Constructing the spatial weights matrix using a local statistic

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.