rf-VIPsWithCollinearity.R

# The purpose of this script is to show that RF variable importance
# will split importance values for collinear variables evenly,
# even if collinearity is low enough so that variables are sepearable 
# and would be correctly separameted by an lm / ANOVA 

set.seed(123)

# simulation parameters
n = 3000
col = 0.7

# create collinear predictors
x1 = runif(n)
x2 = col * x1 + (1-col) * runif(n) 

# response is only influenced by x1
y = x1 + rnorm(n)

# fit RF and show variable importance
library(randomForest)
fit <- randomForest(y ~ x1 + x2, importance=TRUE)
# VP splits importance evenly because of collinearity

par(mfrow = c(1,2))

varImpPlot(fit, type = 2, main = "RF variable importance")

# lm / anova correctly identify x1 as causal variable
anova(lm(y ~ x1 + x2))

barplot(coef(lm(y ~ x1 + x2)), main = "lm estimates")