Demo for the DoWhy causal API

We show a simple example of adding a causal extension to any dataframe.

import dowhy.datasets
import dowhy.api
from dowhy.graph import build_graph_from_str

import numpy as np
import pandas as pd

from statsmodels.api import OLS

data = dowhy.datasets.linear_dataset(beta=5,
        num_common_causes=1,
        num_instruments = 0,
        num_samples=1000,
        treatment_is_binary=True)
df = data['df']
df['y'] = df['y'] + np.random.normal(size=len(df)) # Adding noise to data. Without noise, the variance in Y|X, Z is zero, and mcmc fails.
nx_graph = build_graph_from_str(data["dot_graph"])

treatment= data["treatment_name"][0]
outcome = data["outcome_name"][0]
common_cause = data["common_causes_names"][0]
df

	W0	v0	y
0	0.218115	True	5.192952
1	-2.214109	False	-5.511422
2	-1.604225	False	-2.343443
3	-1.730743	False	-2.996998
4	-2.448299	False	-4.277865
...	...	...	...
995	-2.522898	False	-5.839558
996	0.204025	False	-0.192892
997	-1.183591	False	-3.312228
998	-3.190273	False	-6.103659
999	-1.579944	False	-2.680262

1000 rows × 3 columns

# data['df'] is just a regular pandas.DataFrame
df.causal.do(x=treatment,
             variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
             outcome=outcome,
             common_causes=[common_cause],
            ).groupby(treatment).mean().plot(y=outcome, kind='bar')

<Axes: xlabel='v0'>

df.causal.do(x={treatment: 1},
              variable_types={treatment:'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              method='weighting',
              common_causes=[common_cause]
              ).groupby(treatment).mean().plot(y=outcome, kind='bar')

<Axes: xlabel='v0'>

cdf_1 = df.causal.do(x={treatment: 1},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              graph=nx_graph
              )

cdf_0 = df.causal.do(x={treatment: 0},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              graph=nx_graph
              )

cdf_0

	W0	v0	y	propensity_score	weight
0	-2.155910	False	-3.533915	0.976749	1.023804
1	-0.441365	False	-1.525737	0.704672	1.419100
2	-0.067522	False	-1.295933	0.560761	1.783292
3	-1.382885	False	-2.705320	0.920173	1.086752
4	-0.901488	False	-1.921900	0.837450	1.194100
...	...	...	...	...	...
995	-1.336045	False	-3.185294	0.914225	1.093823
996	-2.543715	False	-4.624259	0.987710	1.012443
997	-2.254571	False	-3.938416	0.980217	1.020183
998	-1.977254	False	-3.226152	0.968902	1.032096
999	-2.201811	False	-3.335031	0.978431	1.022045

1000 rows × 5 columns

cdf_1

	W0	v0	y	propensity_score	weight
0	-1.372984	True	1.117957	0.081052	12.337750
1	0.617011	True	4.452866	0.711133	1.406206
2	0.493633	True	6.485472	0.666967	1.499325
3	-1.276278	True	0.402929	0.093948	10.644226
4	0.166752	True	3.515391	0.536849	1.862721
...	...	...	...	...	...
995	-1.599239	True	1.807711	0.056967	17.554155
996	-1.276278	True	0.402929	0.093948	10.644226
997	-1.276278	True	0.402929	0.093948	10.644226
998	-0.225997	True	5.033551	0.375343	2.664227
999	-1.827456	True	0.308708	0.039604	25.250029

1000 rows × 5 columns

Comparing the estimate to Linear Regression

First, estimating the effect using the causal data frame, and the 95% confidence interval.

(cdf_1['y'] - cdf_0['y']).mean()

$\displaystyle 5.56566625592569$

1.96*(cdf_1['y'] - cdf_0['y']).std() / np.sqrt(len(df))

$\displaystyle 0.173729530342326$

Comparing to the estimate from OLS.

model = OLS(np.asarray(df[outcome]), np.asarray(df[[common_cause, treatment]], dtype=np.float64))
result = model.fit()
result.summary()

OLS Regression Results

Dep. Variable:	y	R-squared (uncentered):	0.931
Model:	OLS	Adj. R-squared (uncentered):	0.931
Method:	Least Squares	F-statistic:	6698.
Date:	Tue, 30 Jan 2024	Prob (F-statistic):	0.00
Time:	17:49:22	Log-Likelihood:	-1385.5
No. Observations:	1000	AIC:	2775.
Df Residuals:	998	BIC:	2785.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
x1	1.7779	0.024	75.608	0.000	1.732	1.824
x2	5.0044	0.059	85.216	0.000	4.889	5.120

Omnibus:	4.605	Durbin-Watson:	1.973
Prob(Omnibus):	0.100	Jarque-Bera (JB):	5.538
Skew:	0.021	Prob(JB):	0.0627
Kurtosis:	3.362	Cond. No.	2.50

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.