Additive model: Difference between revisions

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Revision as of 04:39, 17 November 2009

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TheIn [[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 the one dimensional [[Smoothing|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. Furhtermore, the ''AM'' is more flexible than a [[linear model|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==

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or

: <math>Y= \beta_0+\sum_{j=1}^p f_j(X_{j})+\varepsilon </math>

Where <math>E[ \epsilon ] = 0</math>, <math>Var(\epsilon) = \sigma^2</math> and <math>E[ f_j(X_{j}) ] = 0</math>. The functions <math>f_j(x_{ij})</math> are unknown [[Smooth function|smooth functions]] fit from the data. Fitting the ''AM'' (i.e. the functions <math>f_j(x_{ij})</math>) can be done using the [[Backfittingbackfitting algorithm]] proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).

==See Alsoalso==

*[[Generalized additive model]]

*[[Backfitting algorithm]]

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==References==

*Buja, A., Hastie, T., and Tibshirani, R. (1989). "Linear Smoothers and Additive Models", ''The Annals of Statistics'' 17(2):453-&ndash;555.

*Breiman, L. and Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", ''Journal of the American Statistical Association'' 80:580-&ndash;598.

*Friedman, J.H. and Stuetzle, W. (1981. "Projection Pursuit Regression", ''Journal of the American Statistical Association'' 76:817-&ndash;823

[[Category:Regression analysis]]