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 0.0 0.704525 -0.782334 0.912712 -0.326709 -0.916415 -1.437230 True -1.938350
1 0.0 0.634309 2.653327 -1.244384 -2.164224 -0.709055 -0.278746 True 4.160916
2 0.0 0.843368 0.297434 0.411211 -4.074289 -1.073584 -0.278433 True 1.991565
3 0.0 0.268412 0.554824 -0.206043 -1.696063 -1.265048 -2.254591 False -19.002357
4 0.0 0.357459 2.148252 -1.039844 -1.703303 -0.984250 -0.520179 False -8.445233
... ... ... ... ... ... ... ... ... ...
9995 0.0 0.742030 1.240386 -2.324650 -0.547930 -0.245268 -1.879787 False -13.170984
9996 0.0 0.285081 1.054511 0.515983 -1.054616 -0.102827 1.338401 True 17.235061
9997 0.0 0.096736 0.179916 0.610938 -2.676914 -0.473083 0.213557 False -1.611572
9998 0.0 0.712476 -1.659908 1.376492 -1.216827 -1.183254 -1.398189 True -3.460236
9999 0.0 0.932313 0.689947 1.865426 -0.499661 -2.193923 0.402045 True 2.798228

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

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

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

## Estimate
Mean value: 9.999877153376403
p-value: 0 (significant at alpha=0.05; H0: treatment has no causal effect on outcome)

Causal Estimate is 9.999877153376403

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

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

## Estimate
Mean value: 10.373697557675076

Causal Estimate is 10.373697557675076

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

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

## Estimate
Mean value: 10.023169004709636

Causal Estimate is 10.023169004709636

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

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

## Estimate
Mean value: 9.926494753429123

Causal Estimate is 9.926494753429123

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

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

## Estimate
Mean value: 10.023248250229337

Causal Estimate is 10.023248250229337

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: 9.139479538554168

Causal Estimate is 9.139479538554168

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: 4.595883490660934

Causal Estimate is 4.595883490660934

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

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

## Estimate
Mean value: 9.999918104142566

Causal Estimate is 9.999918104142566

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))

[ ]: