Generalized Additive Model

A GAM is a GLM in which the linear predictor is given by a user-specified sum of smooth functions of the covariates plus a conventional parametric component of the linear predictor. Assume that a sample of n objects has a response variable y and r explanatory variables x₁,. . . , x_r. In these assumptions, the regression equation becomes:

Here, the functions f₁, f₂,…., f_r are different nonlinear functions on variables x. Into the GAM, the linear relationship between the response and predictors are replaced by several nonlinear smooth functions to model and capture the nonlinearities in the data.

We can see the GAM as a generalization of a multiple regression model without interactions between predictors. Among the advantages of this approach, in addition to greater flexibility than the linear model, the good algorithmic convergence rate should also be mentioned for problems with many explanatory variables. The biggest drawback lies in the complexity of the parameter...