# 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 0.0 0.183046 -1.584617 2.594102 -0.873287 -1.351929 0.338049 True 0.005544
1 0.0 0.337697 -1.462517 1.166944 -0.671212 -0.443467 1.013824 True 4.043717
2 0.0 0.327831 0.382340 2.243824 -1.005430 -0.287017 1.296490 True 13.920692
3 0.0 0.443794 -0.680094 -0.513014 0.128646 0.203297 1.552857 True 10.090345
4 0.0 0.010230 -2.172281 -0.228350 -0.420918 -0.669902 1.066579 False -12.109641
... ... ... ... ... ... ... ... ... ...
9995 0.0 0.761943 -1.064414 1.656108 0.791537 1.696921 -0.963975 True 19.122189
9996 0.0 0.543688 -2.417296 1.705982 -2.750969 -1.316622 -0.349984 True -10.805397
9997 0.0 0.218620 -0.965225 0.167992 -1.423925 -0.429401 -0.847815 False -10.747257
9998 0.0 0.287105 1.073352 0.362506 -0.923114 0.677529 -1.199447 False 4.453518
9999 0.0 0.183926 0.186028 0.209745 -0.622012 0.273594 0.827778 True 12.295669

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: EstimandType.NONPARAMETRIC_ATE

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

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

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

## Estimate
Mean value: 9.999867001292966
p-value: [0.]

Causal Estimate is 9.999867001292966


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

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

## Estimate
Mean value: 10.452414271611765

Causal Estimate is 10.452414271611765


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

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

## Estimate
Mean value: 9.988734510040771

Causal Estimate is 9.988734510040771


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

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

## Estimate
Mean value: 9.781574917414902

Causal Estimate is 9.781574917414902


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

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

## Estimate
Mean value: 9.955909411739029

Causal Estimate is 9.955909411739029


## 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    ⎤  -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: 25.792019148577538

Causal Estimate is 25.792019148577538


## 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            ⎤  -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 ['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: 4.778919332524537

Causal Estimate is 4.778919332524537