ELSA: Entropy-based local indicator of spatial association

Abstract

Research on spatial data analysis has developed a number of local indicators of spatial association (LISA), which allow exploration of local patterns in spatial data. These include local Moran’s I and local Geary’s c, as well as Gi and Gi∗ that can be used for continuous or interval variables only. Despite numerous situations where qualitative (nominal/categorical) variables are encountered, few attempts have been devoted to the development of methods to explore the local spatial pattern in categorical data. To our knowledge, there is no indicator of local spatial association that can be used for both continuous and categorical data at the same time.In this paper, we propose a new local indicator of spatial association, called the entropy-based local indicator of spatial association (ELSA), that can be used for both categorical and continuous spatial data. ELSA quantifies the degree of spatial association of a variable at each location relative to the same variable at the neighbouring locations. This indicator simultaneously incorporates both spatial and attribute aspects of spatial association into account. The values of ELSA vary between 0 and 1, which denote highest and lowest spatial association, respectively. We compare ELSA to existing statistics such as Local Moran’s I and test the power and size of the new statistic. We also introduce the ”entrogram”, a novel approach for exploring the global spatial structure within the entire area (like a variogram). This study showed that the ELSA is consistent and robust, and is therefore suitable for applications in a wide range of disciplines. The ELSA algorithm is made available as an R-package (elsa).