Spatial Autocorrelation

Glossary AutoA prefix literally meaning self; spatial autocorrelation means self-correlation, or values within a given variable are correlated, resulting in the variable being correlated with itself. Correlation A description of the nature and degree of a relationship between a pair of quantitative variables. Geary Ratio An index of spatial autocorrelation, involving the computation of squared differences of values that are geographic neighbors (i.e., paired comparisons), that ranges from 0 to 1 for negative, and 1 to approximately 2 for positive, spatial autocorrelation, with an expected value of 1 for zero spatial autocorrelation. Geographic Connectivity/Weights Matrix An n-by-n matrix with the same sequence of row and column location labels, whose entries indicate which pairs of locations are neighbors. Map Pattern The systematic organization of values for some variable across a map resulting in visually conspicuous texture that consists of global, regional, and local trends, gradients, swaths, or mosaics. Moran Coefficient An index of spatial autocorrelation, involving the computation of cross-products of meanadjusted values that are geographic neighbors (i.e., covariations), that ranges from roughly (–1, –0.5) to nearly 0 for negative, and nearly 0 to approximately 1 for positive, spatial autocorrelation, with an expected value of –1/(n – 1) for zero spatial autocorrelation, where n denotes the number of areal units. Moran Scatterplot A scatterplot of standardized versus summed nearby standardized values whose associated bivariate regression slope coefficient is the unstandardized Moran coefficient. Negative Spatial Autocorrelation For the geographic distribution of some variable across a map, high values tend to be geographic neighbors of low values, intermediate values tend to be geographic neighbors of intermediate values, and low values tend to be geographic neighbors of high values. Positive Spatial Autocorrelation For the geographic distribution of some variable across a map, high values tend to be geographic neighbors of high values, intermediate values tend to be geographic neighbors of intermediate values, and low values tend to be geographic neighbors of low values. Redundant Information Information in data that is duplicated, and hence unneeded for spatial statistical analyses; for georeferenced data, this duplication arises from locational closeness that results in mutually shared information, allowing an awareness of nearby values once the value for a given location is known.