Simulating Causal Data: A Step-by-Step Guide
simulate-causal-data.Rmd🧪 Why Simulate Causal Data?
Simulating data helps us validate assumptions and understand the behavior of causal estimators under controlled conditions. It’s also a great tool for teaching.
1. 🎲 Simulate Covariates
set.seed(123)
n <- 1000
X1 <- rnorm(n, mean = 50, sd = 10) # Age
X2 <- rbinom(n, 1, 0.5) # Gender (0/1)
X3 <- rnorm(n, mean = 50000, sd = 15000) # Income
covariates <- data.frame(X1, X2, X3)
head(covariates)## X1 X2 X3
## 1 44.39524 0 37685.20
## 2 47.69823 0 45391.14
## 3 65.58708 0 36468.53
## 4 50.70508 1 59406.03
## 5 51.29288 0 66805.33
## 6 67.15065 1 81908.202. 🧮 Simulate Treatment Assignment
We use a logistic model for treatment assignment based on covariates:
logit <- -3 + 0.05 * X1 + 0.8 * X2 - 0.00002 * X3
prob_treat <- 1 / (1 + exp(-logit))
W <- rbinom(n, 1, prob_treat)3. ✨ Define Potential Outcomes
Y0 <- 0.5 * X1 + 2 * X2 + rnorm(n, 0, 5)
Y1 <- Y0 + 5 # Treatment adds 5 units4. 📊 Create Observed Outcome
Y_obs <- ifelse(W == 1, Y1, Y0)
data <- covariates %>%
mutate(treatment = W,
Y0 = Y0,
Y1 = Y1,
Y_obs = Y_obs)
head(data)## X1 X2 X3 treatment Y0 Y1 Y_obs
## 1 44.39524 0 37685.20 0 21.44608 26.44608 21.44608
## 2 47.69823 0 45391.14 1 22.21033 27.21033 27.21033
## 3 65.58708 0 36468.53 1 25.55272 30.55272 30.55272
## 4 50.70508 1 59406.03 0 23.86612 28.86612 23.86612
## 5 51.29288 0 66805.33 0 38.63889 43.63889 38.63889
## 6 67.15065 1 81908.20 0 35.38825 40.38825 35.388255. 📏 Estimate True vs. Observed Effects
true_ate <- mean(Y1 - Y0)
est_ate <- mean(data$Y_obs[data$treatment == 1]) - mean(data$Y_obs[data$treatment == 0])
cat("True ATE:", round(true_ate, 2), "\n")## True ATE: 5## Estimated ATE (unadjusted): 7.96. 📉 Visualize Propensity Score Overlap
data$prop_score <- prob_treat
ggplot(data, aes(x = prop_score, fill = factor(treatment)))
geom_density(alpha = 0.5)## geom_density: na.rm = FALSE, orientation = NA, outline.type = upper
## stat_density: na.rm = FALSE, orientation = NA
## position_identity
labs(title = "Propensity Score Overlap",
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