A History of the Concept of Spatial Autocorrelation: A Geographer's Perspective

Article excerpt

Spatial autocorrelation is a concept that helps to define the field of spatial analysis. It is central to studies using spatial statistics and spatial econometrics. In this paper, we trace the early development of the concept and explain the academic links that brought the concept to the fore in the late 1960s. In geography, the importance of the work of Michael F. Dacey, Andrew D. Cliff, and J. Keith Ord is emphasized. Later, with the publication of a volume on spatial econometrics by Luc Anselin, spatial research and the use of the concept of spatial autocorrelation received a considerable boost. These developments are outlined together with comments about recent and possible future trends in spatial autocorrelation-based research.

Introduction

Many academic movements begin, reach a popular peak, and slowly decline. A number of pundits like to say that the "quantitative revolution" in geography of the late 1950s and early 1960s died out in the late 1960s and early 1970s. Not usually mentioned in the geographic literature is that the seeds planted in the quantitative revolution produced a steady crop of contributions that has now evolved into a vibrant field, both inside and outside the discipline of geography. By the 1990s, the field of spatial analysis had matured to the point where the methods and concepts it created were becoming fundamental to researchers in a host of disciplines including geography, ecology, epidemiology, sociology, urban planning, geology, and environmental studies. In this paper, I describe this development by choosing the field's fundamental concept, spatial autocorrelation, and tracing its evolution. The main emphasis is to explore the concept's beginnings and its place in the academy. Because the number of contributors to the concept is so large, it would be impossible in a paper of this length to review each contribution. I decided to emphasize those works that, in my estimation, were the landmarks that had the greatest influence on spatially oriented research.

Some of what is contained in this paper was first described in an essay I wrote for the Regional Science and Urban Economics journal (Getis 2007). In my presentation on this subject at the IGU meeting in Brisbane (Getis 2006), I mentioned the contributions of over 50 scholars to this field. I have made the power point of that presentation available at my web-site. Not mentioning contributors' names or describing their work in this article has nothing to do with the significance of their contributions. In this article, I describe what I consider to be the landmarks in the development of the concept.

The definition of spatial autocorrelation

The concept of spatial autocorrelation, although it may be viewed as a special case of correlation, has a meaning all its own. Whereas correlation statistics were designed to show relationships between or among variables, spatial autocorrelation shows the correlation within variables across georeferenced space. Of the several definitions of spatial autocorrelation in the literature, that by Hubert, Golledge, and Constanza (1981) is perhaps the most concise:

  "Given a set 5 containing n geographical units, spatial
  autocorrelation refers to the relationship between some variable
  observed in each of the n localities and a measure of geographical
  proximity defined for all n (n - 1) pairs chosen from n." (p. 224)

The literature on the subject contains many statistics, measures, and parameters that concisely express this relationship for a variety of types of research questions. The statistics originally were designed to identify a theoretical condition in which no spatial autocorrelation is present. In practice, however, the statistics are used not only to test hypotheses of no spatial autocorrelation but also to gauge the degree of spatial autocorrelation extant in the georeferenced data. For a single spatially distributed variable, these statistics are usually made up of two parts: (1) an expression representing a specified, hypothesized causal relationship between designated pairs of observations (autocorrelation), and (2) an expression representing the geometric (spatial) relationship of those same pairs of observations. …