Spatial Autocorrelation: A Statistician’s Reflections

Improvements in both technology and statistical understanding have led to considerable advances in spatial model building over the past 40 years, yet major challenges remain both in model specification and in ensuring that the underlying statistical assumptions are validated. The basic concept in such modeling efforts is that of spatial dependence, often made operational by some measure of spatial autocorrelation. Such measures depend upon the specification or estimation of a set of weights that describe spatial relationships. We examine how the identification of weights has evolved and briefly describe recent developments. After a brief examination of some of the key assumptions commonly made in spatial modeling, we consider the selection of tests of spatial dependence and their application to irregular sub-regions. We then move on to a consideration of local tests and estimation procedures and identify ways in which local procedures may be useful, particularly for large data sets. We conclude with a brief review of a recently developed method for modeling anisotropic spatial processes.