In [[statistics]], an '''additive model''' ('''AM''') is a [[nonparametric regression]] method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981),<ref>{{cite journal |last=Friedman, |first=J. H. and |last2=Stuetzle, |first2=W. (|year=1981)."|title=Projection Pursuit Regression",''|journal=[[Journal of the American Statistical Association''|J. Amer. Statist. Assoc.]] |volume=76:817–823 |issue=376 |pages=817–823 |doi=10.1080/01621459.1981.10477729 }}</ref> and is an essential part of the [[Alternating conditional expectation model|ACE]] algorithm. The ''AM'' uses a 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. Furthermore, the ''AM'' is more flexible than a [[linear regression|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]].
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]]s 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).<ref>{{cite journal |last=Buja, |first=A., |last2=Hastie, |first2=T., and |last3=Tibshirani, |first3=R. (|year=1989)."|title=Linear Smoothers and Additive Models", ''The |journal=[[Annals of Statistics''|Ann. Stat.]] |volume=17( |issue=2):453–555. |pages=453–555 |jstor=2241560 }}</ref>
==See also==
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==Further reading==
*{{cite journal |last=Breiman, |first=L. and |last2=Friedman, |first2=J. H. (|year=1985)."|title=Estimating Optimal Transformations for Multiple Regression and Correlation",''|journal=[[Journal of the American Statistical Association|J. Amer. Statist. Assoc.]]'' |volume=80:580–598 |issue=391 |pages=580–598 |doi=10.1080/01621459.1985.10478157 }}
