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ok, i thought i recreated it with redirect but somehow it isn't showing up.... here is another try. Just a redirect to generalized additive model for now. |
Wrote a special entry on this with links to th eGeneralized version |
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The '''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]].
#REDIRECT [[Generalized additive model]]▼
==Description==
Given a [[data]] set <math>\{y_i,\, x_{i1}, \ldots, x_{ip}\}_{i=1}^n</math> of ''n'' [[statistical unit]]s, where <math>\{x_{i1}, \ldots, x_{ip}\}_{i=1}^n</math> represent predictors and <math>y_i</math> is the outcome, the ''additive model'' takes the form
: <math>E[y_i|x_{i1}, \ldots, x_{ip}] = \sum_{j=1}^p f_j(x_{ij}) </math>
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 [[Backfitting algorithm]] proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).
==See Also==
==References==
*Buja, A., Hastie, T., and Tibshirani, R. (1989). "Linear Smoothers and Additive Models", ''The Annals of Statistics'' 17(2):453-555.
*Breiman, L. and Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", ''Journal of the American Statistical Association'' 80:580-598.
*Friedman, J.H. and Stuetzle, W. (1981. "Projection Pursuit Regression", ''Journal of the American Statistical Association'' 76:817-823
[[Category:Regression analysis]]
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