Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions

TL;DR

This paper introduces an efficient Moran's eigenvector-based method for estimating multiscale spatially varying coefficients in large datasets, significantly reducing computational costs compared to traditional approaches.

Contribution

It develops a novel M-SVC modeling approach that eliminates the dependence on sample size N in likelihood estimation, enabling scalable analysis of large spatial datasets.

Findings

M-SVC is much faster than GWR for large N

The approach accurately estimates multiple SVCs

Implementation available in R package 'spmoran'

Abstract

While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a Moran's eigenvector-based spatially varying coefficients (M-SVC) modeling approach that estimates multiscale SVCs computationally efficiently. This estimation is accelerated through a (i) rank reduction, (ii) pre-compression, and (iii) sequential likelihood maximization. Steps (i) and (ii) eliminate the sample size N from the likelihood function; after these steps, the likelihood maximization cost is independent of N. Step (iii) further accelerates the likelihood maximization so that multiscale SVCs can be estimated even if the number of SVCs, K, is large. The M-SVC approach is compared with geographically weighted regression (GWR) through Monte Carlo simulation experiments. These simulation results show that our approach is far faster than GWR when N is large, despite numerically estimating 2K parameters while GWR numerically estimates only 1 parameter. Then, the proposed approach is applied to a land price analysis as an illustration. The developed SVC estimation approach is implemented in the R package "spmoran."