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In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981)[1] 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.
Given a data set of n statistical units, where represent predictors and is the outcome, the additive model takes the form
![{\displaystyle \mathrm {E} [y_{i}|x_{i1},\ldots ,x_{ip}]=\beta _{0}+\sum _{j=1}^{p}f_{j}(x_{ij})}](http://wikimedia.org/api/rest_v1/media/math/render/svg/81d5cc6bcb970849325c676648504fa8a39a763b)
or
Where , and . The functions are unknown smooth functions fit from the data. Fitting the AM (i.e. the functions ) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).[2]
![{\displaystyle \mathrm {E} [\epsilon ]=0}](http://wikimedia.org/api/rest_v1/media/math/render/svg/f7494dee92fe5ac5a8d8a61fa72e73482ad679d9)
![{\displaystyle \mathrm {E} [f_{j}(X_{j})]=0}](http://wikimedia.org/api/rest_v1/media/math/render/svg/ebc45cdd662236cf2546a2a70c1c03383d50ac3a)
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