Academic journal article Demographic Research

Mapping the Results of Local Statistics: Using Geographically Weighted Regression

Academic journal article Demographic Research

Mapping the Results of Local Statistics: Using Geographically Weighted Regression

Article excerpt



The application of geographically weighted regression (GWR) - a local spatial statistical technique used to test for spatial nonstationarity - has grown rapidly in the social, health, and demographic sciences. GWR is a useful exploratory analytical tool that generates a set of location-specific parameter estimates which can be mapped and analysed to provide information on spatial nonstationarity in the relationships between predictors and the outcome variable.


A major challenge to users of GWR methods is how best to present and synthesize the large number of mappable results, specifically the local parameter parameter estimates and local t-values, generated from local GWR models. We offer an elegant solution.


This paper introduces a mapping technique to simultaneously display local parameter estimates and local t-values on one map based on the use of data selection and transparency techniques. We integrate GWR software and GIS software package (ArcGIS) and adapt earlier work in cartography on bivariate mapping. We compare traditional mapping strategies (i.e., side-by-side comparison and isoline overlay maps) with our method using an illustration focusing on US county infant mortality data.


The resultant map design is more elegant than methods used to date. This type of map presentation can facilitate the exploration and interpretation of nonstationarity, focusing map reader attention on the areas of primary interest.

(ProQuest: ... denotes formulae omitted.)

1. Introduction3

Across the sciences there has been a recent emergence of techniques for examining local relationships in data based on analytical approaches that focus on subsets of data (e.g., locally weighted scatterplot smoothing (LOWESS), a technique developed by Cleveland 1979). Techniques for the analysis of local spatial relationships also have recently emerged (for an overview see Lloyd 2011).

The conventional approach to the empirical analyses of spatial data is to calibrate a global model. The term 'global' implies that all the spatial data are used to compute a single statistic or equation that is essentially an average of the conditions that exist throughout the study area in which the data have been measured. The underlying assumption in a global model is that the relationships between the predictors and the outcome variable are homogeneous (or stationary) across space. More specifically, the global model assumes that the same stimulus provokes the same response in all parts of the study region. However, in practice, the relationships between variables might be nonstationary and vary geographically (Cressie 1993; Jones and Hanham 1995). Spatial nonstationarity exists when the same stimulus provokes a different response in different parts of the study region. If nonstationarity exists then there is a suggestion that different processes are at work within the study region.

Standard global modeling techniques, such as ordinary least squares (OLS) linear regression or spatial regression methods, cannot detect nonstationarity and thus their use may obscure regional variation in the relationships between predictors and the outcome variable. Public policy inference based on the results from global models, where nonstationarity is present but not detected, will be variable and may be even quite poor in specific local/regional settings (Ali, Patridge, and Olfert 2007).

Geographically Weighted Regression (GWR) is a statistical technique that allows variations in relationships between predictors and outcome variable over space to be measured within a single modeling framework (Fotheringham, Brunsdon, and Charlton 2002; National Centre for Geocomputation 2009). As an exploratory technique, GWR provides a great richness in the results obtained for any spatial data set, and should be useful across all disciplines in which spatial data are utilized. …

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