Nonparametric logistic regression using smoothing splines

Abstract

Logistic regression is a well-established technique for modeling a discrete response variable as a function of explanatory variables. The aim of this study is to introduce nonparametric regression using smoothing splines. Nonparametric regression yields a more flexible way of estimating curves and provides a larger set of functions to work from, which is not limited to a family of functions as in the parametric regression framework. Nonparametric regression falls into the framework of the general additive model with the natural cubic spline as the solution to the penalised least square criterion. Models are fitted using natural cubic splines. B-splines will be implemented due to their computational advantages gained from their almost orthogonal structure. Software, PROC IML within SAS, will be written to estimate these models.