Exploring Nonstationarity in Spatial Association

Abstract

This article expands the application of geographical weighting schemes to include indicators of spatial association. Because global measures of spatial association are already spatial models incorporating weights based on the scale of spatial association, calculating distance-based weighting schemes for the spatial association pairs is challenging given that spatial association involves object pairs. It is proposed here that the distance between the focal observation and the object pair be calculated based on the diagonal of a parallelogram formed by the focal point and the two endpoints of the object pair. Traditional local indicators of spatial association are constructed by a decomposition of a global measure into local components of spatial dependency centered on a focal location within a given scale of spatial association, whereas the new geographically weighted (GW) indicator of spatial association aids in measuring the spatial dependency of spatial subregions centered on a focal location within a given frame-of-reference scale. In this sense, they are similar to the spatially varying spatial association indicated by the estimated parameters on the spatially lagged response variable of a GW spatial lag model. Finally, a GW Moran’s I is developed and visualized to illustrate the GW indicator of spatial association.