Variable selection for inhomogeneous spatial point process models

Abstract

AbstractIn this work, we consider variable selection when modelling the intensity and clustering of inhomogeneous spatial point processes, integrating well‐known procedures in the respective fields of variable selection and spatial point process modelling to introduce a simple procedure for variable selection in spatial point process modelling. Specifically, we consider modelling spatial point data with Poisson, pairwise interaction and Neyman–Scott cluster models, and incorporate LASSO, adaptive LASSO, and elastic net regularization methods into the generalized linear model framework for fitting these point models. We perform simulation studies to explore the effectiveness of using each of the three‐regularization methods in our procedure. We then use the procedure in two applications, modelling the intensity and clustering of rainforest trees with soil and geographical covariates using a Neyman–Scott model, and of fast food restaurant locations in New York City with Census variables and school locations using a pairwise interaction model. The Canadian Journal of Statistics 43: 288–305; 2015 © 2015 Statistical Society of Canada