Simultaneous Selection of Variables and Smoothing Parameters in Geoadditive Regression Models

Abstract

In recent years a great deal of research has been devoted to developing complex regression models that allow to deal simultaneously with nonlinear covariate effects and spatial heterogeneity. Such models are referred to as geoadditive models. These models may routinely be estimated using standard statistical software packages. Much less effort, however, has been spent to model and variable selection in the context of complex regression models. In this article we develop an empirical Bayes approach for simultaneous selection of variables and the degree of smoothness in geoadditive models. Our approach allows to decide whether a particular continuous covariate enters the model linearly or nonlinearly or is removed from the model and whether a spatial effect should be added to the model or not.