Examples with outcomes in {0,1}
library(grf)
library(ggplot2)
library(uplifteval)
#
# Case 1: randomized control trial, treatment propensity is feature independent and equal
# for treatment and control cases, 50-50
#
# Treatment/Response Train/Test
set.seed(123)
W = rbinom(n, 1, 0.5)
W.test = rbinom(n, 1, 0.5)
Y = rl(rl(X[,1]) * W - rl(X[,3]) * W + rnorm(n))
Y.test = rl(rl(X.test[,1]) * W.test - rl(X.test[,3]) * W.test + rnorm(n))
tau.forest = causal_forest(X, Y, W)
tau.hat = predict(tau.forest, X.test)
plot_uplift(tau.hat$predictions, W.test, Y.test)
![](data:image/png;base64,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)
#
# Case 2: randomized control trial, treatment propensity is feature independent but unequal
# for treatment and control cases, 80-20
#
# Treatment/Response Train/Test
set.seed(123)
W = rbinom(n, 1, 0.8)
W.test = rbinom(n, 1, 0.8)
Y = rl(rl(X[,1]) * W - rl(X[,3]) * W + rnorm(n))
Y.test = rl(rl(X.test[,1]) * W.test - rl(X.test[,3]) * W.test + rnorm(n))
table(W.test, Y.test)
## Y.test
## W.test 0 1
## 0 211 211
## 1 782 796
## 0 1
## 422 1578
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)