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
dowhy.enable_notebook_rendering()
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 0.742926 0.132401 -0.724461 -0.460337 -0.228409 -2.095329 True -3.368410
1 1.0 0.441858 0.559746 -1.023063 -0.681075 -0.333692 -0.826452 True 1.893179
2 1.0 0.155342 0.369749 -0.154162 -0.198876 0.938036 0.324386 True 11.529116
3 1.0 0.032086 -1.160104 -0.706965 0.868246 2.125732 -0.163555 True 5.505470
4 1.0 0.747433 0.424116 -0.107108 0.151788 -0.221257 -1.050664 True 6.902500
... ... ... ... ... ... ... ... ... ...
9995 1.0 0.818075 -1.395895 -0.929861 0.542032 0.979205 0.284156 True 4.566022
9996 1.0 0.560798 -1.008459 0.882250 0.248719 2.213080 1.018319 True 15.424961
9997 1.0 0.029987 -0.305156 -1.074124 -1.964947 0.510933 -0.456936 False -14.172858
9998 1.0 0.911454 -2.376290 0.020091 0.231346 2.071369 0.612979 True 5.256452
9999 1.0 0.871265 -1.490781 -0.934707 0.735331 1.508539 -0.243239 True 2.563992

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

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

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

## Estimate
Mean value: 10.000216521319416
p-value: 0 (significant at alpha=0.05; H0: treatment has no causal effect on outcome)

Causal Estimate is 10.000216521319416

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))

/home/runner/.cache/pypoetry/virtualenvs/dowhy-n6DJFijf-py3.9/lib/python3.9/site-packages/sklearn/neighbors/_unsupervised.py:179: SyntaxWarning: Parameter p is found in metric_params. The corresponding parameter from __init__ is ignored.
  return self._fit(X)

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

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

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

## Estimate
Mean value: 10.97928168972623

Causal Estimate is 10.97928168972623

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

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

## Estimate
Mean value: 9.801303520892077

Causal Estimate is 9.801303520892077

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

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

## Estimate
Mean value: 9.944371003142793

Causal Estimate is 9.944371003142793

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

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

## Estimate
Mean value: 11.468183299770502

Causal Estimate is 11.468183299770502

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: 10.376117553492584

Causal Estimate is 10.376117553492584

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: 11.32914473759521

Causal Estimate is 11.32914473759521

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

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

## Estimate
Mean value: 10.000706545483858

Causal Estimate is 10.000706545483858

Method 9: Tab-PFN Estimator#

We will use a TabPFN (Prior-Data Fitted Network) as the outcome model to estimate the causal effect via backdoor adjustment.
Best suited for datasets with ≤10,000 samples and ≤500 features; requires ‘pip install tabpfn torch’.

Note: This example uses 10,000 samples thus requires a GPU. For a CPU-compatible walkthrough with smaller datasets, see dowhy_tabpfn_estimator.ipynb.

[16]:

# causal_estimate_tabpfn = model.estimate_effect(identified_estimand,
#         method_name="backdoor.tabpfn",
#         method_params={
#             "n_estimators": 8,
#             "model_type": "auto",
#             "max_num_classes": 10,
#             "use_multi_gpu": False,
#         },
# )
# print(causal_estimate_tabpfn)
# print("Causal Estimate is " + str(causal_estimate_tabpfn.value))

[ ]: