Basis Functions

Basis functions of predictor variables (X) play an important role in the estimation of Multivariate Adaptive Regression Splines (MARSplines). Specifically, MARSplines uses two-sided truncated functions of the form   (as shown below) as basis functions for linear or non-linear expansion which approximates the relationships between the response and predictor variables.

Shown above is a simple example of two basis functions (t-x)+ and (x-t)+. Parameter t is the knot of the basis functions (defining the "pieces" of the piecewise linear regression); these knots (parameters t) are also determined from the data.

For more information, see Multivariate Adaptive Regression Splines (MARSplines) Overview.