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In statistics, a generalized additive model is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions.
GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. They can be interpreted as the discriminative generalization of the naive Bayes generative model.
The model relates a univariate response variable, Y, to some predictor variables, xi. An exponential family distribution is specified for Y along with a link function g relating the expected value of Y to the predictor variables via a structure such as
The functions fi may be functions with a specified parametric form or may be specified non-parametrically, or semi-parametrically, simply as 'smooth functions', to be estimated by non-parametric means. So a typical GAM might use a scatterplot smoothing function, such as a locally weighted mean, for f1, and then use a factor model for f2. This flexibility to allow non-parametric fits with relaxed assumptions on the actual relationship between response and predictor, provides the potential for better fits to data than purely parametric models, but arguably with some loss of interpretability.