Additive Modelling with Penalized Regression Splines and Genetic Algorithms

Abstract

Additive models of the type y=f_1(x_1)+...+f_p(x_p)+e where f_j,j=1,...,p, have unspecified functional form, are flexible statistical regression models which can be used to characterize nonlinear regression effects. The basic tools used for fitting the additive model are the expansion in B-splines and penalization which prevents the problem of overfitting. This penalized B-spline (called P-spline) approach strongly depends on the choice of the amount of smoothing used for components f_j. In this paper we treat the problem of choosing the smoothing parameters by genetic algorithms. In several simulation studies our approach of automatically calculation of the smoothing parameters is compared to alternative methods given in literature. In particular functions with different spatial variability are considered and the effect of constant respectively local adaptive smoothing parameters is evaluated.