- Generalized additive model
In

statistics , the**generalized additive model**(or**GAM**) is astatistical model developed byTrevor Hastie andRob Tibshirani for blending properties ofgeneralized linear model s withadditive models .The model specifies a distribution (such as a

normal distribution , or abinomial distribution ) and a link function "g" relating the expected value of the distribution to the predictors, and attempts to fit functions "f_{i}(x_{i})" to satisfy::$g(operatorname\{E\}(Y))=eta\_0\; +\; f\_1(x\_1)\; +\; f\_2(x\_2)+\; ...\; +\; f\_m(x\_m).,!$The functions "f

_{i}(x_{i})" may be fit using parametric or non-parametric means, thus providing the potential for better fits to data than other methods. The method hence is very general - a typical GAM might use a scatterplot smoothing function such as a locally weighted mean for "f_{1}(x_{1})", and then use a factor model for "f_{2}(x_{2})". By allowing nonparametric fits, well designed GAMs allow good fits to the training data with relaxed assumptions on the actual relationship, perhaps at the expense of interpretability of results.Overfitting can be a problem with GAMs. The number of smoothing parameters can be specified, and this number should be reasonably small, certainly well under the degrees of freedom offered by the data.

Cross-validation can be used to detect and/or reduce overfitting problems with GAMs (or other statistical methods). Other models such as GLMs may be preferable to GAMs unless GAMs improve predictive ability substantially for the application in question.**References***cite book|author = Hastie, T. J. and Tibshirani, R. J.|title = Generalized Additive Models|publisher = Chapman & Hall/CRC|year = 1990|isbn=9780412343902

*cite book|author = Wood, S. N.|title = Generalized Additive Models: An Introduction with R|publisher = Chapman & Hall/CRC|year = 2006|isbn=9781584884743

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