Scalable model selection for spatial additive mixed modeling: application to crime analysis

TL;DR

This paper introduces a fast, scalable method for selecting spatial regression models suitable for large datasets, demonstrated through crime analysis in Japan, improving both accuracy and computational efficiency.

Contribution

It develops a novel dimension reduction-based model selection approach for large-scale spatial regression, implemented in the R package spmoran.

Findings

Accurately selects models in large datasets

Significantly speeds up computation

Effectively predicts crime risk factors

Abstract

A rapid growth in spatial open datasets has led to a huge demand for regression approaches accommodating spatial and non-spatial effects in big data. Regression model selection is particularly important to stably estimate flexible regression models. However, conventional methods can be slow for large samples. Hence, we develop a fast and practical model-selection approach for spatial regression models, focusing on the selection of coefficient types that include constant, spatially varying, and non-spatially varying coefficients. A pre-processing approach, which replaces data matrices with small inner products through dimension reduction dramatically accelerates the computation speed of model selection. Numerical experiments show that our approach selects the model accurately and computationally efficiently, highlighting the importance of model selection in the spatial regression context. Then, the present approach is applied to open data to investigate local factors affecting crime in Japan. The results suggest that our approach is useful not only for selecting factors influencing crime risk but also for predicting crime events. This scalable model selection will be key to appropriately specifying flexible and large-scale spatial regression models in the era of big data. The developed model selection approach was implemented in the R package spmoran.