This paper proposes a novel spatially varying coefficient (SVC) regression through a Geographical Gaussian Process GAM (GGP-GAM): a Generalized Additive Model (GAM) with Gaussian Process (GP) splines parameterised at observation locations.A GGP-GAM was applied to multiple simulated coefficient datasets exhibiting varying degrees of spatial heterogeneity and out-performed the SVC brand-leader, Multiscale Geographically Weighted Regression (MGWR), under a range of fit metrics.Both were then applied to a Brexit case study and compared, with MGWR marginally out-performing GGP-GAM.The theoretical frameworks and implementation of both approaches are discussed: GWR models calibrate multiple models whereas GAMs provide a full single model; GAMs can automatically penalise local collinearity; GWR-based approaches are computationally more demanding; MGWR is still only for Gaussian responses; MGWR bandwidths are intuitive indicators of spatial heterogeneity.GGP-GAM calibration and tuning are also discussed and areas of future work are identified, including the creation of a user-friendly package to support model creation and coefficient mapping, and to facilitate ease of comparison with alternate SVC models.A final observation that GGP-GAMs have the potential to overcome some of the long-standing reservations about GWRbased regression methods and to elevate the perception of SVCs amongst the broader community.

In this article, we respond to ‘A comment on geographically weighted regression with parameter-specific distance metrics’ by Oshan et al. (2019), published in this journal, where several concerns on the parameter-specific distance metric geographically weighted regression (PSDM GWR) technique are raised. In doing so, we review the developmental timeline of the multiscale geographically weighed regression modelling framework with related and equivalent models, including flexible bandwidth GWR, conditional GWR and PSDM GWR. In our response, we have tried to answer all the concerns raised in terms of applicability, veracity, interpretability and computational efficiency of the PSDM GWR model.

Geographically weighted regression (GWR) is an important local technique to model spatially varying relationships. A single distance metric (Euclidean or non-Euclidean) is generally used to calibrate a standard GWR model. However, variations in spatial relationships within a GWR model might also vary in intensity with respect to location and direction. This assertion has led to extensions of the standard GWR model to mixed (or semiparametric)GWR and to flexible bandwidth GWR models. In this article, we present a strongly related extension in fitting a GWR model with parameter-specific distance metrics (PSDM GWR). As with mixed and flexible bandwidth GWR models, a back-fitting algorithm is used for the calibration of the PSDM GWR model. The value of this new GWR model is demonstrated using a London house price data set as a case study. The results indicate that the PSDM GWR model can clearly improve the model calibration in terms of both goodness of fit and prediction accuracy, in contrast to the model fits when only one metric is singly used. Moreover, the PSDM GWR model provides added value in understanding how a regression model’s relationships may vary at different spatial scales, according to the bandwidths and distance metrics selected. PSDM GWR deals with spatial heterogeneities in data relationships in a general way, although questions remain on its model diagnostics, distance metric specification, and computational efficiency, providing options for further research.

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.

When conducting research within a framework of Geographic Information Science (GISc), the scientific validity of this work can be argued as highly dependent upon the extent to which the methods employed are reproducible, and that, in the strictest sense, can only be fully achieved by implementing transparent workflows that utilize both open source software and openly available data. After considering the scientific implications of non-reproducible methods, we provide a review of both open source Geographic Information Systems (GIS) and openly available data, before describing an integrated model for Open GISc. We conclude with a critical review of this embryonic paradigm, with directions for future development in supporting spatial data infrastructure.

A first glance at the title of this book might suggest it to be very specialised. Indeed this perhaps reflects my own expectations before opening it. However, once I start reading it I first realis...

In this study, we demonstrate a novel use of comaps to explore spatially the performance, specification and parameterisation of a non-stationary geostatistical predictor. The comap allows the spatial investigation of the relationship between two geographically referenced variables via conditional distributions. Rather than investigating bivariate relationships in the study data, we use comaps to investigate bivariate relationships in the key outputs of a spatial predictor. In particular, we calibrate moving window kriging (MWK) models, where a local variogram is found at every target location. This predictor has often proved worthy for processes that are heterogeneous, and most standard (global variogram) kriging algorithms can be adapted in this manner. We show that the use of comaps enables a better understanding of our chosen MWK models, which in turn allows a more informed choice when selecting one MWK specification over another. As case studies, we apply four variants of MWK to two heterogeneous example data sets: (i) freshwater acidification critical load data for Great Britain and (ii) London house price data. As both of these data sets are strewn with local anomalies, three of our chosen models are robust (and novel) extensions of MWK, where at least one of which is shown to perform better than a non-robust counterpart.

This article describes the development and application of a modified grouping genetic algorithm (GGA) used to identify sets of optimal ambulance locations. The GGA was modified to consider a special case with only two groups, and the reproduction and mutation schemes were modified to operate more efficiently. It was applied to a case study locating ambulances from a fixed set of alternative locations. The sites were evaluated using data of emergency medical services (EMS) calls summarised over census areas and weighted by network distance. Census areas serviced by the same selected location defined ambulance catchments. The results indicated alternative sites for ambulances to be located, with average EMS response times improved by 1 min 14 s, and showed the impacts of having different numbers of ambulances in current locations and in new locations. The algorithmic developments associated with the modified GGA and the advantages of using census areas as spatial units to summarise data are discussed.

Principal components analysis (PCA) is a widely used technique in the social and physical sciences. However in spatial applications, standard PCA is frequently applied without any adaptation that accounts for important spatial effects. Such a naive application can be problematic as such effects often provide a more complete understanding of a given process. In this respect, standard PCA can be (a) replaced with a geographically weighted PCA (GWPCA), when we want to account for a certain spatial heterogeneity; (b) adapted to account for spatial autocorrelation in the spatial process; or (c) adapted with a specification that represents a mixture of both (a) and (b). In this article, we focus on implementation issues concerning the calibration, testing, interpretation and visualisation of the location-specific principal components from GWPCA. Here we initially consider the basics of (global) principal components, then consider the development of a locally weighted PCA (for the exploration of local subsets in attribute-space) and finally GWPCA. As an illustration of the use of GWPCA (with respect to the implementation issues we investigate), we apply this technique to a study of social structure in Greater Dublin, Ireland.

Dilution of precision (DOP) is a fundamental concept in satellite navigation and surveying. A deeper understanding of this concept can be achieved through the means of 3D immersive visualisation. In this article, we present a method for visualising and exploring the spatial variation of DOP and discuss its presentation within an immersive virtual environment. The work demonstrates a real-time simulation of global positioning system (GPS) satellite geometry, modelled and visualised within a virtual representation of the university campus. The number of satellites visible to the receiver is modelled in real time as a user walks through the university campus. During this process, the changing satellite geometry is visualised in both 3D and aerial views. Various DOP values update to the screen against a pseudo-realistic building backdrop as the user travels. Both the aerial views and the changing volumes of the tetrahedra drawn in 3D provide an effective way of interpreting why exceptionally large or small horizontal DOP and vertical DOP values can occur in an urban context. Because the factors affecting DOPs are inherently 3D, communicating the spatial uncertainty of global positioning system coordinates within an immersive stereo environment has been viewed as a particularly powerful communication tool by both undergraduate and postgraduate students studying GI Science.

This paper describes an automated method for predicting the number of satellites visible to a GPS receiver, at any point on the Earth's surface at any time. Intervisibility analysis between a GPS receiver and each potentially visible GPS satellite is performed using a number of different surface models and satellite orbit calculations. The developed software can work with various ephemeris data, and will compute satellite visibility in real time. Real‐time satellite availability prediction is very useful for mobile applications such as in‐car navigation systems, personal navigations systems and LBS. The implementation of the method is described and the results are reported.

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.

Statistical inference is important for all those who engage in the analysis of spatial data. The issue is becoming increasingly important given the explosion in the availability of spatial data and the proliferation of Geographic Information Systems (GIS) across different academic disciplines and application areas. The aim of this paper is to provide a brief overview of some of the concepts and controversies inherent in statistical inference in the hope of raising the level of awareness within the geographic information science community that different points of view exist when it comes to inference. We argue that the concept of statistical inference in spatial data analysis and spatial modelling is perhaps broader than many GIS users imagine. In particular, we argue that different types of inference exist and that process inference is just as valid as sample inference, even though the latter appears to dominate the GIS literature.

Simulated vector coastlines of known and varied complexity are rasterized at various levels by the quadtree method. The rasterizing error for each combination of coastline and raster size is calculated by a simple Boolean overlay method. The relationship between line complexity, raster size and rasterizing error is investigated and a method of selecting the most appropriate raster size based on the complexity of the source data and the required level of accuracy is presented.

This article is an agreed summary of a workshop held in Sheffield between 18-20 March 1991. The focus here is on three of the themes of the workshop: the mutual benefits of closer links between geographical information systems (GIS) and the methods of spatial data analysis (SDA); the specific areas of SDA that should be linked with GIS; how the linkage should be made in practice. Directions for future research are also reviewed. The emphasis throughout is on statistical SDA and principally from the perspective of human rather than physical geography.