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Additive model building for spatial regression
Author(s) -
Nandy Siddhartha,
Lim Chae Young,
Maiti Tapabrata
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12195
Subject(s) - estimator , additive model , generalized additive model , spatial analysis , consistency (knowledge bases) , lasso (programming language) , regression analysis , regression , statistics , computer science , model selection , mathematics , data mining , econometrics , artificial intelligence , world wide web
Summary 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 l 2 ‐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.