Extrapolation errors in linear model trees

Abstract

Prediction errors from a linear model tend to be larger when extrapolation is involved, particularly when the model is wrong. This article considers the problem of extrapolation and interpolation errors when a linear model tree is used for prediction. It proposes several ways to curtail the size of the errors, and uses a large collection of real datasets to demonstrate that the solutions are effective in reducing the average mean squared prediction error. The article also provides a proof that, if a linear model is correct, the proposed solutions have no undesirable effects as the training sample size tends to infinity.