DoWhy: Different estimation methods for causal inference#

This is a quick introduction to the DoWhy causal inference library. We will load in a sample dataset and use different methods for estimating the causal effect of a (pre-specified)treatment variable on a (pre-specified) outcome variable.

We will see that not all estimators return the correct effect for this dataset.

First, let us add the required path for Python to find the DoWhy code and load all required packages

[1]:

%load_ext autoreload
%autoreload 2

[2]:

import numpy as np
import pandas as pd
import logging

import dowhy
from dowhy import CausalModel
import dowhy.datasets

Now, let us load a dataset. For simplicity, we simulate a dataset with linear relationships between common causes and treatment, and common causes and outcome.

Beta is the true causal effect.

[3]:

data = dowhy.datasets.linear_dataset(beta=10,
        num_common_causes=5,
        num_instruments = 2,
        num_treatments=1,
        num_samples=10000,
        treatment_is_binary=True,
        outcome_is_binary=False,
        stddev_treatment_noise=10)
df = data["df"]
df

[3]:

	Z0	Z1	W0	W1	W2	W3	W4	v0	y
0	1.0	0.420540	-0.278258	0.728096	1.234210	-0.225092	0.019375	True	17.355771
1	1.0	0.269419	1.625433	0.281744	-0.460590	-0.120219	0.366446	True	16.107060
2	1.0	0.277130	0.575462	-0.759209	0.852426	-1.400864	0.263989	True	10.382755
3	1.0	0.795284	-0.034004	-1.979313	1.183313	0.043180	-0.255436	True	5.284863
4	1.0	0.001461	1.146300	0.531869	-2.295174	-1.120785	0.323273	True	5.829430
...	...	...	...	...	...	...	...	...	...
9995	1.0	0.844883	0.882286	0.113607	-0.387080	1.036019	-0.119958	True	13.985591
9996	1.0	0.139265	-0.421890	0.014155	0.333491	0.495016	-1.191373	False	-0.508320
9997	1.0	0.853678	0.780388	-0.333618	0.161790	-0.971771	0.785586	True	11.433230
9998	1.0	0.216467	-0.243671	0.177343	0.935294	-1.665118	2.466833	True	13.487902
9999	1.0	0.670492	-0.396555	-2.256921	0.962781	0.267790	0.119381	True	2.219924

10000 rows × 9 columns

Note that we are using a pandas dataframe to load the data.

Identifying the causal estimand#

We now input a causal graph in the DOT graph format.

[4]:

# With graph
model=CausalModel(
        data = df,
        treatment=data["treatment_name"],
        outcome=data["outcome_name"],
        graph=data["gml_graph"],
        instruments=data["instrument_names"]
        )

[5]:

model.view_model()

../_images/example_notebooks_dowhy_estimation_methods_9_0.png

[6]:

from IPython.display import Image, display
display(Image(filename="causal_model.png"))

../_images/example_notebooks_dowhy_estimation_methods_10_0.png

We get a causal graph. Now identification and estimation is done.

[7]:

identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)
print(identified_estimand)

Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

### Estimand : 2
Estimand name: iv
Estimand expression:
 ⎡                              -1⎤
 ⎢    d        ⎛    d          ⎞  ⎥
E⎢─────────(y)⋅⎜─────────([v₀])⎟  ⎥
 ⎣d[Z₁  Z₀]    ⎝d[Z₁  Z₀]      ⎠  ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z1,Z0})
Estimand assumption 2, Exclusion: If we remove {Z1,Z0}→{v0}, then ¬({Z1,Z0}→y)

### Estimand : 3
Estimand name: frontdoor
No such variable(s) found!

Method 1: Regression#

Use linear regression.

[8]:

causal_estimate_reg = model.estimate_effect(identified_estimand,
        method_name="backdoor.linear_regression",
        test_significance=True)
print(causal_estimate_reg)
print("Causal Estimate is " + str(causal_estimate_reg.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

## Realized estimand
b: y~v0+W0+W2+W4+W3+W1
Target units: ate

## Estimate
Mean value: 10.000090289532139
p-value: [0.]

Causal Estimate is 10.000090289532139

Method 2: Distance Matching#

Define a distance metric and then use the metric to match closest points between treatment and control.

[9]:

causal_estimate_dmatch = model.estimate_effect(identified_estimand,
                                              method_name="backdoor.distance_matching",
                                              target_units="att",
                                              method_params={'distance_metric':"minkowski", 'p':2})
print(causal_estimate_dmatch)
print("Causal Estimate is " + str(causal_estimate_dmatch.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

## Realized estimand
b: y~v0+W0+W2+W4+W3+W1
Target units: att

## Estimate
Mean value: 11.234847498639096

Causal Estimate is 11.234847498639096

Method 3: Propensity Score Stratification#

We will be using propensity scores to stratify units in the data.

[10]:

causal_estimate_strat = model.estimate_effect(identified_estimand,
                                              method_name="backdoor.propensity_score_stratification",
                                              target_units="att")
print(causal_estimate_strat)
print("Causal Estimate is " + str(causal_estimate_strat.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

## Realized estimand
b: y~v0+W0+W2+W4+W3+W1
Target units: att

## Estimate
Mean value: 9.99095855052209

Causal Estimate is 9.99095855052209

Method 4: Propensity Score Matching#

We will be using propensity scores to match units in the data.

[11]:

causal_estimate_match = model.estimate_effect(identified_estimand,
                                              method_name="backdoor.propensity_score_matching",
                                              target_units="atc")
print(causal_estimate_match)
print("Causal Estimate is " + str(causal_estimate_match.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

## Realized estimand
b: y~v0+W0+W2+W4+W3+W1
Target units: atc

## Estimate
Mean value: 9.859696500963553

Causal Estimate is 9.859696500963553

Method 5: Weighting#

We will be using (inverse) propensity scores to assign weights to units in the data. DoWhy supports a few different weighting schemes: 1. Vanilla Inverse Propensity Score weighting (IPS) (weighting_scheme=”ips_weight”) 2. Self-normalized IPS weighting (also known as the Hajek estimator) (weighting_scheme=”ips_normalized_weight”) 3. Stabilized IPS weighting (weighting_scheme = “ips_stabilized_weight”)

[12]:

causal_estimate_ipw = model.estimate_effect(identified_estimand,
                                            method_name="backdoor.propensity_score_weighting",
                                            target_units = "ate",
                                            method_params={"weighting_scheme":"ips_weight"})
print(causal_estimate_ipw)
print("Causal Estimate is " + str(causal_estimate_ipw.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
  d
─────(E[y|W0,W2,W4,W3,W1])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W2,W4,W3,W1,U) = P(y|v0,W0,W2,W4,W3,W1)

## Realized estimand
b: y~v0+W0+W2+W4+W3+W1
Target units: ate

## Estimate
Mean value: 12.157753898021806

Causal Estimate is 12.157753898021806

Method 6: Instrumental Variable#

We will be using the Wald estimator for the provided instrumental variable.

[13]:

causal_estimate_iv = model.estimate_effect(identified_estimand,
        method_name="iv.instrumental_variable", method_params = {'iv_instrument_name': 'Z0'})
print(causal_estimate_iv)
print("Causal Estimate is " + str(causal_estimate_iv.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: iv
Estimand expression:
 ⎡                              -1⎤
 ⎢    d        ⎛    d          ⎞  ⎥
E⎢─────────(y)⋅⎜─────────([v₀])⎟  ⎥
 ⎣d[Z₁  Z₀]    ⎝d[Z₁  Z₀]      ⎠  ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z1,Z0})
Estimand assumption 2, Exclusion: If we remove {Z1,Z0}→{v0}, then ¬({Z1,Z0}→y)

## Realized estimand
Realized estimand: Wald Estimator
Realized estimand type: EstimandType.NONPARAMETRIC_ATE
Estimand expression:
 ⎡ d    ⎤
E⎢───(y)⎥
 ⎣dZ₀   ⎦
──────────
 ⎡ d     ⎤
E⎢───(v₀)⎥
 ⎣dZ₀    ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z1,Z0})
Estimand assumption 2, Exclusion: If we remove {Z1,Z0}→{v0}, then ¬({Z1,Z0}→y)
Estimand assumption 3, treatment_effect_homogeneity: Each unit's treatment ['v0'] is affected in the same way by common causes of ['v0'] and ['y']
Estimand assumption 4, outcome_effect_homogeneity: Each unit's outcome ['y'] is affected in the same way by common causes of ['v0'] and ['y']

Target units: ate

## Estimate
Mean value: 8.292827440916662

Causal Estimate is 8.292827440916662

Method 7: Regression Discontinuity#

We will be internally converting this to an equivalent instrumental variables problem.

[14]:

causal_estimate_regdist = model.estimate_effect(identified_estimand,
        method_name="iv.regression_discontinuity",
        method_params={'rd_variable_name':'Z1',
                       'rd_threshold_value':0.5,
                       'rd_bandwidth': 0.15})
print(causal_estimate_regdist)
print("Causal Estimate is " + str(causal_estimate_regdist.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: iv
Estimand expression:
 ⎡                              -1⎤
 ⎢    d        ⎛    d          ⎞  ⎥
E⎢─────────(y)⋅⎜─────────([v₀])⎟  ⎥
 ⎣d[Z₁  Z₀]    ⎝d[Z₁  Z₀]      ⎠  ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z1,Z0})
Estimand assumption 2, Exclusion: If we remove {Z1,Z0}→{v0}, then ¬({Z1,Z0}→y)

## Realized estimand
Realized estimand: Wald Estimator
Realized estimand type: EstimandType.NONPARAMETRIC_ATE
Estimand expression:
 ⎡        d            ⎤
E⎢──────────────────(y)⎥
 ⎣dlocal_rd_variable   ⎦
─────────────────────────
 ⎡        d             ⎤
E⎢──────────────────(v₀)⎥
 ⎣dlocal_rd_variable    ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z1,Z0})
Estimand assumption 2, Exclusion: If we remove {Z1,Z0}→{v0}, then ¬({Z1,Z0}→y)
Estimand assumption 3, treatment_effect_homogeneity: Each unit's treatment ['v0'] is affected in the same way by common causes of ['v0'] and ['y']
Estimand assumption 4, outcome_effect_homogeneity: Each unit's outcome ['y'] is affected in the same way by common causes of ['v0'] and ['y']

Target units: ate

## Estimate
Mean value: 13.897202752030683

Causal Estimate is 13.897202752030683