INTRODUCTION

Concepts of space and geography play prominent roles in many social science theories. In fields as diverse as anthropology, criminology, demography, political science, sociology, and public health, our theories predict that spatially proximate units are more likely to behave similarly than spatially distant units. These theories, in short, predict positive spatial autocorrelation or spatial dependence, the spatial clustering of similar behaviors, processes, and events among neighboring observations. This common interest in geography across the social sciences is not surprising. The social sciences are defined by their focus on phenomena that are inherently social and interdependent. Shared concerns combine with spatial proximity to promote familiarity. This familiarity in turn breeds both contempt and conflict and interaction and interdependence.

Until recently our ability to incorporate the spatial dimension of our theories in our models was quite limited, relying primarily on dummy variables to capture differences in behavior across geographically disparate units. Such an approach is suboptimal, as it is unable to address some of the central issues posed by spatially dependent data. Consider, for example, Sir Francis Galton's comment in the epigraph to this chapter. Sir Galton's comment in response to Edward Tylor's presentation at the Royal Anthropological Institute in November 1888 clearly ranks among the most influential comments expressed at an academic presentation, remembered as it is more than a century later. Sir Galton's critique, which has since come to be known as Galton's problem, focuses on the critical substantive distinction between two alternative explanations for spatially dependent behavior.