# 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

[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 0.197138 -0.691872 -1.372022 0.172042 0.068358 2.272122 True 14.569498
1 1.0 0.392689 2.136083 0.631596 0.278084 0.751685 1.179255 True 25.966671
2 0.0 0.148152 0.987179 -1.824034 2.129747 -0.955067 0.785807 True 12.042395
3 1.0 0.074800 -0.189526 0.121871 3.458376 -0.396859 0.689570 True 22.021582
4 1.0 0.660747 1.006848 1.177171 0.545159 1.694644 -0.182411 True 24.839222
... ... ... ... ... ... ... ... ... ...
9995 1.0 0.578062 0.525971 -0.046626 1.447205 1.228802 0.013073 True 21.463849
9996 1.0 0.871685 1.218654 -0.213749 1.353362 0.965070 0.291783 True 22.101114
9997 1.0 0.487310 1.169194 0.561423 1.889485 2.236103 2.105835 True 39.656986
9998 0.0 0.787314 -1.524740 1.225265 -0.456722 0.343157 0.691608 True 13.526224
9999 1.0 0.474732 -1.109809 -0.859009 0.206661 -0.013263 1.505976 True 11.790382

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()

[6]:

from IPython.display import Image, display
display(Image(filename="causal_model.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: nonparametric-ate

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

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

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

## Estimate
Mean value: 9.999572410916503
p-value: [0.]

Causal Estimate is 9.999572410916503


## 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: nonparametric-ate

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

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

## Estimate
Mean value: 11.357951481837551

Causal Estimate is 11.357951481837551


## 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: nonparametric-ate

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

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

## Estimate
Mean value: 10.66216491405692

Causal Estimate is 10.66216491405692


## 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: nonparametric-ate

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

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

## Estimate
Mean value: 10.04273212433988

Causal Estimate is 10.04273212433988


## 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: nonparametric-ate

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

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

## Estimate
Mean value: 13.475913708090541

Causal Estimate is 13.475913708090541


## 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: 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: nonparametric-ate
Estimand expression:
⎡ d    ⎤  -1⎡ d     ⎤
E⎢───(y)⎥⋅E  ⎢───(v₀)⎥
⎣dZ₀   ⎦    ⎣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: 11.330006148394025

Causal Estimate is 11.330006148394025


## 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: 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: nonparametric-ate
Estimand expression:
⎡        d            ⎤  -1⎡        d             ⎤
E⎢──────────────────(y)⎥⋅E  ⎢──────────────────(v₀)⎥
⎣dlocal_rd_variable   ⎦    ⎣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 ['local_treatment'] is affected in the same way by common causes of ['local_treatment'] and local_outcome
Estimand assumption 4, outcome_effect_homogeneity: Each unit's outcome local_outcome is affected in the same way by common causes of ['local_treatment'] and local_outcome

Target units: ate

## Estimate
Mean value: 6.947882393971174

Causal Estimate is 6.947882393971174