On the importance of thinking locally for statistics and society

Abstract

Over the past two decades increasing focus has been given to local forms of spatial analysis, both in terms of descriptive statistics and spatial modeling. We term this “thinking locally” Fundamental to thinking locally is that a global approach to spatial analysis may not be suitable and that there may be situations where the conditioned relationships we want to measure vary over space. This paper examines the implications of thinking locally not only for modeling spatial processes but also more broadly in terms of our understanding of behavior in space. We begin with a brief survey of local statistical modeling and what might cause relationships to vary spatially and then describe the operation of one type of local modeling framework – that of (Multiscale) Geographically Weighted Regression – to demonstrate the basic concepts inherent in local models and the type of output that is generated by such models. We then examine the implications of a local approach to statistical analysis focussing on the role of local models compared to spatial regression models, diagnostics for local models, and how a local approach relates to issues of spatial scale which have plagued spatial analysis for decades. Attention is then turned to the implications of a local modeling approach to society, commenting on replicability and how local models can be used to measure previously unmeasurable place-based ‘contextual’ effects. We demonstrate the issues raised throughout the paper with an empirical example of house price determinants.