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]:
import os, sys
sys.path.append(os.path.abspath("../../"))

import dowhy
from dowhy import CausalModel
from rpy2.robjects import r as R
%load_ext rpy2.ipython

#%R install.packages("Matching")
%R library(Matching)

R[write to console]: Loading required package: MASS

R[write to console]: ##
##  Matching (Version 4.9-5, Build Date: 2019-03-05)
##  See http://sekhon.berkeley.edu/matching for additional documentation.
##  Please cite software as:
##   Jasjeet S. Sekhon. 2011. ``Multivariate and Propensity Score Matching
##   Software with Automated Balance Optimization: The Matching package for R.''
##   Journal of Statistical Software, 42(7): 1-52.
##


[1]:
array(['Matching', 'MASS', 'tools', 'stats', 'graphics', 'grDevices',
       'utils', 'datasets', 'methods', 'base'],
      dtype='<U9')

1. Load the data

[2]:
%R data(lalonde)
%R -o lalonde

Run DoWhy analysis: model, identify, estimate

[3]:

model=CausalModel(
        data = lalonde,
        treatment='treat',
        outcome='re78',
        common_causes='nodegr+black+hisp+age+educ+married'.split('+'))
identified_estimand = model.identify_effect()
estimate = model.estimate_effect(identified_estimand,
        method_name="backdoor.propensity_score_weighting")
#print(estimate)
print("Causal Estimate is " + str(estimate.value))
WARNING:dowhy.do_why:Causal Graph not provided. DoWhy will construct a graph based on data inputs.
INFO:dowhy.do_why:Model to find the causal effect of treatment ['treat'] on outcome ['re78']
INFO:dowhy.causal_identifier:Common causes of treatment and outcome:['U', 'age', 'educ', 'black', 'nodegr', 'married', 'hisp']
WARNING:dowhy.causal_identifier:There are unobserved common causes. Causal effect cannot be identified.
WARN: Do you want to continue by ignoring these unobserved confounders? [y/n] y
INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]
INFO:dowhy.causal_estimator:INFO: Using Propensity Score Weighting Estimator
INFO:dowhy.causal_estimator:b: re78~treat+age+educ+black+nodegr+married+hisp
Causal Estimate is 1634.98683597

Sanity check: compare to manual IPW estimate

[4]:
df = model._data
ps = df['ps']
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 1634.98683597