GWmodelS: A software for geographically weighted models

Spatial heterogeneity or non-stationarity has become a popular and necessary concern in exploring relationships between variables. In this regard, geographically weighted (GW) models provide a powerful collection of techniques in its quantitative description. We developed a user-friendly, high-performance and systematic software, named GWmodelS, to promote better and broader usages of such models. Apart from a variety of GW models, including GW descriptive statistics, GW regression models, and GW principal components analysis, data management and mapping tools have also been incorporated with well-designed interfaces

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

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

GWmodelS: a standalone software to train geographically weighted models

With the recent increase in studies on spatial heterogeneity, geographically weighted (GW) models have become an essential set of local techniques, attracting a wide range of users from different domains. In this study, we demonstrate a newly developed standalone GW software, GWmodelS using a community-level house price data set for Wuhan, China. In detail, a number of fundamental GW models are illustrated, including GW descriptive statistics, basic and multiscale GW regression, and GW principle component analysis. Additionally, functionality in spatial data management and batch mapping are presented as essential supplementary activities for GW modeling. The software provides significant advantages in terms of a user-friendly graphical user interface, operational efficiency, and accessibility, which facilitate its usage for users from a wide range of domains

The GWmodel R package: Further Topics for Exploring Spatial Heterogeneity using Geographically Weighted Models

In this study, we present a collection of local models, termed geographically weighted (GW) models, that can be found within the GWmodel R package. A GW model suits situations when spatial data are poorly described by the global form, and for some regions the localised fit provides a better description. The approach uses a moving window weighting technique, where a collection of local models are estimated at target locations. Commonly, model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed. In particular, we present case studies using: (i) GW summary statistics and a GW principal components analysis; (ii) advanced GW regression fits and diagnostics; (iii) associated Monte Carlo significance tests for non-stationarity; (iv) a GW discriminant analysis; and (v) enhanced kernel bandwidth selection procedures. General Election data sets from the Republic of Ireland and US are used for demonstration. This study is designed to complement a companion GWmodel study, which focuses on basic and robust GW models

Comparing spatial patterns

The second author would like to acknowledge Natural Sciences and Engineering Research Council of Canada for funding this paper.The comparison of spatial patterns is a fundamental task in geography and quantitative spatial modelling. With the growth of data being collected with a geospatial element, we are witnessing an increased interest in analyses requiring spatial pattern comparisons (e.g., model assessment and change analysis). In this paper, we review quantitative techniques for comparing spatial patterns, examining key methodological approaches developed both within and beyond the field of geography. We highlight the key challenges using examples from widely known datasets from the spatial analysis literature. Through these examples, we identify a problematic dichotomy between spatial pattern and process—a widespread issue in the age of big geospatial data. Further, we identify the role of complex topology, the interdependence of spatial configuration and composition, and spatial scale as key (research) challenges. Several areas ripe for geographic research are discussed to establish a consolidated research agenda for spatial pattern comparison grounded in quantitative geography. Hierarchical scaling and the modifiable areal unit problem are highlighted as ideas which can be exploited to identify pattern similarities across spatial and temporal scales. Increased use of “time-aware” comparisons of spatial processes are suggested, which properly account for spatial evolution and pattern formation. Simulation-based inference is identified as particularly promising for integrating spatial pattern comparison into existing modelling frameworks. To date, the literature on spatial pattern comparison has been fragmented, and we hope this work will provide a basis for others to build on in future studies.PostprintPeer reviewe

Space matters : geographic variability of electoral turnout determinants in the 2012 London mayoral election

Electoral participation is an important measure of the health of a liberal democracy. The determinants of voter turnout have been examined across a range of elections, but geographical approaches are relatively rare and are mostly performed at large scale aggregations and for national elections. This paper addresses this gap by exploring geographic variability in relationships between the turnout at a local election and socio-demographic variables at a detailed spatial level. Specifically, we focus on the London mayoral election, an important element of the 21st century local government reform in Britain, which, until now, has seldom been analysed from a geographical perspective. By linking the turnout from the 2012 mayoral election to socio-demographic data from the 2011 Census and doing this at the level of London’s 625 wards, for the first time a more detailed picture of the spatially uneven nature of turnout is evidenced than in previous studies which have focused on larger aggregations, typically constituencies. Analysis is approached through spatial analysis using geographically weighted regression (GWR), which enables the investigation of local variations in voting patterns. The results demonstrate that electoral processes do vary over geographic space and that some of the variables that are traditionally assumed to affect the turnout in a specific way, do not do so uniformly over space or even change the direction to the opposite of the traditionally assumed affect in certain locations. Our findings present a starting point for a more detailed investigation as to why this heterogeneity exists and which social processes it relates to.PostprintPeer reviewe

Package ‘GWmodel’

In GWmodel, we introduce techniques from a particular branch of spatial statis- tics,termed geographically-weighted (GW) models. GW models suit situa- tions when data are not described well by some global model, but where there are spatial re- gions where a suitably localised calibration provides a better description. GWmodel in- cludes functions to calibrate: GW summary statistics, GW principal components analy- sis, GW discriminant analysis and various forms of GW regression; some of which are pro- vided in basic and robust (outlier resistant) forms

Package ‘GWmodel’

In GWmodel, we introduce techniques from a particular branch of spatial statis- tics,termed geographically-weighted (GW) models. GW models suit situa- tions when data are not described well by some global model, but where there are spatial re- gions where a suitably localised calibration provides a better description. GWmodel in- cludes functions to calibrate: GW summary statistics, GW principal components analy- sis, GW discriminant analysis and various forms of GW regression; some of which are pro- vided in basic and robust (outlier resistant) forms

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