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 0.0 0.732554 1.518951 -1.560528 -0.697295 0.783474 1.884454 True 16.017025
1 0.0 0.727691 -0.488773 -1.351036 -1.520950 0.862655 -1.403365 False -11.419509
2 0.0 0.767677 0.580477 -1.272592 1.377322 -0.771671 1.070829 True 12.736185
3 1.0 0.240153 0.612261 -0.755482 0.031606 0.710379 1.575453 True 15.933085
4 0.0 0.080666 1.349404 1.412524 0.315636 1.438546 1.440674 True 24.440090
... ... ... ... ... ... ... ... ... ...
9995 1.0 0.742503 -1.124004 0.956927 -1.416743 0.887096 1.666348 True 15.514564
9996 1.0 0.821016 1.342820 -1.015955 3.047684 1.525745 0.537836 True 17.588527
9997 1.0 0.833965 -0.384645 0.327460 -0.960303 1.307140 1.031407 True 14.002239
9998 1.0 0.481139 1.058692 -0.208580 -0.833996 -0.414956 -0.378539 True 8.936321
9999 1.0 0.351566 0.531261 0.767018 1.017878 2.307427 0.326756 True 18.204685

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

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

## Estimate
Mean value: 10.000251050500552
p-value: [0.]

Causal Estimate is 10.000251050500552

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

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

## Estimate
Mean value: 11.41573311376212

Causal Estimate is 11.41573311376212

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

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

## Estimate
Mean value: 10.07293804925533

Causal Estimate is 10.07293804925533

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

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

## Estimate
Mean value: 9.953030453855026

Causal Estimate is 9.953030453855026

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

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

## Estimate
Mean value: 12.86354579992946

Causal Estimate is 12.86354579992946

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: 10.655488150029479

Causal Estimate is 10.655488150029479

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: 17.983392181048394

Causal Estimate is 17.983392181048394

Method 8: Doubly Robust Estimator#

Combines a regression estimator and a propensity score estimator to give back a doubly robust estimate.

[15]:

causal_estimate_doubly_robust = model.estimate_effect(identified_estimand,
        method_name="backdoor.doubly_robust",
        method_params={'propensity_score_column':'propensity_score_dr'}
    )
print(causal_estimate_doubly_robust)
print("Causal Estimate is " + str(causal_estimate_doubly_robust.value))

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

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

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

## Estimate
Mean value: 10.000106263655653

Causal Estimate is 10.000106263655653

[ ]: