bcf.r

bcf <- function(observed, model_name) {
  # another way to correct for back-transformation bias
  # based on this:
  # https://stats.stackexchange.com/questions/361618/how-to-back-transform-a-log-transformed-regression-model-in-r-with-bias-correcti
  
  # 1. Compute exp(Xβ^), i.e. the retransformed but unadjusted prediction
  a <- exp(predict(model_name))
  
  # 2. Regress Y against exp(Xβ^) without an intercept. Call the resulting regression coefficient γ.
  b <- lm(observed ~ a -1) #adding -1 in the formula removes the intercept
  b <- as.numeric(coefficients(b))
  
  # 3. Compute the adjusted retransformed prediction as γexp(Xβ^).
  return(b * exp(predict(model_name)))
}