Additive model building for spatial regression

Siddhartha Nandy, Chae Young Lim, Tapabrata Maiti

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2017 · Volume 79 · Issue 3

Abstract

Spatial regression is an important predictive tool in many scientific applications and an additive model provides a flexible regression relationship between predictors and a response variable. We develop a regularized variable selection technique for building a spatial additive model. We find that the methods developed for independent data do not work well for spatially dependent data. This motivates us to propose a spatially weighted-error norm with a group lasso type of penalty to select additive components in spatial additive models. We establish the selection consistency of the approach proposed where the penalty parameter depends on several factors, such as the order of approximation of additive components, characteristics of the spatial weight and spatial dependence. An extensive simulation study provides a vivid picture of the effects of dependent data structure and choice of a spatial weight on selection results as well as the asymptotic behaviour of the estimators. As an illustrative example, the method is applied to lung cancer mortality data over the period of 2000–2005, obtained from the ‘Surveillance, epidemiology, and end results’ programme, National Cancer Institute, USA.

Keywords

Additive models, Group lasso, High dimension, Spatial dependence, Spatial regression, Variable selection

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