DoWhy: Interpreters for Causal Estimators#

This is a quick introduction to the use of interpreters in the DoWhy causal inference library. We will load in a sample dataset, use different methods for estimating the causal effect of a (pre-specified)treatment variable on a (pre-specified) outcome variable and demonstrate how to interpret the obtained results.

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=1,
        num_common_causes=5,
        num_instruments = 2,
        num_treatments=1,
        num_discrete_common_causes=1,
        num_samples=10000,
        treatment_is_binary=True,
        outcome_is_binary=False)
df = data["df"]
print(df[df.v0==True].shape[0])
df
9312
[3]:
Z0 Z1 W0 W1 W2 W3 W4 v0 y
0 1.0 0.641530 1.713793 1.874253 -0.221093 -0.260537 2 True 3.200747
1 1.0 0.984184 -1.364476 0.434188 -1.051483 1.726858 1 True 0.641686
2 1.0 0.112150 -1.788601 1.366158 -0.314059 0.625328 0 True 1.511378
3 0.0 0.862643 -0.908821 1.569849 -0.357711 0.023052 3 True 2.251931
4 1.0 0.504221 1.398525 1.607802 1.202567 2.692107 0 True 4.636784
... ... ... ... ... ... ... ... ... ...
9995 1.0 0.343120 -0.675573 0.529968 0.742533 1.124644 0 True 2.228309
9996 1.0 0.757563 0.679725 0.544759 -0.869416 1.818628 0 True 1.402397
9997 1.0 0.200282 -0.325732 0.938788 0.266229 -0.357658 3 False 1.306689
9998 1.0 0.272021 -1.751228 0.055265 -1.460678 1.330304 1 False -1.258485
9999 1.0 0.660280 -0.607491 1.759983 -0.183637 0.023034 2 True 2.499802

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 GML 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_interpreter_9_0.png
[6]:
from IPython.display import Image, display
display(Image(filename="causal_model.png"))
../_images/example_notebooks_dowhy_interpreter_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|W0,W1,W3,W2,W4])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W1,W3,W2,W4,U) = P(y|v0,W0,W1,W3,W2,W4)

### Estimand : 2
Estimand name: iv
Estimand expression:
 ⎡                              -1⎤
 ⎢    d        ⎛    d          ⎞  ⎥
E⎢─────────(y)⋅⎜─────────([v₀])⎟  ⎥
 ⎣d[Z₀  Z₁]    ⎝d[Z₀  Z₁]      ⎠  ⎦
Estimand assumption 1, As-if-random: If U→→y then ¬(U →→{Z0,Z1})
Estimand assumption 2, Exclusion: If we remove {Z0,Z1}→{v0}, then ¬({Z0,Z1}→y)

### Estimand : 3
Estimand name: frontdoor
No such variable(s) found!

Method 1: Propensity Score Stratification#

We will be using propensity scores to stratify units in the data.

[8]:
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,W1,W3,W2,W4])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W1,W3,W2,W4,U) = P(y|v0,W0,W1,W3,W2,W4)

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

## Estimate
Mean value: 1.047198557310235

Causal Estimate is 1.047198557310235

Textual Interpreter#

The textual Interpreter describes (in words) the effect of unit change in the treatment variable on the outcome variable.

[9]:
# Textual Interpreter
interpretation = causal_estimate_strat.interpret(method_name="textual_effect_interpreter")
Increasing the treatment variable(s) [v0] from 0 to 1 causes an increase of 1.047198557310235 in the expected value of the outcome [['y']], over the data distribution/population represented by the dataset.

Visual Interpreter#

The visual interpreter plots the change in the standardized mean difference (SMD) before and after Propensity Score based adjustment of the dataset. The formula for SMD is given below.

\(SMD = \frac{\bar X_{1} - \bar X_{2}}{\sqrt{(S_{1}^{2} + S_{2}^{2})/2}}\)

Here, \(\bar X_{1}\) and \(\bar X_{2}\) are the sample mean for the treated and control groups.

[10]:
# Visual Interpreter
interpretation = causal_estimate_strat.interpret(method_name="propensity_balance_interpreter")
../_images/example_notebooks_dowhy_interpreter_18_0.png

This plot shows how the SMD decreases from the unadjusted to the stratified units.

Method 2: 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,W1,W3,W2,W4])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W1,W3,W2,W4,U) = P(y|v0,W0,W1,W3,W2,W4)

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

## Estimate
Mean value: 1.001651403011821

Causal Estimate is 1.001651403011821
[12]:
# Textual Interpreter
interpretation = causal_estimate_match.interpret(method_name="textual_effect_interpreter")
Increasing the treatment variable(s) [v0] from 0 to 1 causes an increase of 1.001651403011821 in the expected value of the outcome [['y']], over the data distribution/population represented by the dataset.

Cannot use propensity balance interpretor here since the interpreter method only supports propensity score stratification estimator.

Method 3: 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”)

[13]:
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,W1,W3,W2,W4])
d[v₀]
Estimand assumption 1, Unconfoundedness: If U→{v0} and U→y then P(y|v0,W0,W1,W3,W2,W4,U) = P(y|v0,W0,W1,W3,W2,W4)

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

## Estimate
Mean value: 1.5024239042119965

Causal Estimate is 1.5024239042119965
[14]:
# Textual Interpreter
interpretation = causal_estimate_ipw.interpret(method_name="textual_effect_interpreter")
Increasing the treatment variable(s) [v0] from 0 to 1 causes an increase of 1.5024239042119965 in the expected value of the outcome [['y']], over the data distribution/population represented by the dataset.
[15]:
interpretation = causal_estimate_ipw.interpret(method_name="confounder_distribution_interpreter", fig_size=(8,8), font_size=12, var_name='W4', var_type='discrete')
../_images/example_notebooks_dowhy_interpreter_27_0.png
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