Geographically weighted visualization: Interactive graphics for scale-varying exploratory analysis

We introduce a series of geographically weighted (GW) interactive graphics, or geowigs, and use them to explore spatial relationships at a range of scales. We visually encode information about geographic and statistical proximity and variation in novel ways through gw-choropleth maps, multivariate gw-boxplots, gw-shading and scalograms. The new graphic types reveal information about GW statistics at several scales concurrently. We impement these views in prototype software containing dynamic links and GW interactions that encourage exploration and refine them to consider directional geographies. An informal evaluation uses interactive GW techniques to consider Guerry's dataset of 'moral statistics', casting doubt on correlations originally proposed through visual analysis, revealing new local anomalies and suggesting multivariate geographic relationships. Few attempts at visually synthesising geography with multivariate statistical values at multiple scales have been reported. The geowigs proposed here provide informative representations of multivariate local variation, particularly when combined with interactions that coordinate views and result in gw-shading. We argue that they are widely applicable to area and point-based geographic data and provide a set of methods to support visual analysis using GW statistics through which the effects of geography can be explored at multiple scales

Locally-varying explanations behind the United Kingdom’s vote to the Leave the European Union

Explanations behind area-based (Local Authority-level) voting preference in the 2016 referendum on membership of the European Union are explored using aggregate-level data. Developing local models, special attention is paid to whether variables explain the vote equally well across the country. Variables describing the post-industrial and economic ‘successfulness’ of Local Authorities most strongly discriminate variation in the vote. To a lesser extent this is the case for variables linked to ‘metropolitan’ and ‘big city’ contexts, which assist the Remain vote, those that distinguish more traditional and ‘nativist’ val- ues, assisting Leave, and those loosely describing material outcomes, again reinforcing Leave. Whilst variables describing economic competitiveness co-vary with voting pref- erence equally well across the country, the importance of secondary variables – those dis- tinguishing metropolitan settings, values and outcomes – does vary by region. For certain variables and in certain areas, the direction of effect on voting preference reverses. For ex- ample, whilst levels of European Union migration mostly assist the Remain vote, in parts of the country the opposite effect is observed

Using geographically weighted regression to explore spatial variation in survey data

Nonresponse can undermine the quality of social survey data. Understanding who does/does not respond to surveys is important for those involved in the collection and analysis of these data. Levels of nonresponse are known to vary geographically. However, there has been little consideration of how the predictors of survey nonresponse might vary geographically within countries. This study examines the possibility of spatial variation in response behavior using regional interactions and geographically weighted regression. Our results suggest that there is geographical variation in response behavior. Relying on “one size fits all” global models in nonresponse modelling might, therefore, be insufficient

GWmodel: an R package for exploring spatial heterogeneity using geographically weighted models

Spatial statistics is a growing discipline providing important analytical techniques in a wide range of disciplines in the natural and social sciences. In the R package GWmodel we present techniques from a particular branch of spatial statistics, termed geographically weighted (GW) models. GW models suit situations when data are not described well by some global model, but where there are spatial regions where a suitably localized calibration provides a better description. The approach uses a moving window weighting technique, where localized models are found at target locations. Outputs are mapped to provide a useful exploratory tool into the nature of the data spatial heterogeneity. Currently, GWmodel includes functions for: GW summary statistics, GW principal components analysis, GW regression, and GW discriminant analysis; some of which are provided in basic and robust forms

Big issues for big data: challenges for critical spatial data analytics

In this paper we consider some of the issues of working with big data and big spatial data and highlight the need for an open and critical framework. We focus on a set of challenges underlying the collection and analysis of big data. In particular, we consider 1) inference when working with usually biased big data, challenging the assumed inferential superiority of data with observations, n, approaching N, the population n -> N. We also emphasise 2) the need for analyses that answer questions of practical significance or with greater emphasis on the size of the effect, rather than the truth or falsehood of a statistical statement; 3) the need to accept messiness in your data and to document all operations undertaken on the data because of this, in support of openness and reproducibility paradigms; and 4) the need to explicitly seek to understand the causes of bias, messiness etc in the data and the inferential consequences of using such data in analyses, by adopting critical approaches to spatial data science. In particular we consider the need to place individual data science studies in a wider social and economic contexts, along with the role of inferential theory in the presence of big data, and issues relating to messiness and complexity in big data

A Template for a New Generic Geographically Weighted R Package gwverse

GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW) framework is increasingly used to accommodate different types of models and analyses, reflecting a wider desire to explore spatial variation in model parameters and outputs. However, the growth in the use of GWR and different GW models has only been partially supported by package development in both R and Python, the major coding environments for spatial analysis. The result is that refinements have been inconsistently included within GWR and GW functions in any given package. This paper outlines the structure of a new gwverse package, that may over time replace GW model, that takes advantage of recent developments in the composition of complex, integrated packages. It conceptualizes gwverse as having a modular structure, that separates core GW functionality and applications such as GWR. It adopts a function factory approach, in which bespoke functions are created and returned to the user based on user-defined parameters. The paper introduces two demonstrator modules that can be used to undertake GWR and identifies a number of key considerations and next steps

A Template for a New Generic Geographically Weighted R Package gwverse

GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW) framework is increasingly used to accommodate different types of models and analyses, reflecting a wider desire to explore spatial variation in model parameters and outputs. However, the growth in the use of GWR and different GW models has only been partially supported by package development in both R and Python, the major coding environments for spatial analysis. The result is that refinements have been inconsistently included within GWR and GW functions in any given package. This paper outlines the structure of a new gwverse package, that may over time replace GW model, that takes advantage of recent developments in the composition of complex, integrated packages. It conceptualizes gwverse as having a modular structure, that separates core GW functionality and applications such as GWR. It adopts a function factory approach, in which bespoke functions are created and returned to the user based on user-defined parameters. The paper introduces two demonstrator modules that can be used to undertake GWR and identifies a number of key considerations and next steps. Volume54, Issue

The importance of scale in spatially varying coefficient modelling

While spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the “spatial scale” of each data relationship is crucially important to make SVC modeling more stable, and in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (i) geographically weighted regression (GWR) with a fixed distance or (ii) an adaptive distance bandwidth (GWRa),(iii) flexible bandwidth GWR (FB-GWR) with fixed distance or (iv) adaptive distance bandwidths (FB-GWRa), (v) eigenvector spatial filtering (ESF), and (vi) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely GWR and ESF, where SVC estimates are naively assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixedbandwidth counterparts (GWR and FB-GWR)

Editorial: crime patterns in time and space: the dynamics of crime opportunities in urban areas

The routine activity approach and associated crime pattern theory emphasise how crime emerges from spatio-temporal routines. In order to understand this crime should be studied in both space and time. However, the bulk of research into crime patterns and related activities has investigated the spatial distributions of crime, neglecting the temporal dimension. Specifically, disaggregation of crime by place and by time, for example hour of day, day of week, month of year, season, or school day versus none school day, is extremely relevant to theory. Modern data make such spatio-temporal disaggregation increasingly feasible, as exemplified in this special issue. First, much larger data files allow disaggregation of crime data into temporal and spatial slices. Second, new forms of data are generated by modern technologies, allowing innovative and new forms of analyses. Crime pattern analyses and routine activity inquiries are now able to explore avenues not previously available. The unique collection of nine papers in this thematic issue specifically examine spatio-temporal patterns of crime to; demonstrate the value of this approach for advancing knowledge in the field; consider how this informs our theoretical understanding of the manifestations of crime in time and space; to consider the prevention implications of this; and to raise awareness of the need for further spatio-temporal research into crime event