Spatial autocorrelation

Spatial autocorrelation is the dependence between values observed at different locations, measured according to how those locations are arranged in space. It can be positive, when nearby values tend to resemble one another, or negative, when nearby values tend to differ.

Spatial weights matrix: A matrix encoding which spatial units are neighbors and how strongly each pair is connected. It formalizes which locations count as nearby when dependence is measured.
Spatial data: Data whose observations are associated with locations, geometries, or spatial relationships. Spatial autocorrelation describes dependence among values attached to spatial observations.
Spatial epidemiology: The study of how health outcomes and their determinants vary across geographic space. Autocorrelation tests whether disease rates cluster beyond what independent locations would produce.
Spatial heterogeneity: Variation in a process or relationship across geographic locations. Changing local means or relationships can produce apparent patterns without being the same as dependence between neighbors.
Moran's I: A statistic that measures global spatial autocorrelation by comparing values with weighted neighboring values. It is a standard measure of whether similar or dissimilar values cluster across a study area.
Spatial dependence: A statistical relationship in which observations at different locations are not independent. Spatial autocorrelation is a specific form of dependence structured by spatial proximity.
Spatial regression: Regression methods that account for spatial dependence in outcomes, predictors, or errors. Autocorrelated observations can violate assumptions of ordinary regression and distort inference.
Simpson's paradox: A reversal of an association when data are grouped or combined across categories. Aggregation across space can reverse observed relationships, complicating autocorrelation-based interpretations.
Geary's C: A statistic of spatial autocorrelation based on squared differences between neighboring observations. Its local-difference emphasis complements Moran's I when quantifying spatial dependence.
Neighborhood (graph theory): A relation specifying which vertices in a graph are considered adjacent to a given vertex. Spatial analyses translate geographic proximity into neighborhood links between observations.

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