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	2.357083	True	9.125432
1	1.083218	True	8.333562
2	-1.405914	True	0.612934
3	0.544866	True	7.162384
4	0.678475	True	5.906530
...	...	...	...
995	1.141585	False	1.742434
996	1.448861	True	9.645512
997	-1.180041	False	-2.199560
998	0.331246	True	4.966359
999	-1.905690	False	-5.905464

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	1.863823	False	5.043438	0.341879	2.925007
1	-0.942918	False	-3.132091	0.628782	1.590376
2	2.051547	False	5.045559	0.324322	3.083357
3	0.272542	False	1.963705	0.503791	1.984952
4	-0.626944	False	-2.131502	0.597230	1.674395
...	...	...	...	...	...
995	0.274917	False	1.188372	0.503541	1.985937
996	2.142835	False	3.724875	0.315955	3.165004
997	1.085725	False	1.130440	0.418905	2.387177
998	1.057579	False	3.510709	0.421793	2.370833
999	0.407694	False	1.097901	0.489564	2.042634

1000 rows × 5 columns

cdf_1

	W0	v0	y	propensity_score	weight
0	0.700487	True	6.066825	0.541168	1.847855
1	3.784091	True	12.722615	0.812076	1.231411
2	-0.491960	True	6.804122	0.416515	2.400874
3	2.036653	True	10.598381	0.674302	1.483014
4	0.350898	True	6.921556	0.504458	1.982325
...	...	...	...	...	...
995	-0.334890	True	5.265809	0.432673	2.311215
996	0.624873	True	8.145840	0.533252	1.875286
997	-0.635418	True	2.679304	0.401911	2.488111
998	1.072236	True	8.313301	0.579712	1.724995
999	0.011895	True	4.776788	0.468810	2.133060

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()

$\displaystyle 5.01140720806203$

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

$\displaystyle 0.233198698453047$

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):	0.966
Model:	OLS	Adj. R-squared (uncentered):	0.966
Method:	Least Squares	F-statistic:	1.425e+04
Date:	Fri, 22 Nov 2024	Prob (F-statistic):	0.00
Time:	16:01:30	Log-Likelihood:	-1453.3
No. Observations:	1000	AIC:	2911.
Df Residuals:	998	BIC:	2920.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
x1	2.4043	0.033	73.345	0.000	2.340	2.469
x2	5.0004	0.052	96.720	0.000	4.899	5.102

Omnibus:	0.868	Durbin-Watson:	1.919
Prob(Omnibus):	0.648	Jarque-Bera (JB):	0.742
Skew:	0.003	Prob(JB):	0.690
Kurtosis:	3.133	Cond. No.	2.05

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.