The importance of scale in spatially varying coefficient modeling

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 fixed bandwidth counterparts (GWR and FB-GWR)

Geographic Information Science

This chapter begins with a definition of geographic information science (GIScience). We then discuss how this research area has been influenced by recent developments in computing and data-intensive analysis, before setting out its core organizing principles from a practical perspective. The following section reflects on the key characteristics of geographic information, the problems posed by large data volumes, the relevance of geographic scale, the remit of geographic simulation, and the key achievements of GIScience to date. Our subsequent review of changing scientific practices and the changing problems facing scientists addresses developments in high-performance computing, heightened awareness of the social context of geographic information systems (GISystems), and the importance of neogeography in providing new data sources, in driving the need for new techniques, and in heightening a human-centric perspective

Geography and computers: Past, present, and future

The discipline of Geography has long been intertwined with the use of computers. This close interaction is likely to increase with the embeddedness of computers and concomitant growth of spatially referenced data. To better understand the current situation, and to be able to better speculate about the future, this article provides two parallel perspectives: first, we offer an historical perspective on the relationship between Geography and computers; second, we document developments—in particular the nascent field of data science—that are currently taking place outside of Geography and to which we argue the discipline should be paying close attention. Combining both perspectives, we identify the benefits of tighter integration between Geography and Data Science and argue for the establishment of a new space—that we term Geographic Data Science—in which cross‐pollination could occur to the benefit of both Geography and the larger data community

Quantitative methods I: Reproducible research and quantitative geography.

Reproducible quantitative research is research that has been documented sufficiently rigorously that a third party can replicate any quantitative results that arise. It is argued here that such a goal is desirable for quantitative human geography, particularly as trends in this area suggest a turn towards the creation of algorithms and codes for simulation and the analysis of Big Data. A number of examples of good practice in this area are considered, spanning a time period from the late 1970s to the present day. Following this, practical aspects such as tools that enable research to be made reproducible are discussed, and some beneficial side effects of adopting the practice are identified. The paper concludes by considering some of the challenges faced by quantitative geographers aspiring to publish reproducible research

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

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)

A suggested framework and guidelines for learning GIS in interdisciplinary research

Interdisciplinary research with geographic information systems (GIS) can be rewarding as researchers from different disciplines have the opportunity to create something novel. GIS, though, is known to be difficult to use and learn. It is imperative for its successful use in projects that those who need to use GIS are able to learn it quickly and easily. To better support interdisciplinary research with GIS, it is necessary to understand what researchers with interdisciplinary experience wanted to use it for and how they learned it. The aim would be to advise geography educators on creating learning resources that could compliment or supplement existing learning approaches used by interdisciplinary researchers to improve the learning experience and uptake of GIS. This article explores the results from an online survey and interviews conducted between July 2014 and August 2015 with participants from the UK, the US and Europe on how interdisciplinary researchers learned GIS and which resources and platforms were utilised. Guidelines and a framework are presented, modifying the Technological Pedagogical and Content Knowledge framework, incorporating informal and context-based learning and GIS concepts from the Geographic Information Science and Technology Body of Knowledge. Findings show that interdisciplinary researchers want to use GIS to capture, analyse and visualise information; they largely use informal learning approaches (e.g. internet searches, watching a video, ask a more experienced person); and they predominantly use ArcGIS, QGIS and web GIS platforms. Future work suggests resources use contextually relevant learning activities and bear in mind nuances of disciplinary language