Geary’s c and Spectral Graph Theory

Spatial autocorrelation, of which Geary’s c has traditionally been a popular measure, is fundamental to spatial science. This paper provides a new perspective on Geary’s c. We discuss this using concepts from spectral graph theory/linear algebraic graph theory. More precisely, we provide three types of representations for it: (a) graph Laplacian representation, (b) graph Fourier transform representation, and (c) Pearson’s correlation coefficient representation. Subsequently, we illustrate that the spatial autocorrelation measured by Geary’s c is positive (resp. negative) if spatially smoother (resp. less smooth) graph Laplacian eigenvectors are dominant. Finally, based on our analysis, we provide a recommendation for applied studies.

Analisis Moran’s I, Geary’s C, dan Getis-Ord G pada Penerapan Jumlah Penderita Kusta di Kabupaten Gowa

Analisis spasial merupakan salah satu metode yang sering digunakan dalam melihat pola penyebaran penyakit menular. Penyakit Kusta atau lepra merupakan penyakit menular kronis yang disebabkan oleh bakteri Mycrobacterium Leprae yang penyebarannya melalui droplet. Penelitian ini bertujuan untuk mengetahui pola spasial pada Kusta dengan menggunakan metode Quadrat Analysis, untuk mengetahui ada atau tidaknya autokorelasi spasial antar daerah dengan menggunakan Moran’s I, Geary’s C, Getis-Ord G, dan pemetaan penyebaran penyakit Kusta di Kabupaten Gowa. Pada penelitian ini diperoleh bahwa pola spasial penyebaran penyakit Kusta pada Tahun 2016 dan 2017 di Kabupaten Gowa bersifat mengelompok (clustered). Pada Tahun 2016 terdapat autokorelasi spasial dengan pengujian Moran’s I dan Geary’s C, sedangkan pengujian Getis-Ord G tidak terdapat autokorelasi spasial antar daerah. Pada Tahun 2017 tidak terdapat autokorelasi spasial antar daerah dengan menggunakan ke tiga pengujian tersebut. Pada Tahun 2016 daerah yang rawan adalah Barombong, daerah yang harus berhati-hati dengan daerah sekitarnya adalah Bontonompo dan daerah yang termasuk kategori aman adalah Tompobulu. Sedangkan pada tahun 2017 daerah yang rawan terhadap penyakit Kusta adalah Bajeng dan Manuju.Kata kunci : Moran’s I, Geary’s C, Getis-Ord G, Moran Scatterplot, Kusta Spatial analysis is one of the methods that is often used to observe spreading pattern of infectious diseases. Leprosy is a chronic infectious disease caused by bacterium Mycrobacterium Leprae which spreads through droplets. This study aims to determine the spatial pattern of leprosy using the Quadrat Analysis method, to determine whether there is spatial autocorrelation between regions using Moran's I, Geary’s C, Getis-Ord G, and mapping the spread of leprosy in Gowa Regency. In this study it was found that the spatial patterns of the spread of leprosy in 2016 and 2017 in Gowa Regency was clustered. In 2016 there were spatial autocorrelations with the tests of Moran's I and Geary's C, while the testing of Getis-Ord G did not have spatial autocorrelation between regions. In 2017 there is no spatial autocorrelation between regions using the three tests. In 2016 the vulnerable areas was Barombong, the area that had to be careful with the surrounding areas was Bontonompo and the area included in the safe category was Tompobulu. Whereas in 2017 areas prone to leprosy were Bajeng and Manuju.Keywords : Moran's I, Geary's C, Getis-Ord G, Moran Scatterplot, Leprosy

Spatial Distribution of Human Development Index in the Regions of Russia

Spatial effects in human development levels among different regions of a territory are important to study in the context of the core-periphery model. We use different methods to study human development index (HDI) for 85 Russian regions. The authors studied the human development index (HDI) for 85 Russian regions. Methods of spatial statistics (econometrics) are used to estimate the ‘spatial gradient’ in economic geography (Moran’s global and local I, Geary’s C, Getis-Ord global G indices). As a weighting matrix we used a contiguity matrix, taking into account the HDI levels only in neighboring regions. Analysis of the global indices of Moran’s I, Geary’s C and Getis-Ord G and Morans scatter plots showed the presence of time-inconsistent spatial autoregressive dependence of the level of HDI in regions of Russia. The ‘spatial gradient’ of the level of human development in Russia is influenced by historically existing imbalances (due to strong oil and gas export-oriented nature of the economy) and insufficient use of human capital. To our view the regional differentiation in human development among the regions is caused primarily by the ‘catching up’ style of Russian economy: human capital is concentrated in regions with already high level of development, although in terms of growth rates Moscow and St. Petersburg are not the leaders. The territorial and geopolitical policies of Russian Federation also influence HDI distribution. For example, huge public investments in the regions of Russian Far East are often ineffective.

Effect of the Centrifugal and Centripetal Effects in Core Versus (Semi)Periphery in Central Europe Countries

The paper focuses on examining regional disparities in Austria, Czech republic, Slovakia and Hungary (CE countries) in spatial perspective on NUTS III level. It took two crucial topics: spatial regional imbalances and polarization of the development. Spatial imbalances over the territory were examined via using the Moran’s coefficient of spatial autocorrelation and the Geary’s C statistics for mutual comparisons of achieving results. Both results showed a significant degree of the inequality. Polarization of the development was examined via measuring the possible centrifugal and centripetal effects, present in the proximity of the core regions of CE countries. Empirical examination showed “contradictory” results, indicating presence of both effects based on Gi(d) statistics introduced by Getis and Ord (1992). Thus we can conclude the spatial imbalance over the territory of CE countries is significant, and we can’t rule out acting of centrifugal and centripetal effects, however distinctly in some core regions.

Spatial aspects of european airports’ partial factor productivity

This research is devoted to discovering of spatial effects in European airports’ partial factor productivity (PFP). A set of study PFP indicators includes infrastructural (air transport movements per runway), labour (workload units per employee), and financial (revenue and profit per workload unit) ratios. We utilised a number of appropriate statistical tests (Moran’s I., Geary’s C., Mantel test, and spatial auto-regression) for revelation of spatial relationships between PFP indicator’s values. The tests were separately applied to samples of Spanish (2009-2010) and UK airports (2011-2012) and provided evidences of significant spatial effects in data.