Code example: ATE and HTE

library(MatchIt)

# Simulierte Daten
set.seed(123)
n <- 1000
age <- rnorm(n, 30, 10)
education <- rnorm(n, 12, 2)
income <- 5000 + 500 * age + 1000 * education + rnorm(n, 0, 1000)

# Treatment-Indikator (Teilnahme am Programm)
treatment <- rbinom(n, 1, plogis(0.3 * age - 0.5 * education))

# Einkommen nach Behandlung
income_post <- income + treatment * (500 + (100 * age)) + rnorm(n, 0, 1000)

# Dataframe erstellen
data <- data.frame(age, education, treatment, income_post)

# 1. Matching anhand der Kovariaten durchführen, wobei der Propensity Score intern berechnet wird
match_it <- matchit(treatment ~ age + education, method = "nearest", data = data, caliper = 0.1)

Warning: Fewer control units than treated units; not all treated units will get
a match.

# 2. Gematchte Daten extrahieren
matched_data <- match.data(match_it)

# 3. Überprüfen der Balance der Kovariaten
print(summary(match_it))

Call:
matchit(formula = treatment ~ age + education, data = data, method = "nearest", 
    caliper = 0.1)

Summary of Balance for All Data:
          Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance         0.9063        0.3869          3.1782     0.3003    0.4320
age             32.9607       18.6048          1.6979     1.6467    0.4140
education       11.9552       12.6203         -0.3352     0.9106    0.0869
          eCDF Max
distance    0.7163
age         0.6822
education   0.1407

Summary of Balance for Matched Data:
          Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
distance         0.6104        0.5947          0.0958     1.0773    0.0378
age             24.4119       22.3733          0.2411     3.0428    0.0544
education       12.4633       12.3546          0.0548     0.9319    0.0281
          eCDF Max Std. Pair Dist.
distance      0.07          0.0986
age           0.11          0.5438
education     0.08          1.0853

Sample Sizes:
          Control Treated
All           195     805
Matched       100     100
Unmatched      95     705
Discarded       0       0

# 4. Visualisierung der Balance der Kovariaten nach Matching
library(ggplot2)
ggplot(matched_data, aes(x = factor(treatment), y = age)) +
  geom_boxplot() +
  labs(title = "Verteilung des Alters nach Treatment", x = "Treatment", y = "Age")

ggplot(matched_data, aes(x = factor(treatment), y = education)) +
  geom_boxplot() +
  labs(title = "Verteilung der Bildung nach Treatment", x = "Treatment", y = "Education")

# 5. Schätzen des Behandlungseffekts
ate_model <- lm(income_post ~ treatment, data = matched_data)
summary(ate_model)

Call:
lm(formula = income_post ~ treatment, data = matched_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-13335.2  -3180.6   -293.4   3351.1  22094.6 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  28552.1      545.5  52.343  < 2e-16 ***
treatment     4210.3      771.4   5.458 1.43e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5455 on 198 degrees of freedom
Multiple R-squared:  0.1308,    Adjusted R-squared:  0.1264 
F-statistic: 29.79 on 1 and 198 DF,  p-value: 1.432e-07

#print(match_it)