Abstract
Recent progress on human geography has seen a marked increase in spatial autocorrelation studies, accompanied by elaboration and development of both its theoretical concepts and its operational techniques. This article presents a critical review of the history of spatial autocorrelation studies, defining its present status and emerging tasks.
The history of spatial autocorrelation studies may be conveniently divided into two stages, before and after the publication of “Spatial autocorrelation” by Cliff and Ord in 1973. The first stage is characterized by its underestimation and by general ignorance of its significance to spatial analysis. During this stage, spatial autocorrelation was used as a ready tool for judging the fulfillment of statistical assumptions, but even when the presence of spatial autocorrelation was statistically detected, any improvement of the statistical methods to incorporate spatial autocorrelation problems was not attempted.
However, during the second stage, there has been a growing recognition of the significance of spatial autocorrelation as a generating agent in the formation and transformation of spatial patterns. If spatial autocorrelation is defined as the lack of independence (i.e. the interdependence) of phenomena in space, any spatial patterns are a product of spatial autocorrelation, and in searching for the explanation of spatial patterns, spatial interdependence provides the key integrative concept.
Parallel with this reversal in attitude, the expanded application of spatial autocorrelation concepts has led to new research trends in the empirical and theoretical study of spatial patterns. New research trends in this field aim at generalizing and elaborating spatial autocorrelation concepts to develop their power of pattern testing. Interrelation between personal pattern recognition and the coeficient of spatial autocorrelation, which attempts to associate spatial autocorrelation with perception studies, has been explored by Gatrell (1977) and Olson (1975).
In the explanatory study of static spatial patterns, notable advancement of model construction has been attained by incorporating spatial lag components into the model as an independent variable. The same idea is applied to the examination of dynamic processes of pattern formation: the process is modeled on the independent variable of spatial-temporal lag components, evaluated from the structure of spatial-temporal autocorrelation. Both lag components are defined by the received spatial and spatial-temporal influences of each cell (sample) from its neighbors.
We can summarize the present situation as a shift of research interest in spatial autocorrelation from the statistical noise to be eliminated to the underlying process of pattern formation. In other words, the shift means a step toward establishment of a truly spatial analysis apart from the mere application of non-spatial statistical methods to spatial data.
However, two significant tasks remain to be elaborated: 1) definition of weight and 2) formulation of spatial and/or spatial/temporal models. In the present article, the main discussion is of the former problem.
An accurate and objective testing and explanation of a pattern can be attained by defining the most appropriate weight matrix, properly evaluated from the underlying spatial structure of the pattern. The concept of spatial autocorrelation (or interdependency) as a pattern organizer gives a promising clue for such identification. We may consider any spatial pattern to have been organized by the operation of spatial autocorrelation, which has generally been as sumed to have spatial isotropic properties. On this assumption, an isotropic weight matrix has been used for the testing and explanation of patterns. However, most of the observed and actual patterns show strong directional biases, suggesting the presence of underlying non-isotropic spatial structure.
