import itertools
from typing import List, Optional, Union
import pandas as pd
import statsmodels.api as sm
from dowhy.causal_estimator import CausalEstimator
from dowhy.causal_estimators.regression_estimator import RegressionEstimator
from dowhy.causal_identifier import IdentifiedEstimand
[docs]class LinearRegressionEstimator(RegressionEstimator):
"""Compute effect of treatment using linear regression.
Fits a regression model for estimating the outcome using treatment(s) and confounders. For a univariate treatment, the treatment effect is equivalent to the coefficient of the treatment variable.
Simple method to show the implementation of a causal inference method that can handle multiple treatments and heterogeneity in treatment. Requires a strong assumption that all relationships from (T, W) to Y are linear.
"""
def __init__(
self,
identified_estimand: IdentifiedEstimand,
test_significance: bool = False,
evaluate_effect_strength: bool = False,
confidence_intervals: bool = False,
num_null_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_STAT_TEST,
num_simulations: int = CausalEstimator.DEFAULT_NUMBER_OF_SIMULATIONS_CI,
sample_size_fraction: int = CausalEstimator.DEFAULT_SAMPLE_SIZE_FRACTION,
confidence_level: float = CausalEstimator.DEFAULT_CONFIDENCE_LEVEL,
need_conditional_estimates: Union[bool, str] = "auto",
num_quantiles_to_discretize_cont_cols: int = CausalEstimator.NUM_QUANTILES_TO_DISCRETIZE_CONT_COLS,
**kwargs,
):
"""
:param identified_estimand: probability expression
representing the target identified estimand to estimate.
:param test_significance: Binary flag or a string indicating whether to test significance and by which method. All estimators support test_significance="bootstrap" that estimates a p-value for the obtained estimate using the bootstrap method. Individual estimators can override this to support custom testing methods. The bootstrap method supports an optional parameter, num_null_simulations. If False, no testing is done. If True, significance of the estimate is tested using the custom method if available, otherwise by bootstrap.
:param evaluate_effect_strength: (Experimental) whether to evaluate the strength of effect
:param confidence_intervals: Binary flag or a string indicating whether the confidence intervals should be computed and which method should be used. All methods support estimation of confidence intervals using the bootstrap method by using the parameter confidence_intervals="bootstrap". The bootstrap method takes in two arguments (num_simulations and sample_size_fraction) that can be optionally specified in the params dictionary. Estimators may also override this to implement their own confidence interval method. If this parameter is False, no confidence intervals are computed. If True, confidence intervals are computed by the estimator's specific method if available, otherwise through bootstrap
:param num_null_simulations: The number of simulations for testing the
statistical significance of the estimator
:param num_simulations: The number of simulations for finding the
confidence interval (and/or standard error) for a estimate
:param sample_size_fraction: The size of the sample for the bootstrap
estimator
:param confidence_level: The confidence level of the confidence
interval estimate
:param need_conditional_estimates: Boolean flag indicating whether
conditional estimates should be computed. Defaults to True if
there are effect modifiers in the graph
:param num_quantiles_to_discretize_cont_cols: The number of quantiles
into which a numeric effect modifier is split, to enable
estimation of conditional treatment effect over it.
:param kwargs: (optional) Additional estimator-specific parameters
"""
super().__init__(
identified_estimand=identified_estimand,
test_significance=test_significance,
evaluate_effect_strength=evaluate_effect_strength,
confidence_intervals=confidence_intervals,
num_null_simulations=num_null_simulations,
num_simulations=num_simulations,
sample_size_fraction=sample_size_fraction,
confidence_level=confidence_level,
need_conditional_estimates=need_conditional_estimates,
num_quantiles_to_discretize_cont_cols=num_quantiles_to_discretize_cont_cols,
**kwargs,
)
self.logger.info("INFO: Using Linear Regression Estimator")
self._linear_model = self.model
[docs] def fit(
self,
data: pd.DataFrame,
treatment_name: str,
outcome_name: str,
effect_modifier_names: Optional[List[str]] = None,
):
"""
Fits the estimator with data for effect estimation
:param data: data frame containing the data
:param treatment: name of the treatment variable
:param outcome: name of the outcome variable
:param effect_modifiers: Variables on which to compute separate
effects, or return a heterogeneous effect function. Not all
methods support this currently.
"""
return super().fit(data, treatment_name, outcome_name, effect_modifier_names=effect_modifier_names)
[docs] def construct_symbolic_estimator(self, estimand):
expr = "b: " + ",".join(estimand.outcome_variable) + "~"
var_list = estimand.treatment_variable + estimand.get_backdoor_variables()
expr += "+".join(var_list)
if self._effect_modifier_names:
interaction_terms = [
"{0}*{1}".format(x[0], x[1])
for x in itertools.product(estimand.treatment_variable, self._effect_modifier_names)
]
expr += "+" + "+".join(interaction_terms)
return expr
[docs] def predict_fn(self, model, features):
return model.predict(features)
def _build_model(self):
features = self._build_features()
model = sm.OLS(self._outcome, features).fit()
return (features, model)
def _estimate_confidence_intervals(self, confidence_level, method=None):
if self._effect_modifier_names:
# The average treatment effect is a combination of different
# regression coefficients. Complicated to compute the confidence
# interval analytically. For example, if y=a + b1.t + b2.tx, then
# the average treatment effect is b1+b2.mean(x).
# Refer Gelman, Hill. ARM Book. Chapter 9
# http://www.stat.columbia.edu/~gelman/arm/chap9.pdf
# TODO: Looking for contributions
raise NotImplementedError
else:
conf_ints = self.model.conf_int(alpha=1 - confidence_level)
# For a linear regression model, the causal effect of a variable is equal to the coefficient corresponding to the
# variable. Hence, the model by default outputs the confidence interval corresponding to treatment=1 and control=0.
# So for custom treatment and control values, we must multiply the confidence interval by the difference of the two.
return (self._treatment_value - self._control_value) * conf_ints.to_numpy()[
1 : (len(self._treatment_name) + 1), :
]
def _estimate_std_error(self, method=None):
if self._effect_modifier_names:
raise NotImplementedError
else:
std_error = self.model.bse[1 : (len(self._treatment_name) + 1)]
# For a linear regression model, the causal effect of a variable is equal to the coefficient corresponding to the
# variable. Hence, the model by default outputs the standard error corresponding to treatment=1 and control=0.
# So for custom treatment and control values, we must multiply the standard error by the difference of the two.
return (self._treatment_value - self._control_value) * std_error.to_numpy()
def _test_significance(self, estimate_value, method=None):
pvalue = self.model.pvalues[1 : (len(self._treatment_name) + 1)]
return {"p_value": pvalue.to_numpy()}