Adaptive linear models for regression: Improving prediction when population has changed

Abstract

The general setting of regression analysis is to identify a relationship between a response variable Y and one or several explanatory variables X by using a learning sample. In a prediction framework, the main assumption for predicting Y on a new sample of observations is that the regression model Y = f( X) + ϵ is still valid. Unfortunately, this assumption is not always true in practice and the model could have changed. We therefore propose to adapt the original regression model to the new sample by estimating a transformation between the original regression function f( X) and the new one f ∗( X). The main interest of the proposed adaptive models is to allow the build of a regression model for the new population with only a small number of observations using the knowledge on the reference population. The efficiency of this strategy is illustrated by applications on artificial and real datasets, including the modeling of the housing market in different U.S. cities. A package for the R software dedicated to the adaptive linear models is available on the author’s web page.