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

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.
#data['dot_graph'] = 'digraph { v ->y;X0-> v;X0-> y;}'

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

	W0	v0	y
0	0.883800	True	6.032204
1	2.151652	True	8.274524
2	0.565327	True	5.615925
3	1.943763	True	9.943361
4	1.025108	True	6.526274
...	...	...	...
995	-1.452482	False	-1.081065
996	1.532964	False	2.817101
997	-0.350965	True	1.761346
998	-1.642007	False	-3.852874
999	0.641072	False	2.620429

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],
                     proceed_when_unidentifiable=True).groupby(treatment).mean().plot(y=outcome, kind='bar')

<AxesSubplot: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],
              proceed_when_unidentifiable=True).groupby(treatment).mean().plot(y=outcome, kind='bar')

<AxesSubplot:xlabel='v0'>

cdf_1 = df.causal.do(x={treatment: 1},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              dot_graph=data['dot_graph'],
              proceed_when_unidentifiable=True)

cdf_0 = df.causal.do(x={treatment: 0},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              dot_graph=data['dot_graph'],
              proceed_when_unidentifiable=True)

cdf_0

	W0	v0	y	propensity_score	weight
0	1.117996	False	2.497059	0.333225	3.000976
1	0.238462	False	0.509070	0.455258	2.196556
2	0.213945	False	2.279505	0.458815	2.179528
3	0.425245	False	-0.297296	0.428336	2.334615
4	2.301323	False	3.431520	0.200139	4.996525
...	...	...	...	...	...
995	0.621286	False	1.458936	0.400531	2.496683
996	1.642750	False	3.409962	0.268860	3.719407
997	0.409933	False	-0.635569	0.430529	2.322722
998	-0.063154	False	0.953209	0.499221	2.003123
999	1.532964	False	2.817101	0.281662	3.550353

1000 rows × 5 columns

cdf_1

	W0	v0	y	propensity_score	weight
0	1.055191	True	5.738184	0.658568	1.518446
1	1.676538	True	7.187013	0.735005	1.360535
2	0.111945	True	4.353155	0.526346	1.899889
3	-0.840229	True	3.503758	0.389082	2.570151
4	0.556640	True	5.125285	0.590361	1.693878
...	...	...	...	...	...
995	0.018338	True	6.145009	0.512687	1.950507
996	0.094625	True	5.329991	0.523821	1.909048
997	0.711712	True	4.394407	0.612092	1.633741
998	1.928415	True	8.157832	0.762678	1.311169
999	-0.280647	True	5.377214	0.469032	2.132052

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()

$\displaystyle 5.092590494260132$

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

$\displaystyle 0.17478007931409847$

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):	0.970
Model:	OLS	Adj. R-squared (uncentered):	0.970
Method:	Least Squares	F-statistic:	1.620e+04
Date:	Tue, 02 Mar 2021	Prob (F-statistic):	0.00
Time:	20:29:26	Log-Likelihood:	-1414.1
No. Observations:	1000	AIC:	2832.
Df Residuals:	998	BIC:	2842.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
x1	1.7444	0.031	55.843	0.000	1.683	1.806
x2	5.0338	0.052	97.742	0.000	4.933	5.135

Omnibus:	4.501	Durbin-Watson:	1.900
Prob(Omnibus):	0.105	Jarque-Bera (JB):	4.538
Skew:	0.147	Prob(JB):	0.103
Kurtosis:	2.851	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.