3.13 - Other Methods in Nonlinear Regression

Abstract

This chapter covers some of the other nonlinear regression methods including classification and regression trees (CART), projection pursuit regression (PPR), and multivariate adaptive regression splines (MARS). These methods can provide attractive alternatives to more common methods and can also provide a useful insight into the nature of the data and relationship between the variables. CART and MARS are partition-based methods since they choose the most relevant variables. PPR is a projection-based method since it projects all the input variables on a linear hyperplane before application of the nonlinear activation function. The chapter provides theoretical and methodological insights into these methods, discusses their pros and cons from a practical point of view, and illustrates their features with the help of simulated examples.