Attenuation Bias Simulation

attenuation.R

# Set seed for reproducibility
set.seed(123)

# Number of observations
n <- 1000

# Simulate a perfectly measured outcome (Y_perfect)
# Treatment effect
treatment_effect <- 5
base_noise <- rnorm(n, mean = 0, sd = 1)  # Base noise for the perfect outcome

# Simulate the treatment assignment (randomized)
treatment <- rbinom(n, 1, 0.5)  # Random assignment to treatment (0 or 1)

# Perfectly measured outcome
Y_perfect <- treatment_effect * treatment + base_noise

# Simulate the noisy outcome
# Assume half respond sincerely and half respond randomly
random_respondents <- sample(1:n, size = n / 2)  # Randomly select half to respond randomly

Y_noisy <- Y_perfect  # Start with Y_perfect for everyone
Y_noisy[random_respondents] <- rnorm(n / 2, mean = 0, sd = 5)  # Replace with random noise for half

# Perform linear regression on both the perfectly measured and noisy outcomes
model_perfect <- lm(Y_perfect ~ treatment)
model_noisy <- lm(Y_noisy ~ treatment)

# Summarize the results
summary(model_perfect)
summary(model_noisy)

# Compare the estimated treatment effects
cat("Treatment effect on perfectly measured outcome:\n")
cat("Estimate:", coef(model_perfect)[2], "\n\n")

cat("Treatment effect on noisy outcome (half random responses):\n")
cat("Estimate:", coef(model_noisy)[2], "\n")