Local measures of spatial association are statistics used to detect variations of a variable of interest across space when the spatial relationship of the variable is not constant across the study region, known as spatial non-stationarity or spatial heterogeneity. Unlike global measures that summarize the overall spatial autocorrelation of the study area in one single value, local measures of spatial association identify local clusters (observations nearby have similar attribute values) or spatial outliers (observations nearby have different attribute values). Like global measures, local indicators of spatial association (LISA), including local Moran’s I and local Geary’s C, incorporate both spatial proximity and attribute similarity. Getis-Ord Gi*, another popular local statistic, identifies spatial clusters at various significance levels, known as hot spots (unusually high values) and cold spots (unusually low values). This so-called “hot spot analysis” has been extended to examine spatiotemporal trends in data. Bivariate local Moran’s I describes the statistical relationship between one variable at a location and a spatially lagged second variable at neighboring locations, and geographically weighted regression (GWR) allows regression coefficients to vary at each observation location. Visualization of local measures of spatial association is critical, allowing researchers of various disciplines to easily identify local pockets of interest for future examination.
This entry describes the three key principles in Geography, referred to as the Laws of Geography. The first law was proposed by Tobler and manifests the spatial autocorrelation (dependence) of geographic variation, that is “near things are more related than distant things”. The second law was by Goodchild and addresses the spatial heterogeneity of the geographic variation, that is “uncontrolled variation” of geographic feature. The third law was proposed by Zhu and his colleagues and illustrates the geographic similarity of geographic variation, that is “The more similar the geographic configurations of two points (areas), the more similar the values (processes) of the target variable at these two points (areas)”, or the more similar in geographic configuration between two locations the more similar the outcomes between the two locations. These principles (laws) manifest the duality of geographic reality: spatial dependence/spatial heterogeneity, geographic similarity/geographic individuality. This duality calls for the integration of the nomothetic and ideographic approaches in geographic analysis.