Collider simulation

 # Setting seed for reproducibility

set.seed(123)

# Number of observations

n = 1000

# Generating independent variables X1 and X2

X1 = rnorm(n)

X2 = rnorm(n)

# Positive Correlation Scenario

# Collider positively influenced by both X1 and X2

Collider_Positive = X1 + X2 + rnorm(n)

# Negative Correlation Scenario

# Collider positively influenced by X1 and negatively by X2

Collider_Negative = X1 - X2 + rnorm(n)

# Checking correlations

# Before conditioning

cat("Correlation between X1 and X2 before conditioning: ", cor(X1, X2), "\n")

# After conditioning - Positive Scenario

cat("Positive Scenario - After conditioning on the collider: ",

    cor(X1[Collider_Positive > median(Collider_Positive)], 

        X2[Collider_Positive > median(Collider_Positive)]), "\n")

# After conditioning - Negative Scenario

cat("Negative Scenario - After conditioning on the collider: ",

    cor(X1[Collider_Negative > median(Collider_Negative)], 

        X2[Collider_Negative > median(Collider_Negative)]), "\n")