DoWhy example on the Lalonde dataset

Thanks to [@mizuy](https://github.com/mizuy) for providing this example. Here we use the Lalonde dataset and apply IPW estimator to it.

1. Load the data

[1]:
import dowhy.datasets

lalonde = dowhy.datasets.lalonde_dataset()

2. Run DoWhy analysis: model, identify, estimate

[2]:
from dowhy import CausalModel


model=CausalModel(
        data = lalonde,
        treatment='treat',
        outcome='re78',
        common_causes='nodegr+black+hisp+age+educ+married'.split('+'))
identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)
estimate = model.estimate_effect(identified_estimand,
        method_name="backdoor.propensity_score_weighting",
        target_units="ate",
        method_params={"weighting_scheme":"ips_weight"})

print("Causal Estimate is " + str(estimate.value))

import statsmodels.formula.api as smf
reg=smf.wls('re78~1+treat', data=lalonde, weights=lalonde.ips_stabilized_weight)
res=reg.fit()
res.summary()
Causal Estimate is 1639.8542908702111
[2]:
WLS Regression Results
Dep. Variable: re78 R-squared: 0.015
Model: WLS Adj. R-squared: 0.013
Method: Least Squares F-statistic: 6.743
Date: Tue, 06 Dec 2022 Prob (F-statistic): 0.00972
Time: 09:41:05 Log-Likelihood: -4544.7
No. Observations: 445 AIC: 9093.
Df Residuals: 443 BIC: 9102.
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept 4555.0709 406.707 11.200 0.000 3755.757 5354.385
treat[T.True] 1639.8543 631.498 2.597 0.010 398.750 2880.959
Omnibus: 303.267 Durbin-Watson: 2.085
Prob(Omnibus): 0.000 Jarque-Bera (JB): 4770.872
Skew: 2.709 Prob(JB): 0.00
Kurtosis: 18.098 Cond. No. 2.47


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

3. Interpret the estimate

The plot below shows how the distribution of a confounder, “married” changes from the original data to the weighted data. In both datasets, we compare the distribution of “married” across treated and untreated units.

[3]:
estimate.interpret(method_name="confounder_distribution_interpreter",var_type='discrete',
                   var_name='married', fig_size = (10, 7), font_size = 12)
../_images/example_notebooks_dowhy_lalonde_example_6_0.png

4. Sanity check: compare to manual IPW estimate

[4]:
df = model._data
ps = df['propensity_score']
y = df['re78']
z = df['treat']

ey1 = z*y/ps / sum(z/ps)
ey0 = (1-z)*y/(1-ps) / sum((1-z)/(1-ps))
ate = ey1.sum()-ey0.sum()
print("Causal Estimate is " + str(ate))

# correct -> Causal Estimate is 1634.9868359746906
Causal Estimate is 1639.854290870213