Spatial Autocorrelation
Authors: Griffith Dan 
Published: April 2016

Spatial autocorrelation (SA)—the correlation among georeferenced observations arising from their relative locations in geographic space—has a history dating to the mid-1900s, although conceptual awareness of it dates back to the early 1900s. But SA is everywhere. It manifests itself in one- and two-dimensional synchronizations, exemplified by the experiment involving multiple metronomes sitting on a board that rests on two soda cans (illustrating an indirect, common factor SA source), or the aggregate flashing of fireflies created by their emission into the air of chemicals that stimulate nearby fireflies to light (illustrating a direct spatial interaction SA source). This latter outcome also can arise from mimicking behavior, as occurs with bandit bumble bees in a single meadow (i.e., when they rob a yellow rattler’s flower of nectar, their entry holes side in a given field tend to be unambiguously on only its left or right hand). The degree of organization in the geographic patterns that emerge signifies the level of positive SA. Such SA resulted in Heckscher discovering a new species of firefly in 2013. This type of SA is the basis of Nobel winner Schelling’s models of segregation, and The Economist (20 April 2013, p. 16) stating that regardless of class in Britain, geographical clusters of voters act like “political opinions derive from the air people breathe.” Moderate positive SA characterizes slider puzzles, magnetic sculpture toys, and television pictures. Meanwhile, negative SA relates to spatial patterns of competition. Although this nature of SA is rarely encountered in practice, it is illustrated by the Grand Prairie Independent School District’s (GPISD) attempts to increase the amount of money it receives from the state of Texas by holding annual events to attract students from surrounding school districts to attend its schools (Dallas Morning News, 9 January 2014); GPISD attempts to increase its enrollments by decreasing enrollments in its neighboring school districts. A timeline for the evolution of the SA concept helps establish its historically relevant literature. In the early 1800s, Laplace recognized autocorrelation—albeit serial for time series—by acknowledging that between day variations in barometric pressure readings tend to be much greater than within day readings. From 1914 to 1935, spatial series observational correlations were recognized by Student, then Yule, then both Stephan and Neprash, and then Fisher. This recognition set the stage for establishing the concept of SA. Moran and Geary did so in the early 1950s. In parallel, writing in French, Matheron and Krige also did so within the context of geostatistics. Next, more formal models of SA were formulated, first by Whittle, then by Mead, and finally by Cliff and Ord, whose numerous publications popularized the concept in the 1970s. One outcome of Cliff and Ord’s work was the coining of the phrase spatial econometrics in 1979 by Paelinck and Klaassen. Finally, as the century drew to a close, Griffith established the foundation of eigenvector spatial filtering, which extends SA analysis to the entire family of non-normal random variables.