In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The AM uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM, like many other machine-learning methods, include model selection, overfitting, and multicollinearity.

Description

Given a data set of n statistical units, where represent predictors and y_i is the outcome, the additive model takes the form or Where, and. The functions f_j(x_{ij}) are unknown smooth functions fit from the data. Fitting the AM (i.e. the functions f_j(x_{ij})) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).