Friedman J H, Roosen C B
Department of Statistics and Stanford Linear Accelerator Center, Stanford University, CA 94305-4065, USA.
Stat Methods Med Res. 1995 Sep;4(3):197-217. doi: 10.1177/096228029500400303.
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.
多元自适应回归样条（MARS）是一种用于对高维数据进行灵活建模的方法。该模型采用乘积样条基函数展开的形式，其中基函数的数量以及与每个基函数相关的参数（乘积次数和节点位置）均由数据自动确定。此过程的灵感来源于递归划分（如CART），并具备捕捉高阶交互作用的能力。然而，它在对几乎是可加性的关系或最多涉及少数变量交互作用的关系进行建模时，具有更强的能力和灵活性，且能生成具有连续导数的连续模型。此外，该模型可以以一种分别识别可加性贡献和与不同多变量交互作用相关贡献的形式来表示。本文总结了基本的MARS算法，以及针对二元响应、分类预测变量、嵌套变量和缺失值的扩展。文中给出了解释MARS标准FORTRAN实现输出结果的提示，并提供了一个将MARS应用于一组临床数据的示例。
