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Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS-GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS-GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.

The measure of a household's income should include not only monetary components but also non-monetary components and in-kind benefits, such as imputed rent. Imputed rent is the rent an owner can expect to receive were the house on the rental market. This study examined the impact of net imputed rent on the distribution of income in a spatial context. The spatial impact of net imputed rent, mortgage payments, private rent, public rent (social housing schemes) and reverse mortgage/annuity on the spatial distribution of disposable income was examined for the year 2011. A spatial microsimulation model, simulated model of the Irish local economy (SMILE), was used to simulated disposable income at a detailed spatial scale. Rental and property values are estimated at a spatial scale adopting the kriging methodology. The created rental and property data were merged into the SMILE simulated dataset to examine the impact of housing on the spatial distribution of disposable income at a small area level. Results show that the imputed cash flows from property ownership decreases the income share of those at the bottom of the income distribution and is inequality increasing, except in the case of those aged 65 +. Spatially the benefits of housing are greatest in urban areas where property values are highest. The small area measurements of imputed rent highlight the dis-equalising impact imputed rent and housing wealth has on inequality; the rich being able to consume more housing.

This chapter investigates the changing patterns of clinical Misery (depression, anxiety disorders), through patterns of Antidepressants and Anxiolytics (AD) prescribing rates (prescriptions per person). Misery measured in this way, has increased >40% nationally with greater increases in some areas. Rates were linked to individual deprivation domain scores (housing, crime, employment, etc), which in 2010 were evenly associated with AD prescribing rates. The impacts of austerity policies are evident in the increases in the association of Barriers to Housing and Services and Health, Deprivation and Disability deprivation scores with AD prescribing rates since 2015, and with Employment in 2019. The discussion describes a detailed research agenda for examining Misery, noting the need to shift narratives away from flimsy concepts of Well-being, and number of key rubrics for big data analysis are outlined. In these, the importance of data folding, investigation and visualizations are emphasized - 10km hexbins were used here to summarise annual prescribing rates. These form a key sequence in big data analysis of View -> Identify -> Refine -> Zoom.

Geodemographics is a tool to summarize the characteristics of spatial units based on socio-economic data. It has been used over several decades to classify the characteristics of areas based on the similarities in such data, generally working by identifying groups or clusters of similar areas. It has seen use in the academic and private sectors but mostly became popular by 1980s for market research purposes – this rise in use drew attention to many issues that needed to be addressed in the literature. The purpose of this paper is to provide a geodemographic classification for the smallest scale administrative units in Ireland (Small Areas) based on the latest 2016 census population data. A further aim is to support reproducible research by following the methodology of an earlier study for the 2011 Census and to bring up the opportunity to compare the cluster results between the 2011 and 2016 census data. The comparison output provides useful insights for policy discussions in the Irish context. One of the other focal points of this study is to bring some clarity regarding some criticisms of geodemographics from an academic perspective. The paper also argues for the use of open data, open source software and supports open analysis.

In the context of debates about segregation within the UK, this paper maps the residential geography of two groups of White British school children, one of which was in secondary school in 2011 and the other in 2017. To present that geography, hexograms are introduced as a complement to visually balanced cartograms, both of which seek to address the problems of invisibility and distortion encountered with more conventional choropleth and cartogram maps. The nature of these problems is introduced, our solutions discussed, and the methods applied to the case study, which allow changes in the geography to be seen.

Although 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: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) 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 REESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are nai vely 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).

On Thursday 23 June 2016, a majority of the UK electorate voted in favour of leaving the European Union by a margin of 51.9% to 48.1%. Throughout the night, as the results were reported, the media spoke about London, Scotland and Northern Ireland versus the rest of the UK in regard to their support for the European Union. In this commentary, we look at the geographical distribution of the share of the Leave votes and model it against the share of the electorate, by local authority and by region, using a multilevel framework. The model identifies differences between countries and differences between regions but also more localised variations that depart from those trends. Areas with an older population were more likely to attract a higher share of the Leave vote, as were those with higher proportions of residents in lower supervisory and technical occupations, and with residents born outside of the UK but in the European Union. The referendum has revealed a less than United Kingdom, with notable differences between Scotland, Northern Ireland and much of London, and parts of the East Midlands, West Midlands and the East. However, London is not as pro-European Union as might be anticipated given its social, ethnic and demographic composition, which may help explain why the Leave campaign won with a small margin.

A perennial problem when mapping demographic, social and other area-based data is that rural areas usually are of greater physical size than their urban counterparts. The consequence is that the places with fewest people dominate the map space, whereas those with the most are rendered small and illegible. A classic example is what happens if the results of the UK election are mapped, in this case for the 2015 election. As the left side of Figure 1 reveals, the outcomes for London visually are unintelligible.

In this study, we introduce the R package shp2graph, which provides tools to convert a spatial network into an &lsquo, igraph&rsquo, graph of the igraphR package. This conversion greatly empowers a spatial network study, as the vast array of graph analytical tools provided in igraph are then readily available to the network analysis, together with the inherent advantages of being within the R statistical computing environment and its vast array of statistical functions. Through three urban road network case studies, the calculation of road network distances with shp2graph and with igraph is demonstrated through four key stages: (i) confirming the connectivity of a spatial network, (ii) integrating points/locations with a network, (iii) converting a network into a graph, and (iv) calculating network distances (and travel times). Throughout, the required R commands are given to provide a useful tutorial on the use of shp2graph.

This paper describes an experimental project that aims to investigate the scope of methodological and technical possibilities of using 360° videos for experiencing authored drama. In particular, it examines how a work written for the medium of theatre, with a traditional audience-drama relationship of viewer invisibility and non-participation, might translate into a viewing experience as a VR drama. The technical and dramaturgical issues arising from this are discussed. Specifically, the shared voyeuristic quality of both media is examined. Is the invisible viewer of VR drama in the invidious role of Glaucon’s iniquitous shepherd Gyges, or does the medium give invisibility a cloak of aesthetic value?

In this study, the geographically weighted regression (GWR) model is adapted to benefit from a broad range of distance metrics, where it is demonstrated that a well-chosen distance metric can improve model performance. How to choose or define such a distance metric is key, and in this respect, a ‘Minkowski approach’ is proposed that enables the selection of an optimum distance metric for a given GWR model. This approach is evaluated within a simulation experiment consisting of three scenarios. The results are twofold: (1) a well-chosen distance metric can significantly improve the predictive accuracy of a GWR model; and (2) the approach allows a good approximation of the underlying ‘optimal distance metric’, which is considered useful when the ‘true’ distance metric is unknown.

Geographically Weighted Regression (GWR) is a local technique that models spatially varying relationships, where Euclidean distance is traditionally used as default in its calibration. However, empirical work has shown that the use of non-Euclidean distance metrics in GWR can improve model performance, at least in terms of predictive fit. Furthermore, the relationships between the dependent and each independent variable may have their own distinctive response to the weighting computation, which is reflected by the choice of distance metric. Thus, we propose a back-fitting approach to calibrate a GWR model with parameter-specific distance metrics. To objectively evaluate this new approach, a simple simulation experiment is carried out that not only enables an assessment of prediction accuracy, but also parameter accuracy. The results show that the approach can provide both more accurate predictions and parameter estimates, than that found with standard GWR. Accurate localised parameter estimation is crucial to GWR's main use as a method to detect and assess relationship non-stationarity.

This year marks the 21st anniversary of the International GeoComputation Conference Series. To celebrate the occasion, Environment and Planning B invited some members of the geocomputational community to reflect on its achievements, some of the unrealised potential, and to identify some of the on-going challenges.

In many physical geography settings, principal component analysis (PCA) is applied without consideration for important spatial effects, and in doing so, tends to provide an incomplete understanding of a given process. In such circumstances, a spatial adaptation of PCA can be adopted, and to this end, this study focuses on the use of geographically weighted principal component analysis (GWPCA). GWPCA is a localized version of PCA that is an appropriate exploratory tool when a need exists to investigate for a certain spatial heterogeneity in the structure of a multivariate data set. This study provides enhancements to GWPCA with respect to: (i) finding the scale at which each localized PCA should operate; and (ii) visualizing the copious amounts of output that result from its application. An extension of GWPCA is also proposed, where it is used to detect multivariate spatial outliers. These advancements in GWPCA are demonstrated using an environmental freshwater chemistry data set, where a commentary on the use of preprocessed (transformed and standardized) data is also presented. The study is structured as follows: (1) the GWPCA methodology; (2) a description of the case study data; (3) the GWPCA application, demonstrating the value of the proposed advancements; and (4) conclusions. Most GWPCA functions have been incorporated within the GWmodel R package.

Given an initial spatial sampling campaign, it is often of importance to conduct a second, more targeted campaign based on the properties of the first. Here a net- work re-design modifies the first one by adding and/or removing sites so that maximum information is preserved. Commonly, this optimisation is constrained by limited sampling funds and a reduced sample network is sought. To this extent, we demonstrate the use of geographically weighted methods combined with a location-allocation algorithm, as a means to design a second-phase sampling campaign in univariate, bivariate and multivariate contexts. As a case study, we use a freshwater chemistry data set covering much of Great Britain. Applying the two-stage procedure enables the optimal identification of a pre- specified number of sites, providing maximum spatial and univariate/bivariate/multivariate water chemistry informa- tion for the second campaign. Network re-designs that account for the buffering capacity of a freshwater site to acidification are also conducted. To complement the use of basic methods, robust alternatives are used to reduce the effect of anomalous observations on the re-designs. Our non-stationary re-design framework is general and provides a relatively simple and a viable alternative to geostatistical re-design procedures that are commonly adopted. Particu- larly in the multivariate case, it represents an important methodological advance.

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler’s first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, non- Euclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.

There is a plethora of factors that dictate where parents and families choose to seek unscheduled healthcare for their child; and the complexity of these decisions can present a challenge for policy makers and healthcare planners as these behaviours can have a significant impact on resources in the health system. The systematic review will seek to identify the factors that influence parents’ and families’ preferences and decision making when seeking unscheduled paediatric healthcare. Five databases will be searched for published studies (CINAHL, PubMed, SCOPUS, PsycInfo, EconLit) and grey literature will also be searched. Inclusion and exclusion criteria will be applied and articles assessed for quality. A narrative approach will be used to synthesise the evidence that emerges from the review. By collating the factors that influence decision-making and attendance at these services, the review can inform future health policies and strategies seeking to expand primary care to support the provision of accessible and responsive care. The systematic review will also inform the design of a discrete choice experiment (DCE) which will seek to determine parental and family preferences for unscheduled paediatric healthcare. Policies such as Sláintecare that seek to expand primary care and reduce hospital admissions from emergency departments need to be cognisant of the nuanced and complex factors that govern patients’ behaviour.

Outlier detection is often a key task in a statistical analysis and helps guard against poor decision-making based on results that have been influenced by anomalous observations. For multivariate data sets, large Mahalanobis distances in raw data space or large Mahalanobis distances in principal components analysis, transformed data space, are routinely used to detect outliers. Detection in principal components analysis space can also utilise goodness of fit distances. For spatial applications, however, these global forms can only detect outliers in a non-spatial manner. This can result in false positive detections, such as when an observation’s spatial neighbours are similar, or false negative detections such as when its spatial neighbours are dissimilar. To avoid mis-classifications, we demonstrate that a local adaptation of various global methods can be used to detect multivariate spatial outliers. In particular, we account for local spatial effects via the use of geographically weighted data with either Mahalanobis distances or principal components analysis. Detection performance is assessed using simulated data as well as freshwater chemistry data collected over all of Great Britain. Results clearly show value in both geographically weighted methods to outlier detection.

This paper presents a new approach and procedure for directly processing vector-based data sets to generalise maps depicting real-world phenomena. It shows how map generalisation and seamless matching of the edges of adjacent area features can be achieved. With this approach, the combined use of selected methods has led to a ground-breaking novel procedure for vector-based map generalisation guaranteeing outputting with neither self-intersection nor cross-intersection. The approach employs turning points and convex hull points as a set of characteristic points. These points define the shape and characteristics of real-world geographical features with delineating lines, which have complex rendering layouts, many turnings and inherent subfeatures. The set of characteristic points are used as splitting points to partition lines into monotonic chains. Line simplification with an intuitive point reduction technique using the Douglas–Peucker algorithm is confined within monotonic chains to guarantee no self-intersection. In addition, the paper describes the most suitable and intuitive means to deal with gaps and overlaps potentially resulting from cross-intersections without adding or deleting any anchoring point. Distinctively different from the approaches of previous studies, the research was undertaken through an iterative process of exploratory programming, experimentation, validation and testing of results produced. This process was repeated until an integrated total solution was reached. It sheds new light on the fields of geocomputation, geographic information systems (GIS) and digital cartography.

Geodemographic classifications have progressed from manual classifications of areas through to complex, highly marketable products used in both the public and private sectors. As their production became commercialized, input variables moved beyond census variables to include other, often not publicly available datasets, and hence the resultant black-box approach increased in sophistication, but was less open to scrutiny. In the UK this was somewhat reversed with the production of the Output Area Classification (OAC) from the 2001 census. As an alternative approach, in this paper we demonstrate the production of a geodemographic classification for the Republic of Ireland, using a different approach to OAC, and extending the ethos of transparency and reproducibility.

GIScience 2016 Short Paper Proceedings A moan, a discursion into the visualisation of very large spatial data and some rubrics for identifying big questions A. Comber 1 , C. F. Brunsdon 2 , M. Charlton, R. Harris 3 School of Geography, University of Leeds, LS2 9JT, UK Email: a.comber@leeds.ac.uk NUI Maynooth, Maynooth, Co Kildare, Ireland Email: {christopher.brunsdon; martin.charlton} @nuim.ie School of Geographical Sciences, University of Bristol, BS8 1SS. Email: rich.harris@bris.ac.uk Abstract This short paper links 2 areas of big data science in the context of GIScience: inferential analysis and visualisation. It discusses ideas around integration and analysis of large, spatial referenced datasets and considers how results of these can best be visualised. It advocates a critical approach to big data visualization and warns of the inherent dangers of simply identifying patterns, whether through data mining, modeling or visualization. It adds to ongoing debates by suggesting techniques and rubrics, possibly even hinting at a manifesto. 1. Introduction There is an increasing amount of data of all kinds available to scientists that provide opportunities to gain novel insights about all kinds of phenomena. The availability of these data is being driven by 2 factors. 1) The large amount of open data and wider recognition of the value that can be added to that data (Molloy, 2011) by linking it to other data and by developing novel data analyses; 2) The many new forms of data generated every day by citizens, either passively or actively (See et al., 2016) on GPS- and web-enabled tablets, devices has resulted in an explosion of citizen contributed, crowdsourced or volunteered data. Much has been written about the characteristics of these very large datasets: from the 3 or 5 or is it 7Vs? to the 3Ds (Dynamic, Diverse, Dense to which Dirty should be added), and perhaps more interestingly, their existence has stimulated a number of theoretical and practical considerations. This ranges from the need to revisit classic measures of and tools for statistical inference (Brunsdon, in press) to the need to redesign some of the more commonly used software tools to handle the data volumes. The role of GIScience relates to location, which may be precise in the form of latitude and longitude or approximate for example using a small census area reference or a post-code. However, despite being in this age of so called ‘Big Data’ the real challenge is to identify and answer ‘Big Questions’ which so far the research community, including the GIScience community, has failed to do. 2. Large quantities of spatially referenced data There are large quantities of spatially referenced data of many different types, describing many different phenomena. This provides opportunities for new forms of knowledge. A typical data-mining / computer science approach is encapsulated by the following quote: ‘Scouring databases and other data stores for insight is often compared to the proverbial search for a needle in a haystack, but … big data turns that idea on its head’ and quoting Viktor Mayer-Schonberger ‘With big data, we don’t know what the needle is. We can let the data speak and use it to generate really intriguing questions’ 1 .GIScience offers suites of http://data-informed.com/big-datas-value-much-larger-than-specific-business-questions/