Propensity Score Weighting (PSW) for Causal Inference
propensity-score-weighting.Rmd⚖️ Propensity Score Weighting (PSW)
PSW is a technique used to adjust for confounding in observational studies by reweighting units based on their estimated probability of receiving treatment.
1. 🧪 Simulate Confounded Data
set.seed(123)
n <- 1000
X1 <- rnorm(n)
X2 <- rbinom(n, 1, 0.5)
logit_p <- -0.5 + 0.7 * X1 + 1.2 * X2
p_treat <- 1 / (1 + exp(-logit_p))
W <- rbinom(n, 1, p_treat)
# True treatment effect is 3
Y <- 3 * W + 0.5 * X1 + 0.8 * X2 + rnorm(n)
data <- data.frame(X1, X2, W, Y)
head(data)## X1 X2 W Y
## 1 -0.56047565 0 0 -0.7918415
## 2 -0.23017749 0 1 3.1218491
## 3 1.55870831 0 1 3.2377650
## 4 0.07050839 1 1 5.0544818
## 5 0.12928774 0 0 0.2387797
## 6 1.71506499 1 1 4.04226422. 🎯 Estimate Propensity Scores
ps_model <- glm(W ~ X1 + X2, data = data, family = binomial())
data$pscore <- predict(ps_model, type = "response")3. ⚖️ Compute Weights (Inverse Probability of Treatment Weights)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.047 1.377 1.671 1.996 2.268 9.8544. 🧮 Estimate Weighted Treatment Effect
design <- svydesign(ids = ~1, weights = ~wt, data = data)
model_psw <- svyglm(Y ~ W, design = design)
summary(model_psw)##
## Call:
## svyglm(formula = Y ~ W, design = design)
##
## Survey design:
## svydesign(ids = ~1, weights = ~wt, data = data)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.37767 0.05965 6.331 3.67e-10 ***
## W 2.99871 0.08407 35.671 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.307041)
##
## Number of Fisher Scoring iterations: 25. 📊 Visualize Propensity Score Overlap
ggplot(data, aes(x = pscore, fill = factor(W)))
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 Distribution by Treatment",
x = "Propensity Score", fill = "Treatment")## $x
## [1] "Propensity Score"
##
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## [1] "Treatment"
##
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## [1] "Propensity Score Distribution by Treatment"
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