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

Estimating spatial regression models on large, irregularly structured data networks poses significant computational hurdles. The Pairwise Likelihood (PL) proposed by Arbia (2014) offers a pathway to simplify the estimations by selecting a subset of pairs of observations, but the process of selection of the pairs remains a critical challenge, particularly when the data volume and complexity grow. This paper introduces a novel approach that employs a grid-based sampling strategy to strategically select observation pairs. Our simulation studies show clearly the new method’s main advantage consisting of a dramatic reduction in computational time—often by orders of magnitude—when compared to other benchmark methods. This substantial acceleration is achieved with an acceptable trade-off of statistical efficiency. An empirical application further validates the practical utility of the proposed method. As a consequence, the proposed method emerges as a highly scalable and effective tool for spatial and network analysis on very large datasets, offering a compelling balance where substantial gains in computational feasibility are realized for a limited cost in statistical precision.