Predictive Modeling Applications in Actuarial Science

Chapter 15 - Generalized Additive Models and Nonparametric Regression


Patrick L. Brockett | University of Texas at Austin

Shuo-Li Chuang | University of Texas at Austin

Utai Pitaktong | University of Texas at Austin

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Generalized Additive Models (GAMs) provide a further generalization of both linear regression and generalized linear models (GLM) by allowing the relationship between the response variable y and the individual predictor variables xj to be an additive but not necessarily a monomial function of the predictor variables xj. Also, as with the GLM, a nonlinear link function can connect the additive concatenation of the nonlinear functions of the predictors to the mean of the response variable giving flexibility in distribution form as discussed in the GLM chapter. The key factor in creating the GAM is the determination and construction of the functions of the predictor variables (called smoothers). Different methods of fit and functional forms for the smoothers are discussed. The GAM can be considered as more data driven (to determine the smoothers) as opposed to model driven (the additive monomial functional form assumption in linear regression and GLM).

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