Abstract
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.
Highlights
Various authors developed indicators of spatial analysis in order to prove the existence of spatial autocorrelation and to quantify relations of spatial dependence
The theoretical semivariogram was adjusted through an Exponential function, the nugget effect (C0) corresponds to 2.000 and the contribution (C1) to 1.800
The G-SIVAR indicator can identify and quantify the spatial association of spatially distributed data adequately and it is consistent with the Moran index, showing the advantage of being applicable to quantitative and qualitative data, as well as providing a more detailed analysis of the structure of the variable
Summary
Introduction and backgroundSpatially correlated data exists in various areas of study, such as: epidemiology (Goovaerts, 2006; Goovaerts, 2009; Sousa et al, 2017), geology (Lee et al, 2007; Orton et al, 2016; Tamayo-Mas et al, 2016); environment (Pearce et al, 2009; Park, 2013) and urban and transport planning (Pitombo et al, 2015; Sidharthan et al, 2011; Xie and Yan, 2013; Lindner and Pitombo, 2018). Current approaches emphasize the need to include spatial components in the analysis and modelling of such data as traditional non-spatial modelling presupposes data independence (Sener et al, 2010). Using spatial models to estimate spatially dependent variables requires prior and exploratory investigation underlying the spatial dependence of these data. Among the exploratory spatial data analysis techniques, we highlight the use of indicators of spatial association. Various authors (for example, Moran, 1950; Geary, 1954; Getis and Ord, 1992; Anselin, 1995) developed indicators of spatial analysis in order to prove the existence of spatial autocorrelation and to quantify relations of spatial dependence. Most indexes refer to the similarity between values of the same variable in different locations and are applicable to quantitative variables
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