Additive model

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 e.g. 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" include model selection, overfitting, and multicollinearity.
Description.
Given a data set formula_1 of "n" statistical units, where formula_2 represent predictors and formula_3 is the outcome, the "additive model" takes the form
or
Where formula_6, formula_7 and formula_8. The functions formula_9 are unknown smooth functions fit from the data. Fitting the "AM" (i.e. the functions formula_9) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).