import numpy as np
import pandas as pd
import statsmodels.api as sm
from sklearn import linear_model
import itertools
from dowhy.causal_estimators.regression_estimator import RegressionEstimator
[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, *args, **kwargs):
super().__init__(*args, **kwargs)
self.logger.info("INFO: Using Linear Regression Estimator")
self._linear_model = self.model
[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
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()}