Samiksha Jaiswal (Editor)

Additive model

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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) 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 { y i , x i 1 , … , x i p } i = 1 n of n statistical units, where { x i 1 , … , x i p } i = 1 n represent predictors and y i is the outcome, the additive model takes the form

E [ y i | x i 1 , … , x i p ] = β 0 + ∑ j = 1 p f j ( x i j )

or

Y = β 0 + ∑ j = 1 p f j ( X j ) + ε

Where E [ ϵ ] = 0 , V a r ( ϵ ) = σ 2 and E [ f j ( X j ) ] = 0 . The functions f j ( x i j ) are unknown smooth functions fit from the data. Fitting the AM (i.e. the functions f j ( x i j ) ) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).

References

Additive model Wikipedia
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