Global and local spatial autocorrelation: methods of calculation and mapping

The first law of geography by V. Tobler — “everything influences everything, but what is closer influences more” — implies that the distribution of any phenomenon in the world is determined by a geographical factor. Spatial dependence, or the so-called neighborhood effect, is of interest to researchers for various reasons, including, for example, the potential for spatial interpolation, when observation at a given point can provide information about phenomena in nearby ones. In turn, spatial dependence can be expressed in positive or negative spatial autocorrelation of phenomena in neighboring objects of analysis. According to the second law of geography formulated by V. Tobler in 2004, a phenomenon external to the geographical area being analyzed affects what happens inside it. These words can be deciphered as a statement that a phenomenon is influenced not only by the properties of the region in which it is located, but also by phenomena characteristic of other regions (say, adjacent ones, while proximity can also be measured differently). The article provides a classification of spatial autocorrelation methods and describes three basic spatial autocorrelation indices: Moran's, Geary's and Gettys-Ord's. An algorithm for calculation and mapping is given.