Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.

A recent addition to the suite of techniques for local statistical modeling is the implementation of the multiscale geographically weighted regression (MGWR), a multiscale extension to geographically weighted regression (GWR). Using a back-fitting algorithm, MGWR relaxes the restrictive assumption in GWR that all processes being modeled operate at the same spatial scale and allows the estimation of a unique indicator of scale, the bandwidth, for each process. However, the current MGWR framework is limited to use with continuous data making it unsuitable for modeling data that do not typically exhibit a Gaussian distribution. This study expands the application of the MGWR framework to scenarios involving discrete response outcomes (count data following a Poisson’s distribution). Use of this new MGWR Poisson regression (MGWPR) model is demonstrated with a simulated data set and then with COVID-19 case counts within New York City at the zip code level. The results from the simulated data underscore the superiority of the MGWPR model in effectively capturing spatial processes that influence count data patterns, particularly those operating across diverse spatial scales. For empirical data, the results reveal significant spatial variations in relationships between socio-ecological factors and COVID-19 cases – variations often missed by traditional ‘global’ models.

Models designed to capture spatially varying processes are now employed extensively in the social and environmental sciences. The main strength of such models is their ability to represent relationships that vary across locations through locally varying parameter estimates. However, local models of spatial processes also provide information on the nature of these spatially varying relationships through the estimation of a ‘bandwidth’ parameter. This paper examines bandwidth at a conceptual, operational and empirical level within the framework of geographically weighted regression, one of the more frequently employed local spatial models. We outline how bandwidth relates to three characteristics of spatial processes: variation, dependence and strength.

The measurement of spatial dependence within a set of observations or the residuals from a regression is one of the most common operations within spatial analysis. However, there appears to be a lack of appreciation for the fact that these measurements are generally based on an a priori definition of a spatial weights matrix and hence are limited to detecting spatial dependence at a single spatial scale. This paper highlights the scale-dependence problem with current measures of spatial dependence and defines a new, multi-scale approach to defining a spatial weights matrix based on a discrete Fourier transform. This approach is shown to be able to detect statistically significant spatial dependence which other multi-scale approaches to measuring spatial dependence cannot. The paper thus serves as a warning not to rely on traditional measures of spatial dependence and offers a more comprehensive, and scale-free, approach to measuring such dependence.

A cornerstone of the scientific method, the ability to reproduce and replicate the results of research has gained widespread attention across the sciences in recent years. A corresponding burst of energy into how to make research more reproducible and replicable has led to numerous innovations. This article outlines some of the opportunities for geospatial researchers to contribute to and learn from the broader reproducibility literature. We review practices developed in related disciplines to improve the reproducibility and replicability of research and outline current efforts to adapt those practices to geospatial analyses. The article then highlights the open questions, opportunities, and potential new directions in geospatial research related to R&R. We stress that the path ahead will likely require a mixture of computational, geospatial, and behavioral research that collectively addresses the many sides of reproducibility and replicability issues.

Geographically Weighted Regression (GWR) has been broadly used in various fields to model spatially non-stationary relationships. Multi-scale Geographically Weighted Regression (MGWR) is a recent advancement to the classic GWR model. MGWR is superior in capturing multi-scale processes over the traditional single-scale GWR model by using different bandwidths for each covariate. However, the multiscale property of MGWR brings additional computation costs. The calibration process of MGWR involves iterative back-fitting under the additive model (AM) framework. Currently, MGWR can only be applied on small datasets within a tolerable time and is prohibitively time-consuming to run with moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to the MGWR calibration. This improved computational method reduces both memory footprint and runtime to allow MGWR modelling to be applied to moderate-to-large datasets (up to 100,000 observations). These improvements are integrated into the mgwr python package and the MGWR 2.0 software, both of which are freely available to download.

Geographically Weighted Regression (GWR) is a widely used tool for exploring spatial heterogeneity of processes over geographic space. GWR computes location-specific parameter estimates, which makes its calibration process computationally intensive. The maximum number of data points that can be handled by current open-source GWR software is approximately 15,000 observations on a standard desktop. In the era of big data, this places a severe limitation on the use of GWR. To overcome this limitation, we propose a highly scalable, open-source FastGWR implementation based on Python and the Message Passing Interface (MPI) that scales to the order of millions of observations. FastGWR optimizes memory usage along with parallelization to boost performance significantly. To illustrate the performance of FastGWR, a hedonic house price model is calibrated on approximately 1.3 million single-family residential properties from a Zillow dataset for the city of Los Angeles, which is the first effort to apply GWR to a dataset of this size. The results show that FastGWR scales linearly as the number of cores within the High-Performance Computing (HPC) environment increases. It also outperforms currently available open-sourced GWR software packages with drastic speed reductions – up to thousands of times faster – on a standard desktop.

A recent paper in this journal proposed a form of geographically weighted regression (GWR) that is termed parameter-specific distance metric geographically weighted regression (PSDM GWR). The central focus of the PSDM generalization of the GWR framework is that it allows the kernel function that weights nearby data to be specified with a distinct distance metric. As with the recent paper on Multiscale GWR (MGWR), the PSDM framework presents a form of GWR that also allows for parameter-specific bandwidths to be computed. As a result, a secondary focus of the PSDM GWR framework is to reduce the computational overhead associated with searching a massive parameter space to find a set of optimal parameter-specific bandwidths and parameter-specific distance metrics. In this comment, we discuss several concerns with the PSDM GWR framework in terms of model interpretability, complexity, and computational efficiency. We also recommend some best practices when using these models, suggest how to more holistically assess model variations, and set out an agenda to constructively focus future research endeavors.

Human mobility is important for understanding the evolution of size and structure of urban areas, the spatial distribution of facilities, and the provision of transportation services. Until recently, exploring human mobility in detail was challenging because data collection methods consisted of cumbersome manual travel surveys, space-time diaries, or interviews. The development of location-aware sensors has significantly altered the possibilities for acquiring detailed data on human movements. Although this has spurred many methodological developments in identifying human movement patterns, many of these methods operate solely from the analytical perspective and ignore the environmental context within which the movement takes place. In this paper we attempt to widen this view and present an integrated approach to the analysis of human mobility using a combination of volunteered GPS trajectories and contextual spatial information. We propose a new framework for the identification of dynamic (travel modes) and static (significant places) behaviour using trajectory segmentation, data mining, and spatio-temporal analysis. We are interested in examining if and how travel modes depend on the residential location, age, or gender of the tracked individuals. Further, we explore theorised ‘third places’, which are spaces beyond main locations (home/work) where individuals spend time to socialise. Can these places be identified from GPS traces? We evaluate our framework using a collection of trajectories from 205 volunteers linked to contextual spatial information on the types of places visited and the transport routes they use. The result of this study is a contextually enriched data set that supports new possibilities for modelling human movement behaviour.

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.

Digital elevation model (DEM) elevation accuracy and spatial resolution are typically considered before a given DEM is used for the assessment of coastal flooding, sea-level rise or erosion risk. However, limitations of DEMs arising from their original data source can often be overlooked during DEM selection. Global elevation error statistics provided by DEM data suppliers can provide a useful indicator of actual DEM error, but these statistics can understate elevation errors occurring outside of idealised ground reference areas. The characteristic limitations of a range of DEM sources that may be used for the assessment of coastal inundation and erosion risk are tested using high-resolution photogrammetric, low- and medium-resolution global positioning system (GPS)-derived and very high-resolution terrestrial laser scanning point data sets. Errors detected in a high-resolution photogrammetric DEM are found to be substantially beyond quoted error, demonstrating the degree to which quoted DEM accuracy can understate local DEM error and highlighting the extent to which spatial resolution can fail to provide a reliable indicator of DEM accuracy. Superior accuracies and inundation prediction results are achieved based on much lower-resolution GPS points confirming conclusions drawn in the case of the photogrammetric DEM data. This suggests a scope for the use of GPS-derived DEMs in preference to the photogrammetric DEM data in large-scale risk-mapping studies. DEM accuracies and superior representation of micro-topography achieved using high-resolution terrestrial laser scan data confirm its advantages for the prediction of subtle inundation and erosion risk. However, the requirement for data fusion of GPS to remove ground-vegetation error highlighted limitations for the use of side-scan laser scan data in densely vegetated areas.

GIS elemental unit representations of spatial data are often defined in terms of points, lines and areas. However, another type of spatial data that is becoming frequently captured, but as yet is largely ignored in GIS, is that of video. While digital video recording is a commonly encountered medium in modern society and encompasses many forms, from simple personal camcorders through to sophisticated survey and surveillance systems, its geographical representation in a GIS has not been fully examined or realised. In the majority of cases the video footage is usually captured while the device and/or the objects being viewed are in motion. What is of particular interest is when video streams can be, or have been, associated with spatial data such as location and orientation to create geographically referenced videographic data, which, for simplicity, will be defined as spatial video. Fundamentally, the nature of video is to record space, so when spatial properties can be accurately acquired and associated with this footage, an important geographical element can be considered for integration and analysis within a GIS. Existing spatial video systems, both commercial and research, are predominantly used in survey or LBS roles and are usually bespoke and application specific. These systems do not model spatial video to any recognised standards that is generalised to be both data and platform independent. They do not support GIS integration and/or analysis from a purely spatial content perspective. A video-image/remote-sensing centric approach prevails where usage options range from simple visualisation interfaces to interactive computer vision systems. What has been largely overlooked is a spatial approach where the inherent geographical extent recorded in each video frame can be modelled and used in a geo-spatial analysis context. While this modelling approach has not been fully realised, it does exist in a GIS form based on Open Geospatial Consortium standards, where the spatial context of video is defined in a structure called a ViewCone. However, a ViewCone only defines a 2D model of the geographical extent of each frame and is restricted to a three-or-five sided polygon representation. Thus, this article examines the potential of modelling spatial video through the use of elemental data types within GIS; gives some examples of using this approach; describes some problems in using spatial video within GIS; and then demonstrates how these problems are being solved. This is done in three stages: Firstly, a detailed overview of spatial video in its current GIS role is provided – this is achieved through a complete introduction to the distinct elements of spatial video followed by a review of its use in both commercial and academic application areas. Secondly, a brief theoretical overview of an alternative GIS-constrained ViewCone data structure is given that defines a more flexible spatial video model for both 2D and 3D GIS analysis and visualisation. Thirdly, a selective sample of results is presented based on an implementation of this approach being applied to a constrained spatial video data source in a specific study area.

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.

Increasingly, methods of spatial analysis are being integrated within geographical information systems. As this integration occurs, it is important to ensure that, (i) users of GIS recognize the limitations of spatial analysis, (ii) researchers continue to work on removing the existing impediments to accurate spatial analysis, and (iii) developers of GIS consider these limitations. In this article we discuss eight general impediments that arise in spatial analyses that span a diverse range of substantive applications. Geographical information systems offer not only the opportunity to integrate various methods of spatial analysis, but also the chance to learn more about the underlying impediments.