Constructing the Spatial Weights Matrix Using a Local Statistic

TLDR

Spatial weights matrices are essential for regression models that require spatial structure, and the local statistic concept relies on a critical distance beyond which clustering does not increase. The study constructs a spatial weights matrix that distinguishes units with distance effects from those without, using a two‑part framework. The authors develop a two‑variable local statistics model (LSM) based on the Gi* statistic and evaluate it through simulations against multiple spatial weight specifications on random and clustered spatial patterns. The LSM outperformed conventional weight specifications according to AIC, spatial autoregressive coefficient tests, and Moran's I residual diagnostics, with its flexibility explaining the superior performance.

Abstract

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G i * local statistic. The local statistic concept depends on the designation of a critical distance, d c , defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.