# Copyright 2022 - 2026 The PyMC Labs Developers
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Regression discontinuity design
"""
import warnings # noqa: I001
from typing import Any, Literal
import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
from patsy import build_design_matrices, dmatrices
from sklearn.base import RegressorMixin
import xarray as xr
from causalpy.custom_exceptions import (
DataException,
FormulaException,
)
from causalpy.constants import HDI_PROB, LEGEND_FONT_SIZE
from causalpy.plot_utils import plot_xY
from causalpy.pymc_models import LinearRegression, PyMCModel
from causalpy.reporting import EffectSummary, _effect_summary_rd
from causalpy.utils import (
_is_variable_dummy_coded,
convert_to_string,
round_num,
)
from .base import BaseExperiment
[docs]
class RegressionDiscontinuity(BaseExperiment):
"""
A class to analyse sharp regression discontinuity experiments.
:param data:
A pandas dataframe
:param formula:
A statistical model formula
:param treatment_threshold:
A scalar threshold value at which the treatment is applied
:param model:
A PyMC or sklearn model. Defaults to LinearRegression.
:param running_variable_name:
The name of the predictor variable that the treatment threshold is based upon
:param epsilon:
A small scalar value which determines how far above and below the treatment
threshold to evaluate the causal impact.
:param bandwidth:
Data outside of the bandwidth (relative to the discontinuity) is not used to fit
the model.
:param donut_hole:
Observations within this distance from the treatment threshold are excluded from
model fitting. Used as a robustness check when observations closest to the
threshold may be problematic (e.g., due to manipulation or heaping). Defaults
to 0.0 (no exclusion). Must be non-negative and less than bandwidth if bandwidth
is finite.
Example
--------
>>> import causalpy as cp
>>> df = cp.load_data("rd")
>>> seed = 42
>>> result = cp.RegressionDiscontinuity(
... df,
... formula="y ~ 1 + x + treated + x:treated",
... model=cp.pymc_models.LinearRegression(
... sample_kwargs={
... "draws": 100,
... "target_accept": 0.95,
... "random_seed": seed,
... "progressbar": False,
... },
... ),
... treatment_threshold=0.5,
... )
"""
supports_ols = True
supports_bayes = True
_default_model_class = LinearRegression
[docs]
def __init__(
self,
data: pd.DataFrame,
formula: str,
treatment_threshold: float,
model: PyMCModel | RegressorMixin | None = None,
running_variable_name: str = "x",
epsilon: float = 0.001,
bandwidth: float = np.inf,
donut_hole: float = 0.0,
**kwargs: Any,
) -> None:
super().__init__(model=model)
self.expt_type = "Regression Discontinuity"
self.data = data
self.formula = formula
self.running_variable_name = running_variable_name
self.treatment_threshold = treatment_threshold
self.epsilon = epsilon
self.bandwidth = bandwidth
self.donut_hole = donut_hole
self.input_validation()
self._build_design_matrices()
self._prepare_data()
self.algorithm()
def _build_design_matrices(self) -> None:
"""Build design matrices from formula and data, applying bandwidth and donut hole filtering."""
x_vals = self.data[self.running_variable_name]
c = self.treatment_threshold
mask = pd.Series(True, index=self.data.index)
if self.bandwidth is not np.inf:
mask &= np.abs(x_vals - c) <= self.bandwidth
if self.donut_hole > 0:
mask &= np.abs(x_vals - c) >= self.donut_hole
self.fit_data = self.data.loc[mask]
if len(self.fit_data) <= 10:
filter_desc = []
if self.bandwidth is not np.inf:
filter_desc.append(f"bandwidth={self.bandwidth}")
if self.donut_hole > 0:
filter_desc.append(f"donut_hole={self.donut_hole}")
if filter_desc:
msg = (
f"Choice of {' and '.join(filter_desc)} parameters has led to only "
f"{len(self.fit_data)} remaining datapoints. "
f"Consider adjusting these parameters."
)
else:
msg = f"Only {len(self.fit_data)} datapoints in the dataset."
warnings.warn(msg, UserWarning, stacklevel=2)
y, X = dmatrices(self.formula, self.fit_data)
self._y_design_info = y.design_info
self._x_design_info = X.design_info
self.labels = X.design_info.column_names
self.y, self.X = np.asarray(y), np.asarray(X)
self.outcome_variable_name = y.design_info.column_names[0]
def _prepare_data(self) -> None:
"""Convert design matrices to xarray DataArrays."""
self.X = xr.DataArray(
self.X,
dims=["obs_ind", "coeffs"],
coords={
"obs_ind": np.arange(self.X.shape[0]),
"coeffs": self.labels,
},
)
self.y = xr.DataArray(
self.y,
dims=["obs_ind", "treated_units"],
coords={"obs_ind": np.arange(self.y.shape[0]), "treated_units": ["unit_0"]},
)
[docs]
def algorithm(self) -> None:
"""Run the experiment algorithm: fit model, predict, and calculate discontinuity."""
# fit model
if isinstance(self.model, PyMCModel):
# fit the model to the observed (pre-intervention) data
COORDS = {
"coeffs": self.labels,
"obs_ind": np.arange(self.X.shape[0]),
"treated_units": ["unit_0"],
}
self.model.fit(X=self.X, y=self.y, coords=COORDS)
elif isinstance(self.model, RegressorMixin):
self.model.fit(X=self.X, y=self.y)
else:
raise ValueError("Model type not recognized")
# score the goodness of fit to all data
self.score = self.model.score(X=self.X, y=self.y)
# get the model predictions of the observed data
if self.bandwidth is not np.inf:
fmin = self.treatment_threshold - self.bandwidth
fmax = self.treatment_threshold + self.bandwidth
xi = np.linspace(fmin, fmax, 200)
else:
xi = np.linspace(
np.min(self.data[self.running_variable_name]),
np.max(self.data[self.running_variable_name]),
200,
)
self.x_pred = pd.DataFrame(
{self.running_variable_name: xi, "treated": self._is_treated(xi)}
)
(new_x,) = build_design_matrices([self._x_design_info], self.x_pred)
self.pred = self.model.predict(X=np.asarray(new_x))
# calculate discontinuity by evaluating the difference in model expectation on
# either side of the discontinuity
# NOTE: `"treated": np.array([0, 1])`` assumes treatment is applied above
# (not below) the threshold
self.x_discon = pd.DataFrame(
{
self.running_variable_name: np.array(
[
self.treatment_threshold - self.epsilon,
self.treatment_threshold + self.epsilon,
]
),
"treated": np.array([0, 1]),
}
)
(new_x,) = build_design_matrices([self._x_design_info], self.x_discon)
self.pred_discon = self.model.predict(X=np.asarray(new_x))
# ******** THIS IS SUBOPTIMAL AT THE MOMENT ************************************
if isinstance(self.model, PyMCModel):
self.discontinuity_at_threshold = (
self.pred_discon["posterior_predictive"].sel(obs_ind=1)["mu"]
- self.pred_discon["posterior_predictive"].sel(obs_ind=0)["mu"]
)
else:
self.discontinuity_at_threshold = np.squeeze(
self.pred_discon[1]
) - np.squeeze(self.pred_discon[0])
# ******************************************************************************
def _is_treated(self, x: np.ndarray | pd.Series) -> np.ndarray:
"""Returns ``True`` if `x` is greater than or equal to the treatment threshold.
.. warning::
Assumes treatment is given to those ABOVE the treatment threshold.
"""
return np.greater_equal(x, self.treatment_threshold)
[docs]
def summary(self, round_to: int | None = None) -> None:
"""
Print summary of main results and model coefficients
:param round_to:
Number of decimals used to round results. Defaults to 2. Use "None" to return raw numbers.
"""
print("Regression Discontinuity experiment")
print(f"Formula: {self.formula}")
print(f"Running variable: {self.running_variable_name}")
print(f"Threshold on running variable: {self.treatment_threshold}")
print(f"Bandwidth: {self.bandwidth}")
print(f"Donut hole: {self.donut_hole}")
print(f"Observations used for fit: {len(self.fit_data)}")
print("\nResults:")
print(
f"Discontinuity at threshold = {convert_to_string(self.discontinuity_at_threshold)}"
)
print("\n")
self.print_coefficients(round_to)
[docs]
def plot(
self,
*,
round_to: int | None = 2,
hdi_prob: float = HDI_PROB,
figsize: tuple[float, float] | None = None,
show: bool = True,
legend_kwargs: dict[str, Any] | None = None,
) -> tuple[plt.Figure, plt.Axes]:
"""Plot the regression discontinuity results.
Parameters
----------
round_to : int, optional
Number of decimals used to round numerical results in the figure
title (e.g. the Bayesian :math:`R^2`). Defaults to 2. Use
``None`` to render raw numbers.
hdi_prob : float
Probability mass of the highest density interval drawn around the
posterior predictive band, and the central credible interval
reported in the figure title for the discontinuity at threshold.
Must be in ``(0, 1]``. Ignored for OLS models. Defaults to
:data:`~causalpy.constants.HDI_PROB` (currently 0.94).
figsize : tuple of (float, float), optional
Width and height of the figure in inches, passed to
:func:`matplotlib.pyplot.subplots`. Defaults to ``None`` (use
matplotlib's default).
show : bool
Whether to automatically display the plot. Defaults to ``True``.
legend_kwargs : dict, optional
Keyword arguments to adjust legend placement and styling.
Supported keys: ``loc``, ``bbox_to_anchor``, ``fontsize``,
``frameon``, ``title`` (``bbox_transform`` is accepted alongside
``bbox_to_anchor``). The existing legend is modified **in
place** so that custom handles are preserved.
Returns
-------
fig : matplotlib.figure.Figure
The figure that was created.
ax : matplotlib.axes.Axes
The axes object containing the plot.
"""
return self._render_plot(
show=show,
legend_kwargs=legend_kwargs,
round_to=round_to,
hdi_prob=hdi_prob,
figsize=figsize,
)
def _bayesian_plot(
self,
round_to: int | None = 2,
hdi_prob: float = HDI_PROB,
figsize: tuple[float, float] | None = None,
**kwargs: Any,
) -> tuple[plt.Figure, plt.Axes]:
"""Generate plot for regression discontinuity designs.
Parameters
----------
round_to : int, optional
Number of decimals used to round results. Defaults to 2. Use ``None``
to return raw numbers.
hdi_prob : float, optional
Probability mass of the highest density interval drawn around the
posterior predictive band, and the central credible interval
reported in the figure title for the discontinuity at threshold.
Must be in ``(0, 1]``. Defaults to
:data:`~causalpy.constants.HDI_PROB` (currently 0.94).
figsize : tuple of (float, float), optional
Width and height of the figure in inches. Defaults to ``None``
(use matplotlib's default).
"""
fig, ax = plt.subplots(figsize=figsize)
# Plot data: use two layers only when there are excluded observations
has_exclusion = len(self.fit_data) < len(self.data)
if has_exclusion:
sns.scatterplot(
self.data,
x=self.running_variable_name,
y=self.outcome_variable_name,
color="lightgray",
ax=ax,
label="excluded data",
)
sns.scatterplot(
self.fit_data,
x=self.running_variable_name,
y=self.outcome_variable_name,
color="k",
ax=ax,
label="fit data" if has_exclusion else "data",
)
# Plot model fit to data
plot_xY(
self.x_pred[self.running_variable_name],
self.pred["posterior_predictive"].mu.isel(treated_units=0),
ax=ax,
hdi_prob=hdi_prob,
plot_hdi_kwargs={"color": "C1"},
label="Posterior mean",
)
# create strings to compose title
title_info = f"{round_num(self.score['unit_0_r2'], round_to)} (std = {round_num(self.score['unit_0_r2_std'], round_to)})"
r2 = f"Bayesian $R^2$ on fit data = {title_info}"
percentiles = self.discontinuity_at_threshold.quantile(
[(1 - hdi_prob) / 2, 1 - (1 - hdi_prob) / 2]
).values
ci = (
rf"$CI_{{{hdi_prob * 100:.0f}\%}}$"
+ f"[{round_num(percentiles[0], round_to)}, {round_num(percentiles[1], round_to)}]"
)
discon = f"""
Discontinuity at threshold = {round_num(self.discontinuity_at_threshold.mean(), round_to)},
"""
ax.set(title=r2 + "\n" + discon + ci)
# Treatment threshold line
ax.axvline(
x=self.treatment_threshold,
ls="-",
lw=3,
color="r",
label="treatment threshold",
)
# Add donut hole boundary lines if donut_hole > 0
if self.donut_hole > 0:
ax.axvline(
x=self.treatment_threshold - self.donut_hole,
ls="--",
lw=2,
color="orange",
label="donut boundary",
)
ax.axvline(
x=self.treatment_threshold + self.donut_hole,
ls="--",
lw=2,
color="orange",
)
ax.legend(fontsize=LEGEND_FONT_SIZE)
return (fig, ax)
def _ols_plot(
self,
round_to: int | None = None,
figsize: tuple[float, float] | None = None,
**kwargs: Any,
) -> tuple[plt.Figure, plt.Axes]:
"""Generate plot for regression discontinuity designs.
Parameters
----------
round_to : int, optional
Number of decimals used to round results.
figsize : tuple of (float, float), optional
Width and height of the figure in inches. Defaults to ``None``
(use matplotlib's default).
"""
fig, ax = plt.subplots(figsize=figsize)
# Plot data: use two layers only when there are excluded observations
has_exclusion = len(self.fit_data) < len(self.data)
if has_exclusion:
sns.scatterplot(
self.data,
x=self.running_variable_name,
y=self.outcome_variable_name,
color="lightgray",
ax=ax,
label="excluded data",
)
sns.scatterplot(
self.fit_data,
x=self.running_variable_name,
y=self.outcome_variable_name,
color="k",
ax=ax,
label="fit data" if has_exclusion else "data",
)
# Plot model fit to data
ax.plot(
self.x_pred[self.running_variable_name],
self.pred,
"k",
markersize=10,
label="model fit",
)
# create strings to compose title
r2 = f"$R^2$ on fit data = {round_num(float(self.score), round_to)}"
discon = f"Discontinuity at threshold = {round_num(self.discontinuity_at_threshold, round_to)}"
ax.set(title=r2 + "\n" + discon)
# Treatment threshold line
ax.axvline(
x=self.treatment_threshold,
ls="-",
lw=3,
color="r",
label="treatment threshold",
)
# Add donut hole boundary lines if donut_hole > 0
if self.donut_hole > 0:
ax.axvline(
x=self.treatment_threshold - self.donut_hole,
ls="--",
lw=2,
color="orange",
label="donut boundary",
)
ax.axvline(
x=self.treatment_threshold + self.donut_hole,
ls="--",
lw=2,
color="orange",
)
ax.legend(fontsize=LEGEND_FONT_SIZE)
return (fig, ax)
[docs]
def effect_summary(
self,
*,
direction: Literal["increase", "decrease", "two-sided"] = "increase",
alpha: float = 0.05,
min_effect: float | None = None,
**kwargs: Any,
) -> EffectSummary:
"""
Generate a decision-ready summary of causal effects for Regression Discontinuity.
Parameters
----------
direction : {"increase", "decrease", "two-sided"}, default="increase"
Direction for tail probability calculation (PyMC only, ignored for OLS).
alpha : float, default=0.05
Significance level for HDI/CI intervals (1-alpha confidence level).
min_effect : float, optional
Region of Practical Equivalence (ROPE) threshold (PyMC only, ignored for OLS).
Returns
-------
EffectSummary
Object with .table (DataFrame) and .text (str) attributes
"""
return _effect_summary_rd(
self,
direction=direction,
alpha=alpha,
min_effect=min_effect,
)
