Additive Modelling of Electricity Demand with mgcv

Generalized Additive Models (Hastie and Tibshirani, Statistical Science, 1(3):297–318, 1986, GAMs) are flexible regression models, where the relation between the response distribution and several covariates is modelled nonparametrically, typically via spline bases expansions. Here we focus on standard GAMs, where only one parameter of the response distribution (typically controlling the mean or location) is modelled additively, while the remaining parameters do not depend on the covariates. More flexible GAMs for location, scale, and shape (Rigby and Stasinopoulos, Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3):507–554, 2005), where potentially all response distribution parameters can vary with the covariates, are presented in Chap. 3 , which also cover distribution-free quantile GAMs. This chapter illustrates how to build, fit, and visualize GAM models using the mgcv R package. However, such models can be handled using a variety of software, hence Sect. 2.2.4 mentions some of the alternatives to mgcv.