Sampled Grid Pairwise Likelihood (SG-PL): An Efficient Approach for Spatial Regression on Large Data

TL;DR

The paper introduces SG-PL, a grid-based sampling method for spatial regression that significantly reduces computational time on large datasets while maintaining acceptable statistical efficiency.

Contribution

SG-PL is a novel, scalable approach that improves the efficiency of spatial regression by strategically selecting observation pairs through grid sampling.

Findings

SG-PL reduces computational time by orders of magnitude.

The method maintains a manageable level of statistical efficiency loss.

Empirical validation confirms practical utility on large datasets.

Abstract

Estimating spatial regression models on large, irregularly structured datasets poses significant computational hurdles. While Pairwise Likelihood (PL) methods offer a pathway to simplify these estimations, the efficient selection of informative observation pairs remains a critical challenge, particularly as data volume and complexity grow. This paper introduces the Sampled Grid Pairwise Likelihood (SG-PL) method, a novel approach that employs a grid-based sampling strategy to strategically select observation pairs. Simulation studies demonstrate SG-PL's principal advantage: a dramatic reduction in computational time -- often by orders of magnitude -- when compared to benchmark methods. This substantial acceleration is achieved with a manageable trade-off in statistical efficiency. An empirical application further validates SG-PL's practical utility. Consequently, SG-PL emerges as a highly scalable and effective tool for spatial analysis on very large datasets, offering a compelling balance where substantial gains in computational feasibility are realized for a limited cost in statistical precision, a trade-off that increasingly favors SG-PL with larger N.