An introduction to multivariate adaptive regression splines

Abstract

Multivariate Adaptive Regression Splines (MARS) is a method for flexible modelling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by recursive partitioning (e.g. CART) and shares its ability to capture high order interactions. However, it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables, and produces continuous models with continuous derivatives. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with different multivariable interactions. This paper summarizes the basic MARS algorithm, as well as extensions for binary response, categorical predictors, nested variables and missing values. It presents tips on interpreting the output of the standard FORTRAN implementation of MARS, and provides an example of MARS applied to a set of clinical data.