Spatial Data and Spatial Statistics

Abstract

Advances in information technology as well as organizational changes in both the public and private sectors have led to increased availability of small area data. If the benefits of having such data are to be fully realized, we need statistical methods that give rise to parameter estimates with good properties including standard errors reliably estimated. To achieve this goal, four challenges associated with spatial and spatial-temporal data need to be met head-on: spatial dependence, spatial heterogeneity, data sparsity, and uncertainty. We start this chapter by reviewing each of the four challenges. We then describe spatial statistical modelling drawing a distinction between theory-driven and data-driven modelling. We also compare Bayesian and frequentist approaches to inference and argue that Bayesian inference is more appropriate to an observational science. The chapter then discusses the two principal approaches to modelling spatial and spatial-temporal data: spatial econometric and spatial hierarchical regression modelling. While the two approaches are, in many respects, complementary, hierarchical modelling which breaks down complex models into distinct modules offers a number of clear advantages and in combination with Bayesian inference meets the four challenges described at the outset thereby providing a positive answer to the question of whether we can have the best of both worlds: spatial and spatial-temporal precision and statistical precision.