rs)
mu_fitted[cell_mask] = X_fit @ beta_rs
except (np.linalg.LinAlgError, ValueError):
mu_fitted[cell_mask] = np.mean(y_fit)
ss_res = np.sum((y - mu_fitted) ** 2)
ss_tot = np.sum((y - np.mean(y)) ** 2)
r_squared = 1 - (ss_res / ss_tot) if ss_tot > 0 else 0.0
return att, se, r_squared, pscore_stats, epv_all
def _fit_predict_mu(
self,
y: np.ndarray,
covX: np.ndarray,
subgroup_mask: np.ndarray,
time_mask: np.ndarray,
n_total: int,
weights: Optional[np.ndarray] = None,
) -> np.ndarray:
"""Fit OLS (or WLS with survey weights) on a subgroup-time cell, predict for all observations."""
fit_mask = subgroup_mask & time_mask
n_fit = int(np.sum(fit_mask))
if n_fit == 0:
return np.zeros(n_total)
X_fit = covX[fit_mask]
y_fit = y[fit_mask]
try:
if weights is not None:
# WLS: transform by sqrt(weights) for weighted least squares
w_fit = weights[fit_mask]
# Check positive-weight effective sample — subpopulation()
# can zero weights leaving rows but an underidentified WLS.
n_eff = int(np.count_nonzero(w_fit > 0))
n_cols = X_fit.shape[1]
if n_eff <= n_cols:
if np.sum(w_fit) > 0:
return np.full(n_total, np.average(y_fit, weights=w_fit))
return np.full(n_total, np.mean(y_fit))
sqrt_w = np.sqrt(w_fit)
beta, _, _ = solve_ols(
X_fit * sqrt_w[:, np.newaxis],
y_fit * sqrt_w,
rank_deficient_action=self.rank_deficient_action,
)
else:
beta, _, _ = solve_ols(
X_fit,
y_fit,
rank_deficient_action=self.rank_deficient_action,
)
# Replace NaN coefficients (dropped columns) with 0 for prediction
beta = np.where(np.isnan(beta), 0.0, beta)
except ValueError:
if self.rank_deficient_action == "error":
raise
if weights is not None:
return np.full(n_total, np.average(y_fit, weights=weights[fit_mask]))
return np.full(n_total, np.mean(y_fit))
except np.linalg.LinAlgError:
if weights is not None:
return np.full(n_total, np.average(y_fit, weights=weights[fit_mask]))
return np.full(n_total, np.mean(y_fit))
# Prediction uses original-scale X (unchanged)
return covX @ beta
def _compute_did_rc(
self,
y: np.ndarray,
post: np.ndarray,
PA4: np.ndarray,
PAa: np.ndarray,
pscore: np.ndarray,
covX: np.ndarray,
or_ctrl_pre: np.ndarray,
or_ctrl_post: np.ndarray,
or_trt_pre: np.ndarray,
or_trt_post: np.ndarray,
hessian: Optional[np.ndarray],
est_method: str,
n: int,
weights: Optional[np.ndarray] = None,
) -> Tuple[float, np.ndarray]:
"""
Compute a single pairwise DiD (subgroup j vs 4) for RC data.
Returns ATT and per-observation influence function.
Matches R's triplediff::compute_did_rc().
"""
if est_method == "ipw":
return self._compute_did_rc_ipw(
y,
post,
PA4,
PAa,
pscore,
covX,
hessian,
n,
weights=weights,
)
elif est_method == "reg":
return self._compute_did_rc_reg(
y,
post,
PA4,
PAa,
covX,
or_ctrl_pre,
or_ctrl_post,
or_trt_pre,
or_trt_post,
n,
weights=weights,
)
else:
return self._compute_did_rc_dr(
y,
post,
PA4,
PAa,
pscore,
covX,
or_ctrl_pre,
or_ctrl_post,
or_trt_pre,
or_trt_post,
hessian,
n,
weights=weights,
)
def _compute_did_rc_ipw(
self,
y: np.ndarray,
post: np.ndarray,
PA4: np.ndarray,
PAa: np.ndarray,
pscore: np.ndarray,
covX: np.ndarray,
hessian: Optional[np.ndarray],
n: int,
weights: Optional[np.ndarray] = None,
) -> Tuple[float, np.ndarray]:
"""IPW DiD for a single pairwise comparison (RC)."""
# Riesz representers (IPW weights * indicators)
riesz_treat_pre = PA4 * (1 - post)
riesz_treat_post = PA4 * post
riesz_control_pre = pscore * PAa * (1 - post) / (1 - pscore)
riesz_control_post = pscore * PAa * post / (1 - pscore)
# Incorporate survey weights into Riesz representers
if weights is not None:
riesz_treat_pre = riesz_treat_pre * weights
riesz_treat_post = riesz_treat_post * weights
riesz_control_pre = riesz_control_pre * weights
riesz_control_post = riesz_control_post * weights
# Hajek-normalized cell-time means
def _hajek(riesz, y_vals):
denom = np.mean(riesz)
if denom <= 0:
return np.zeros_like(riesz), 0.0
eta = riesz * y_vals / denom
return eta, float(np.mean(eta))
eta_treat_pre, att_treat_pre = _hajek(riesz_treat_pre, y)
eta_treat_post, att_treat_post = _hajek(riesz_treat_post, y)
eta_control_pre, att_control_pre = _hajek(riesz_control_pre, y)
eta_control_post, att_control_post = _hajek(riesz_control_post, y)
att = (att_treat_post - att_treat_pre) - (att_control_post - att_control_pre)
# Influence function
inf_treat_pre = eta_treat_pre - riesz_treat_pre * att_treat_pre / np.mean(riesz_treat_pre)
inf_treat_post = eta_treat_post - riesz_treat_post * att_treat_post / np.mean(
riesz_treat_post
)
inf_treat = inf_treat_post - inf_treat_pre
inf_control_pre = eta_control_pre - riesz_control_pre * att_control_pre / np.mean(
riesz_control_pre
)
inf_control_post = eta_control_post - riesz_control_post * att_control_post / np.mean(
riesz_control_post
)
inf_control = inf_control_post - inf_control_pre
# Propensity score correction for influence function
if hessian is not None:
score_ps = (PA4 - pscore)[:, None] * covX
if weights is not None:
score_ps = score_ps * weights[:, None]
asy_lin_rep_ps = score_ps @ hessian
# Riesz representers already incorporate survey weights,
# so use np.mean (not np.average with weights) to avoid double-weighting.
M2_pre = np.mean(
(riesz_control_pre * (y - att_control_pre))[:, None] * covX,
axis=0,
) / np.mean(riesz_control_pre)
M2_post = np.mean(
(riesz_control_post * (y - att_control_post))[:, None] * covX,
axis=0,
) / np.mean(riesz_control_post)
inf_control_ps = asy_lin_rep_ps @ (M2_post - M2_pre)
inf_control = inf_control + inf_control_ps
inf_func = inf_treat - inf_control
return att, inf_func
def _compute_did_rc_reg(
self,
y: np.ndarray,
post: np.ndarray,
PA4: np.ndarray,
PAa: np.ndarray,
covX: np.ndarray,
or_ctrl_pre: np.ndarray,
or_ctrl_post: np.ndarray,
or_trt_pre: np.ndarray,
or_trt_post: np.ndarray,
n: int,
weights: Optional[np.ndarray] = None,
) -> Tuple[float, np.ndarray]:
"""Regression adjustment DiD for a single pairwise comparison (RC)."""
# Helper: weighted or unweighted mean
def _wmean(x):
if weights is not None:
return np.average(x, weights=weights)
return np.mean(x)
# Riesz representers
riesz_treat_pre = PA4 * (1 - post)
riesz_treat_post = PA4 * post
riesz_control = PA4 # weights for OR prediction
# ATT components
reg_att_treat_pre = riesz_treat_pre * y
reg_att_treat_post = riesz_treat_post * y
reg_att_control = riesz_control * (or_ctrl_post - or_ctrl_pre)
eta_treat_pre = _wmean(reg_att_treat_pre) / _wmean(riesz_treat_pre)
eta_treat_post = _wmean(reg_att_treat_post) / _wmean(riesz_treat_post)
eta_control = _wmean(reg_att_control) / _wmean(riesz_control)
att = (eta_treat_post - eta_treat_pre) - eta_control
# Influence function
# OLS asymptotic linear representation for pre/post
# When survey weights present, include them in both score and bread
# for consistency with the weighted OLS fit
weights_ols_pre = PAa * (1 - post)
if weights is not None:
wols_x_pre = (weights_ols_pre * weights)[:, None] * covX
wols_eX_pre = (weights_ols_pre * weights * (y - or_ctrl_pre))[:, None] * covX
XpX_pre = wols_x_pre.T @ covX / n
else:
wols_x_pre = weights_ols_pre[:, None] * covX
wols_eX_pre = (weights_ols_pre * (y - or_ctrl_pre))[:, None] * covX
XpX_pre = wols_x_pre.T @ covX / n
try:
XpX_inv_pre = np.linalg.inv(XpX_pre)
except np.linalg.LinAlgError:
XpX_inv_pre = np.linalg.pinv(XpX_pre)
asy_lin_rep_ols_pre = wols_eX_pre @ XpX_inv_pre
weights_ols_post = PAa * post
if weights is not None:
wols_x_post = (weights_ols_post * weights)[:, None] * covX
wols_eX_post = (weights_ols_post * weights * (y - or_ctrl_post))[:, None] * covX
XpX_post = wols_x_post.T @ covX / n
else:
wols_x_post = weights_ols_post[:, None] * covX
wols_eX_post = (weights_ols_post * (y - or_ctrl_post))[:, None] * covX
XpX_post = wols_x_post.T @ covX / n
try:
XpX_inv_post = np.linalg.inv(XpX_post)
except np.linalg.LinAlgError:
XpX_inv_post = np.linalg.pinv(XpX_post)
asy_lin_rep_ols_post = wols_eX_post @ XpX_inv_post
inf_treat_pre = (reg_att_treat_pre - riesz_treat_pre * eta_treat_pre) / _wmean(
riesz_treat_pre
)
inf_treat_post = (reg_att_treat_post - riesz_treat_post * eta_treat_post) / _wmean(
riesz_treat_post
)
inf_treat = inf_treat_post - inf_treat_pre
inf_control_1 = reg_att_control - riesz_control * eta_control
if weights is not None:
M1 = np.average(riesz_control[:, None] * covX, axis=0, weights=weights)
else:
M1 = np.mean(riesz_control[:, None] * covX, axis=0)
inf_control_2_post = asy_lin_rep_ols_post @ M1
inf_control_2_pre = asy_lin_rep_ols_pre @ M1
inf_control = (inf_control_1 + inf_control_2_post - inf_control_2_pre) / _wmean(
riesz_control
)
inf_func = inf_treat - inf_control
return att, inf_func
def _compute_did_rc_dr(
self,
y: np.ndarray,
post: np.ndarray,
PA4: np.ndarray,
PAa: np.ndarray,
pscore: np.ndarray,
covX: np.ndarray,
or_ctrl_pre: np.ndarray,
or_ctrl_post: np.ndarray,
or_trt_pre: np.ndarray,
or_trt_post: np.ndarray,
hessian: Optional[np.ndarray],
n: int,
weights: Optional[np.ndarray] = None,
) -> Tuple[float, np.ndarray]:
"""Doubly robust DiD for a single pairwise comparison (RC)."""
or_ctrl = post * or_ctrl_post + (1 - post) * or_ctrl_pre
# Riesz representers
riesz_treat_pre = PA4 * (1 - post)
riesz_treat_post = PA4 * post
riesz_control_pre = pscore * PAa * (1 - post) / (1 - pscore)
riesz_control_post = pscore * PAa * post / (1 - pscore)
riesz_d = PA4
riesz_dt1 = PA4 * post
riesz_dt0 = PA4 * (1 - post)
# Incorporate survey weights into Riesz representers
if weights is not None:
riesz_treat_pre = riesz_treat_pre * weights
riesz_treat_post = riesz_treat_post * weights
riesz_control_pre = riesz_control_pre * weights
riesz_control_post = riesz_control_post * weights
riesz_d = riesz_d * weights
riesz_dt1 = riesz_dt1 * weights
riesz_dt0 = riesz_dt0 * weights
# DR cell-time components
def _safe_ratio(num, denom):
return num / denom if denom > 0 else 0.0
eta_treat_pre = riesz_treat_pre * (y - or_ctrl) * _safe_ratio(1, np.mean(riesz_treat_pre))
eta_treat_post = (
riesz_treat_post * (y - or_ctrl) * _safe_ratio(1, np.mean(riesz_treat_post))
)
eta_control_pre = (
riesz_control_pre * (y - or_ctrl) * _safe_ratio(1, np.mean(riesz_control_pre))
)
eta_control_post = (
riesz_control_post * (y - or_ctrl) * _safe_ratio(1, np.mean(riesz_control_post))
)
# Efficiency correction (OR bias correction)
eta_d_post = riesz_d * (or_trt_post - or_ctrl_post) * _safe_ratio(1, np.mean(riesz_d))
eta_dt1_post = riesz_dt1 * (or_trt_post - or_ctrl_post) * _safe_ratio(1, np.mean(riesz_dt1))
eta_d_pre = riesz_d * (or_trt_pre - or_ctrl_pre) * _safe_ratio(1, np.mean(riesz_d))
eta_dt0_pre = riesz_dt0 * (or_trt_pre - or_ctrl_pre) * _safe_ratio(1, np.mean(riesz_dt0))
att_treat_pre = float(np.mean(eta_treat_pre))
att_treat_post = float(np.mean(eta_treat_post))
att_control_pre = float(np.mean(eta_control_pre))
att_control_post = float(np.mean(eta_control_post))
att_d_post = float(np.mean(eta_d_post))
att_dt1_post = float(np.mean(eta_dt1_post))
att_d_pre = float(np.mean(eta_d_pre))
att_dt0_pre = float(np.mean(eta_dt0_pre))
att = (
(att_treat_post - att_treat_pre)
- (att_control_post - att_control_pre)
+ (att_d_post - att_dt1_post)
- (att_d_pre - att_dt0_pre)
)
# --- Influence function ---
# OLS asymptotic linear representations (control subgroup)
weights_ols_pre = PAa * (1 - post)
if weights is not None:
wols_x_pre = (weights_ols_pre * weights)[:, None] * covX
wols_eX_pre = (weights_ols_pre * weights * (y - or_ctrl_pre))[:, None] * covX
XpX_pre = wols_x_pre.T @ covX / n
else:
wols_x_pre = weights_ols_pre[:, None] * covX
wols_eX_pre = (weights_ols_pre * (y - or_ctrl_pre))[:, None] * covX
XpX_pre = wols_x_pre.T @ covX / n
try:
XpX_inv_pre = np.linalg.inv(XpX_pre)
except np.linalg.LinAlgError:
XpX_inv_pre = np.linalg.pinv(XpX_pre)
asy_lin_rep_ols_pre = wols_eX_pre @ XpX_inv_pre
weights_ols_post = PAa * post
if weights is not None:
wols_x_post = (weights_ols_post * weights)[:, None] * covX
wols_eX_post = (weights_ols_post * weights * (y - or_ctrl_post))[:, None] * covX
XpX_post = wols_x_post.T @ covX / n
else:
wols_x_post = weights_ols_post[:, None] * covX
wols_eX_post = (weights_ols_post * (y - or_ctrl_post))[:, None] * covX
XpX_post = wols_x_post.T @ covX / n
try:
XpX_inv_post = np.linalg.inv(XpX_post)
except np.linalg.LinAlgError:
XpX_inv_post = np.linalg.pinv(XpX_post)
asy_lin_rep_ols_post = wols_eX_post @ XpX_inv_post
# OLS representations (treated subgroup)
weights_ols_pre_treat = PA4 * (1 - post)
if weights is not None:
wols_x_pre_treat = (weights_ols_pre_treat * weights)[:, None] * covX
wols_eX_pre_treat = (weights_ols_pre_treat * weights * (y - or_trt_pre))[:, None] * covX
XpX_pre_treat = wols_x_pre_treat.T @ covX / n
else:
wols_x_pre_treat = weights_ols_pre_treat[:, None] * covX
wols_eX_pre_treat = (weights_ols_pre_treat * (y - or_trt_pre))[:, None] * covX
XpX_pre_treat = wols_x_pre_treat.T @ covX / n
try:
XpX_inv_pre_treat = np.linalg.inv(XpX_pre_treat)
except np.linalg.LinAlgError:
XpX_inv_pre_treat = np.linalg.pinv(XpX_pre_treat)
asy_lin_rep_ols_pre_treat = wols_eX_pre_treat @ XpX_inv_pre_treat
weights_ols_post_treat = PA4 * post
if weights is not None:
wols_x_post_treat = (weights_ols_post_treat * weights)[:, None] * covX
wols_eX_post_treat = (weights_ols_post_treat * weights * (y - or_trt_post))[
:, None
] * covX
XpX_post_treat = wols_x_post_treat.T @ covX / n
else:
wols_x_post_treat = weights_ols_post_treat[:, None] * covX
wols_eX_post_treat = (weights_ols_post_treat * (y - or_trt_post))[:, None] * covX
XpX_post_treat = wols_x_post_treat.T @ covX / n
try:
XpX_inv_post_treat = np.linalg.inv(XpX_post_treat)
except np.linalg.LinAlgError:
XpX_inv_post_treat = np.linalg.pinv(XpX_post_treat)
asy_lin_rep_ols_post_treat = wols_eX_post_treat @ XpX_inv_post_treat
# Propensity score linear representation
score_ps = (PA4 - pscore)[:, None] * covX
if weights is not None:
score_ps = score_ps * weights[:, None]
if hessian is not None:
asy_lin_rep_ps = score_ps @ hessian
else:
asy_lin_rep_ps = np.zeros_like(score_ps)
# Treat influence function components
m_riesz_treat_pre = np.mean(riesz_treat_pre)
m_riesz_treat_post = np.mean(riesz_treat_post)
inf_treat_pre = (
(eta_treat_pre - riesz_treat_pre * att_treat_pre / m_riesz_treat_pre)
if m_riesz_treat_pre > 0
else np.zeros(n)
)
inf_treat_post = (
(eta_treat_post - riesz_treat_post * att_treat_post / m_riesz_treat_post)
if m_riesz_treat_post > 0
else np.zeros(n)
)
# OR correction for treated
# Riesz representers already incorporate survey weights,
# so use np.mean (not weighted average) to avoid double-weighting.
M1_post = (
(-np.mean((riesz_treat_post * post)[:, None] * covX, axis=0) / m_riesz_treat_post)
if m_riesz_treat_post > 0
else np.zeros(covX.shape[1])
)
M1_pre = (
(-np.mean((riesz_treat_pre * (1 - post))[:, None] * covX, axis=0) / m_riesz_treat_pre)
if m_riesz_treat_pre > 0
else np.zeros(covX.shape[1])
)
inf_treat_or_post = asy_lin_rep_ols_post @ M1_post
inf_treat_or_pre = asy_lin_rep_ols_pre @ M1_pre
# Control influence function components
m_riesz_control_pre = np.mean(riesz_control_pre)
m_riesz_control_post = np.mean(riesz_control_post)
inf_control_pre = (
(eta_control_pre - riesz_control_pre * att_control_pre / m_riesz_control_pre)
if m_riesz_control_pre > 0
else np.zeros(n)
)
inf_control_post = (
(eta_control_post - riesz_control_post * att_control_post / m_riesz_control_post)
if m_riesz_control_post > 0
else np.zeros(n)
)
# PS correction for control
M2_pre = (
(
np.mean(
(riesz_control_pre * (y - or_ctrl - att_control_pre))[:, None] * covX, axis=0
)
/ m_riesz_control_pre
)
if m_riesz_control_pre > 0
else np.zeros(covX.shape[1])
)
M2_post = (
(
np.mean(
(riesz_control_post * (y - or_ctrl - att_control_post))[:, None] * covX, axis=0
)
/ m_riesz_control_post
)
if m_riesz_control_post > 0
else np.zeros(covX.shape[1])
)
inf_control_ps = asy_lin_rep_ps @ (M2_post - M2_pre)
# OR correction for control
M3_post = (
(-np.mean((riesz_control_post * post)[:, None] * covX, axis=0) / m_riesz_control_post)
if m_riesz_control_post > 0
else np.zeros(covX.shape[1])
)
M3_pre = (
(
-np.mean((riesz_control_pre * (1 - post))[:, None] * covX, axis=0)
/ m_riesz_control_pre
)
if m_riesz_control_pre > 0
else np.zeros(covX.shape[1])
)
inf_control_or_post = asy_lin_rep_ols_post @ M3_post
inf_control_or_pre = asy_lin_rep_ols_pre @ M3_pre
# Efficiency correction
m_riesz_d = np.mean(riesz_d)
m_riesz_dt1 = np.mean(riesz_dt1)
m_riesz_dt0 = np.mean(riesz_dt0)
inf_eff1 = (eta_d_post - riesz_d * att_d_post / m_riesz_d) if m_riesz_d > 0 else np.zeros(n)
inf_eff2 = (
(eta_dt1_post - riesz_dt1 * att_dt1_post / m_riesz_dt1)
if m_riesz_dt1 > 0
else np.zeros(n)
)
inf_eff3 = (eta_d_pre - riesz_d * att_d_pre / m_riesz_d) if m_riesz_d > 0 else np.zeros(n)
inf_eff4 = (
(eta_dt0_pre - riesz_dt0 * att_dt0_pre / m_riesz_dt0)
if m_riesz_dt0 > 0
else np.zeros(n)
)
inf_eff = (inf_eff1 - inf_eff2) - (inf_eff3 - inf_eff4)
# OR combination
mom_post = (
np.mean(
(riesz_d[:, None] / m_riesz_d - riesz_dt1[:, None] / m_riesz_dt1) * covX, axis=0
)
if (m_riesz_d > 0 and m_riesz_dt1 > 0)
else np.zeros(covX.shape[1])
)
mom_pre = (
np.mean(
(riesz_d[:, None] / m_riesz_d - riesz_dt0[:, None] / m_riesz_dt0) * covX, axis=0
)
if (m_riesz_d > 0 and m_riesz_dt0 > 0)
else np.zeros(covX.shape[1])
)
inf_or_post = (asy_lin_rep_ols_post_treat - asy_lin_rep_ols_post) @ mom_post
inf_or_pre = (asy_lin_rep_ols_pre_treat - asy_lin_rep_ols_pre) @ mom_pre
inf_treat_or = inf_treat_or_post + inf_treat_or_pre
inf_control_or = inf_control_or_post + inf_control_or_pre
inf_or = inf_or_post - inf_or_pre
inf_treat = inf_treat_post - inf_treat_pre + inf_treat_or
inf_control = inf_control_post - inf_control_pre + inf_control_ps + inf_control_or
inf_func = inf_treat - inf_control + inf_eff + inf_or
return att, inf_func
[docs]
def get_params(self) -> Dict[str, Any]:
"""
Get estimator parameters (sklearn-compatible).
Returns
-------
Dict[str, Any]
Estimator parameters.
"""
return {
"estimation_method": self.estimation_method,
"robust": self.robust,
"cluster": self.cluster,
"alpha": self.alpha,
"pscore_trim": self.pscore_trim,
"rank_deficient_action": self.rank_deficient_action,
"epv_threshold": self.epv_threshold,
"pscore_fallback": self.pscore_fallback,
}
[docs]
def set_params(self, **params) -> "TripleDifference":
"""
Set estimator parameters (sklearn-compatible).
Parameters
----------
**params
Estimator parameters.
Returns
-------
self
"""
for key, value in params.items():
if hasattr(self, key):
setattr(self, key, value)
else:
raise ValueError(f"Unknown parameter: {key}")
return self
[docs]
def summary(self) -> str:
"""
Get summary of estimation results.
Returns
-------
str
Formatted summary.
"""
if not self.is_fitted_:
raise RuntimeError("Model must be fitted before calling summary()")
assert self.results_ is not None
return self.results_.summary()
[docs]
def print_summary(self) -> None:
"""Print summary to stdout."""
print(self.summary())
# =============================================================================
# Convenience function
# =============================================================================
[docs]
def triple_difference(
data: pd.DataFrame,
outcome: str,
group: str,
partition: str,
time: str,
covariates: Optional[List[str]] = None,
estimation_method: str = "dr",
robust: bool = True,
cluster: Optional[str] = None,
alpha: float = 0.05,
rank_deficient_action: str = "warn",
epv_threshold: float = 10,
pscore_fallback: str = "error",
survey_design: object = None,
) -> TripleDifferenceResults:
"""
Estimate Triple Difference (DDD) treatment effect.
Convenience function that creates a TripleDifference estimator and
fits it to the data in one step.
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).
partition : str
Name of the partition/eligibility indicator column (0/1).
1 = eligible partition (e.g., women, targeted demographic).
time : str
Name of the time period indicator column (0/1).
1 = post-treatment period.
covariates : list of str, optional
List of covariate column names to adjust for.
estimation_method : str, default="dr"
Estimation method: "dr" (doubly robust), "reg" (regression),
or "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.
alpha : float, default=0.05
Significance level for confidence intervals.
rank_deficient_action : str, default="warn"
Action when design matrix is rank-deficient:
- "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.
pscore_fallback : str, default="error"
Action when propensity score estimation fails:
- "error": Raise (default)
- "unconditional": Fall back to unconditional propensity
Returns
-------
TripleDifferenceResults
Object containing estimation results.
Examples
--------
>>> from diff_diff import triple_difference
>>> results = triple_difference(
... data,
... outcome='earnings',
... group='policy_state',
... partition='female',
... time='post_policy',
... covariates=['age', 'education']
... )
>>> print(f"ATT: {results.att:.3f} (SE: {results.se:.3f})")
"""
estimator = TripleDifference(
estimation_method=estimation_method,
robust=robust,
cluster=cluster,
alpha=alpha,
rank_deficient_action=rank_deficient_action,
epv_threshold=epv_threshold,
pscore_fallback=pscore_fallback,
)
return estimator.fit(
data=data,
outcome=outcome,
group=group,
partition=partition,
time=time,
covariates=covariates,
survey_design=survey_design,
)