G-Sivar: A Global Spatial Indicator Based on Variogram

Abstract

Among the exploratory spatial data analysis tools, there are indicators of spatial association, which measure the degree of spatial dependence of analysed data and can be applied to quantitative data. Another procedure available is geostatistics, which is based on the variogram, describing quantitatively and qualitatively the spatial structure of a variable. The aim of this paper is to use the concept of the variogram to develop a global indicator of spatial association (Global Spatial Indicator Based on Variogram-G-SIVAR). The G-SIVAR indicator has a satisfactory performance for spatial association, with sensibility for anisotropy cases. Because the indicator is based on geostatistics, it is appropriate for quantitative and qualitative data. The developed indicator is derived from theoretical global variogram, providing more details of the spatial structure of the data. The G-SIVAR indicator is based on spatial dissimilarity, while traditional indexes, such as Moran's I, are based on spatial similarity.

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“…Many studies carried out only Exploratory Spatial Data Analysis (ESDA), considering different research fields (Anselin, 1996;Unwin and Unwin;1998;Messner et al, 1999;Le Gallo and Ertur;2003). Among the ESDA procedures, the degree of spatial dependence can be measured by spatial indicators (Naizer et al, 2019). Over many decades, different authors proposed spatial indicators to corroborate the existence of spatial autocorrelation (Moran, 1950;Geary, 1954;Getis and Ord, 1992;Anselin, 1995).…”

“…Global indexes qualify the database, while local indexes characterize the spatial association of observations, identifying spatial association pockets. Most indexes could be applied to quantitative variables (Anselin, 1995;Naizer et al, 2019).…”

“…The global indicator G-SIVAR (Naizer et al, 2019) is based on assumptions of geostatistics, more specifically, on the semivariogram tool (theoretical and experimental). The G-SIVAR indicator is based on the standardized values of the theoretical variogram (ordinate axis), associated with a hypothesis test for spatial randomness.…”

“…It indicates the dissimilarity of the data and ranges from 0 to 1, where value 1 shows the complete absence of spatial autocorrelation, and value 0 indicates the entire presence of spatial autocorrelation. The original studies of Moran (1950) and Naizer et al (2019) should be consulted if the reader wants more details about the mathematical formalism used.…”