Generalized Spatial Regression with Differential Regularization

TL;DR

This paper introduces a generalized spatial regression model with differential regularization for analyzing geostatistical and areal data over irregular domains, utilizing finite element methods for efficient estimation.

Contribution

It presents a novel generalized additive model incorporating differential regularization and finite element methods for spatial data analysis over complex domains.

Findings

Effective modeling of spatially-varying covariates.

Application to criminality data in Portland.

Demonstrates computational efficiency and flexibility.

Abstract

We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA.