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 0.599617 0.987522 0.718951 -1.829025 1.559528 0.263296 True 16.127581
1 1.0 0.590161 1.270548 -0.148518 -2.817064 2.580094 -0.144950 True 13.174968
2 1.0 0.434652 2.008862 0.553826 -0.495537 0.864872 -0.328797 True 20.382370
3 1.0 0.648042 0.746165 0.727334 0.435350 0.450554 0.302142 True 17.097433
4 0.0 0.818920 2.428914 0.164319 -0.657531 0.894878 1.045400 True 23.242296
... ... ... ... ... ... ... ... ... ...
9995 0.0 0.187351 2.242982 0.366498 -1.518279 -1.556618 1.321761 False 11.386254
9996 1.0 0.635914 -0.816283 1.846904 -1.091740 -1.438953 0.769818 True 11.892775
9997 0.0 0.727264 -0.092182 -0.233206 -1.330694 1.117642 1.107769 True 9.800697
9998 1.0 0.804116 -0.004247 0.774242 0.916395 1.357830 0.915869 True 15.896472
9999 1.0 0.697577 -0.276008 1.671590 -0.458146 -0.635614 0.144806 True 13.779887

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

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

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

## Estimate
Mean value: 9.999659607307734
p-value: [0.]

Causal Estimate is 9.999659607307734

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

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

## Estimate
Mean value: 10.422181419263403

Causal Estimate is 10.422181419263403

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

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

## Estimate
Mean value: 9.916507562837996

Causal Estimate is 9.916507562837996

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

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

## Estimate
Mean value: 10.11696283352416

Causal Estimate is 10.11696283352416

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

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

## Estimate
Mean value: 10.518223102337979

Causal Estimate is 10.518223102337979

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: 9.958382916353516

Causal Estimate is 9.958382916353516

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: 3.6440812061614367

Causal Estimate is 3.6440812061614367