Additive Smooth Modelling with Splines

Linear regression summarises the link between a variable of interest and one or several explanatory variables through a parametric relationship. Hastie and Tibshirani (1986) extended this approach by allowing a non-parametric description of the dependence between the variable of interest and the explanatory variables. In this report, we review the notion of smooths, present different approaches to selection of the smoothing parameter, and describe several spline bases, in the lines of Wood (2006). We show evidence of smoking as a cause of deaths from larynx cancer by applying Gaussian Markov random fields and thin plate regression splines on data covering 544 German districts from 1986 to 1990.