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The concept of scale is inherent to, and consequential for, the modeling of geographical processes. However, scale also causes huge problems because the results of many types of spatial analysis appear to be dependent on the scale of the units for which data are reported (measurement scale). Consequently, when the same spatial models are calibrated at different scales of aggregations, the results are often vastly different (the well-known Modifiable Areal Unit Problem or MAUP). With the advent of local models and the fundamental difference in their scale of application compared to global models, this issue is further exacerbated in unexpected ways. For example, a global model and local model calibrated using data measured at the same aggregation scale can also result in different and sometimes contradictory inferences (the classic Simpson's Paradox). Here we provide a geographical perspective on why and how contrasting inferences might result from the calibration of a local and global model using the same data. Further, we examine the viability of such an occurrence using a synthetic experiment and two empirical examples. Finally, we discuss how such a perspective might inform the analyst’s conundrum: when the respective inferences run counter to one another, do we believe the local or global model results?

Scale is a central concept in the geographical sciences and is an intrinsic property of many spatial systems. It also serves as an essential thread in the fabric of many other physical and social sciences, which has contributed to the use of different terminology for similar manifestations of what we refer to as ‘scale’, leading to a surprising amount of diversity around this fundamental concept and its various ‘multiscale’ extensions. To address this, we review common abstractions about spatial scale and how they are employed in quantitative research. We also explore areas where the conceptualizations of multiple spatial scales can be differentiated. This is achieved by first bridging terminology and concepts, and then conducting a scoping review of the topic. A typology for spatial scale is discussed that can be used to categorize its multifarious meanings and measures. This typology is then used to distinguish what we term ‘process scale,’ from other types of spatial scale and to highlight current trends in uncovering aspects of process scale. We end with suggestions on how to further build knowledge regarding spatial processes through the lens of spatial scale.

The concept of scale is inherent to, and consequential for, the modeling of geographical processes. However, scale also causes huge problems because the results of many types of spatial analysis appear to be dependent on the scale of the units for which data are reported (measurement scale). With the advent of local models and the fundamental difference in their scale of application compared to global models, this issue is exacerbated in unexpected ways. For example, a global model and local model calibrated using data measured at the same aggregation scale can also result in different and sometimes contradictory inferences (the classic Simpson’s Paradox). Here we provide a geographical perspective on why and how contrasting inferences might result from the calibration of a local and global model using the same data. Further, we examine the viability of such an occurrence using a synthetic experiment and two empirical examples. Finally, we discuss how such a perspective might inform the analyst’s conundrum: when the respective inferences run counter to one another, do we believe the local or global model results?

Studies of spatially varying parameter estimates obtained in the calibration of various types of local statistical models are commonplace. The variation in such estimates is typically explained in terms of spatially varying processes. This paper highlights that an alternative explanation for spatially varying parameter estimates, in terms of non-linearity, should be examined prior to relating such variation to spatially varying processes. This can be achieved by a simple screening procedure which is described and demonstrated and which can easily be applied to the results of any local model. The problem is highlighted, and the solution demonstrated, with a set of simulated data and then with a real-world data set. The paper also highlights the obverse situation whereby the inappropriate application of a GAM produces spurious nonlinear results when the real relationships are linear but spatially varying.

We discuss the nature of processes relating to human behaviour and how to model such processes when they vary over space. In so doing, we describe the role of local modelling and how the bandwidth ...

This article attempts to identify and separate the role of spatial “context” in shaping voter preferences from the role of other socioeconomic determinants. It does this by calibrating a multiscale...

This introduction provides a brief review of the motivation, background, and context of the Forum. It explains the roles of the six papers in the Forum and the importance of reproducibility and rep...

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 ...

Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion such as the Akaike Information Criterion (AIC) and then parameter estimation and inference are conditional on the choice of this bandwidth. In this paper, we find that bandwidth selection is subject to uncertainty in both single-scale and multi-scale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights, and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty.

This study evaluates the influences of air pollution in China using a recently proposed model—multi-scale geographically weighted regression (MGWR). First, we review previous research on the determinants of air quality. Then, we explain the MGWR model, together with two global models: ordinary least squares (OLS) and OLS containing a spatial lag variable (OLSL) and a commonly used local model: geographically weighted regression (GWR). To detect and account for any variation of the spatial autocorrelation of air pollution over space, we construct two extra local models which we call GWR with lagged dependent variable (GWRL) and MGWR with lagged dependent variable (MGWRL) by including the lagged form of the dependent variable in the GWR model and the MGWR model, respectively. The performances of these six models are comprehensively examined and the MGWR and MGWRL models outperform the two global models as well as the GWR and GWRL models. MGWRL is the most accurate model in terms of replicating the observed air quality index (AQI) values and removing residual dependency. The superiority of the MGWR framework over the GWR framework is demonstrated—GWR can only produce a single optimized bandwidth, while MGWR provides covariate-specific optimized bandwidths which indicate the different spatial scales that different processes operate.

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 centr...

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.

Scotland has an organised colorectal cancer screening programme; however, despite proactively offering screening opportunities free to the at-risk population, and also despite using a screening test which may be completed at home, screening participation levels are unequal. Understanding causal pathways linking participation with other population characteristics may be aided by identifying how relationships between the two patterns vary across different localities, and such knowledge may also inform decisions regarding geographical targeting of screening promotion efforts. In this analysis, models calibrated using multiscale geographically weighted regression enabled the assessment of spatial variations of determinants of screening participation levels. The models were calibrated for localities across west central Scotland (n=409), where participation levels were relatively low, using aggregated individual-level screening records within a two-year window (2009-2011). Area deprivation was found to have a strong negative impact on participation levels across the study area, and ethnic population concentration had a significant impact on male participation levels on localities within Glasgow city. Estimates of local intercepts pointed to a systemic difference in screening participation between the two health board regions in the study area. Overall the results suggest that work to increase screening participation was necessary. They also suggest that barriers to participation could be addressed locally, and that differences between health board regions required further investigation.

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.

Recent work in local spatial modeling has affirmed and broadened interest in multivariate local spatial analysis. Two broad approaches have emerged: Geographically Weighted Regression (GWR) which follows a frequentist perspective and Bayesian Spatially Varying Coefficients models. Although several comparisons between the two approaches exist, recent developments, particularly in GWR, mean that these are incomplete and missing some important axes of comparison. Consequently, there is a need for a more thorough comparison of the two families of local estimators, including recent developments in multiscale variants and their relative performance under controlled conditions. We find that while both types of local models generally perform similarly on a series of criteria, some interesting and important differences exist.

Scale is a fundamental geographic concept, and a substantial literature exists discussing the various roles that scale plays in different geographical contexts. Relatively little work exists, though, that provides a means of measuring the geographic scale over which different processes operate. Here we demonstrate how geographically weighted regression (GWR) can be adapted to provide such measures. GWR explores the potential spatial nonstationarity of relationships and provides a measure of the spatial scale at which processes operate through the determination of an optimal bandwidth. Classical GWR assumes that all of the processes being modeled operate at the same spatial scale, however. The work here relaxes this assumption by allowing different processes to operate at different spatial scales. This is achieved by deriving an optimal bandwidth vector in which each element indicates the spatial scale at which a particular process takes place. This new version of GWR is termed multiscale geographically we...

This research investigates both spatial and temporal elements of the apartment pricing process in Seoul, South Korea by modeling the determinants of apartment prices over a ten-year period from 2006 to 2015 with a hedonic price model containing a spatio-temporal lag model calibrated by geographically weighted regression (GWR). The results yield information on both spatial and temporal variations in the processes affecting apartment prices and demonstrate the use of GWR for generating local spatial dependency measures which are conditioned on various covariates rather than being simple descriptions of pattern. The study utilizes a combined approach to account for both spatial dependency in housing prices and spatial heterogeneity in the processes generating those prices. The results suggest that there are spatial variations in the determinants of apartment prices and that these spatial variations are fairly consistent over time. The effect of the spatial lag on house prices exhibits strong spatial variation which again is reasonably consistent over time.

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data-generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well-understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.

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 prohibitive on moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to 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 MGWR 2.0 software, both of which are freely available to download.

Obesity rates are recognized to be at epidemic levels in the United States, posing significant threats to both the health and financial security of the nation. The causes of obesity can vary but are often complex and multifactorial, and while many contributors can be targeted for interventions, an understanding of where these interventions are needed is necessary in order to implement effective policy. This has prompted an interest in incorporating geographic context into the analysis and modeling of obesity determinants, especially through the use of geographically weighted regression (GWR). This paper provides a critical review of previous GWR models of obesogenic processes and then presents a novel application of multiscale (M)GWR using the Phoenix metropolitan area as a case study. The results show that a mix of global and local processes are able to best model obesity rates in Phoenix and that MGWR is superior to both GWR and ordinary least squares. Best practices for building and interpreting MGWR models are suggested and policy formation strategies are recommended.

AIMS: To investigate spatial congruence between ecological niches and genotype in two allopatric species of desert tortoise that are species of conservation concern. LOCATION: Mojave and Sonoran Desert ecoregions; California, Nevada, Arizona, Utah, USA. METHODS: We compare ecological niches of Gopherus agassizii and Gopherus morafkai using species distribution modelling (SDM) and then calibrate a pooled‐taxa distribution model to explore local differences in species–environment relationships based on the spatial residuals of the pooled‐taxa model. We use multiscale geographically weighted regression (MGWR) applied to those residuals to estimate local species–environment relationships that can vary across the landscape. We identify multivariate clusters in these local species–environment relationships and compare them against models of (a) a geographically based taxonomic designation for two sister species and (b) an environmental ecoregion designation, with respect to their ability to predict a genotype association index for these two species. RESULTS: We find non‐identical niches for these species, with differences that span physiographic and vegetation niche dimensions. We find evidence for two distinct clusters of local species–environment relationships that when mapped, predict an index of genotype association for the two sister taxa better than did either the geographically based taxonomic designation or an environmental ecoregion designation. MAIN CONCLUSIONS: Exploring local species–environment relationships by coupling SDM and MGWR can benefit studies of biogeography and conservation. We find that niche separation in habitat selection conforms to genotypic differences between sister taxa of tortoise in a recent secondary contact zone. This result may inform decision making by agencies with regulatory or land management authority for the two sister taxa addressed here.

The majority of work in mortality modeling involves factor-based approaches, with little use of information on the determinants and interpretable risk factors of mortality. At the same time, in the demographic community, there has been a lack of research attention towards the study of mortality from a spatial perspective. This work is a step towards addressing this, by providing an investigation of the presence of spatial variability in the determinants of mortality rates. Specifically, by using the age-adjusted mortality rates of the counties of the contiguous United States, this research applies a multiscale geographically weighted regression (MGWR) approach to examine the spatial variations in the relationships between mortality rates and a diverse group of associated determinants. The results of this study demonstrate that the MGWR approach produces an interpretable and accurate account of the global, regional and local effects acting on the mortality rates of the United States. Thus, this work lays the groundwork for the consideration of spatial varying effects on mortality rates which operate at different spatial scales.

Geographically weighted regression (GWR) extends the familiar regression framework by estimating a set of parameters for any number of locations within a study area, rather than producing a single parameter estimate for each relationship specified in the model. Recent literature has suggested that GWR is highly susceptible to the effects of multicollinearity between explanatory variables and has proposed a series of local measures of multicollinearity as an indicator of potential problems. In this paper, we employ a controlled simulation to demonstrate that GWR is in fact very robust to the effects of multicollinearity. Consequently, the contention that GWR is highly susceptible to multicollinearity issues needs rethinking.

One of the key concerns in spatial analysis and modeling is to study and analyze the processes that generate our observations of the real world. The typical global models employed to do this, however, fail to identify spatial variations in these processes because they assume that the processes being investigated are spatially stationary. In many real-life situations, spatial variations in relationships seem plausible and at least worth examining so that the assumption of global stationarity is, at best, unhelpful and, at worst, unrealistic. In contrast, local spatial models allow for potential variations in relationships over space leading to greater insights into the data-generating processes. In this study, a framework for localizing spatial interaction models, based on geographically weighted techniques, is developed. Using the framework, we construct a family of spatially weighted interaction models (SWIM) that can help in detecting, visualizing, and analyzing spatial nonstationarity in spatial intera...

Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated dataset with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.

This article describes the problem of multiple testing within a Geographically Weighted Regression framework and presents a possible solution to the problem which is based on a family-wise error rate for dependent processes. We compare the solution presented here to other solutions such as the Bonferroni correction and the Byrne, Charlton, and Fotheringham proposal which is based on the Benjamini and Hochberg False Discovery Rate. We conclude that our proposed correction is superior to others and that generally some correction in the conventional t-test is necessary to avoid false positives in GWR.

The real estate market has long provided an active application area for spatial–temporal modeling and analysis and it is well known that house prices tend to be not only spatially but also temporally correlated. In the spatial dimension, nearby properties tend to have similar values because they share similar characteristics, but house prices tend to vary over space due to differences in these characteristics. In the temporal dimension, current house prices tend to be based on property values from previous years and in the spatial–temporal dimension, the properties on which current prices are based tend to be in close spatial proximity. To date, however, most research on house prices has adopted either a spatial perspective or a temporal one; relatively little effort has been devoted to situations where both spatial and temporal effects coexist. Using ten years of house price data in Fife, Scotland (2003–2012), this research applies a mixed model approach, semiparametric geographically weighted regression...

Both space and time are fundamental in human activities as well as in various physical processes. Spatiotemporal analysis and modeling has long been a major concern of geographical information science (GIScience), environmental science, hydrology, epidemiology, and other research areas. Although the importance of incorporating the temporal dimension into spatial analysis and modeling has been well recognized, challenges still exist given the complexity of spatiotemporal models. Of particular interest in this article is the spatiotemporal modeling of local nonstationary processes. Specifically, an extension of geographically weighted regression (GWR), geographical and temporal weighted regression (GTWR), is developed in order to account for local effects in both space and time. An efficient model calibration approach is proposed for this statistical technique. Using a 19-year set of house price data in London from 1980 to 1998, empirical results from the application of GTWR to hedonic house price modeling demonstrate the effectiveness of the proposed method and its superiority to the traditional GWR approach, highlighting the importance of temporally explicit spatial modeling.

Hedonic price modelling has long been a powerful tool to estimate house prices in the real estate market. Increasingly, traditional global hedonic price models that largely ignore spatial effects are being superseded by models that deal with spatial dependency and spatial heterogeneity. In addition, many novel methods integrating spatial economics, statistics and geographical information science (GIScience) have been developed recently to incorporate temporal effects into hedonic house price modelling. Here, a local spatial modelling technique, geographically weighted regression (GWR), which accounts for spatial heterogeneity in housing utility functions is applied to a 19-year set of house price data in London (1980–1998) in order to explore spatiotemporal variations in the determinants of house prices. Further, based on the local parameter estimates derived from GWR, a new method integrating GWR and time series (TS) forecasting techniques, GWR–TS, is proposed to predict future local parameters and thus future house prices. The results obtained from GWR demonstrate variations in local parameter estimates over both space and time. The forecasted future values of local estimates as well as house prices indicate that the proposed GWR–TS method is a useful addition to hedonic price modelling.

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.

Traditional methods of counting bicyclists are resource-intensive and generate data with sparse spatial and temporal detail. Previous research suggests big data from crowdsourced fitness apps offer a new source of bicycling data with high spatial and temporal resolution. However, crowdsourced bicycling data are biased as they oversample recreational riders. Our goals are to quantify geographical variables, which can help in correcting bias in crowdsourced, data and to develop a generalized method to correct bias in big crowdsourced data on bicycle ridership in different settings in order to generate maps for cities representative of all bicyclists at a street-level spatial resolution. We used street-level ridership data for 2016 from a crowdsourced fitness app (Strava), geographical covariate data, and official counts from 44 locations across Maricopa County, Arizona, USA (training data), and 60 locations from the city of Tempe, within Maricopa (test data). First, we quantified the relationship between Strava and official ridership data volumes. Second, we used a multi-step approach with variable selection using LASSO followed by Poisson regression to integrate geographical covariates, Strava, and training data to correct bias. Finally, we predicted bias-corrected average annual daily bicyclist counts for Tempe and evaluated the model&rsquo, s accuracy using the test data. We found a correlation between the annual ridership data from Strava and official counts (R2 = 0.76) in Maricopa County for 2016. The significant variables for correcting bias were: The proportion of white population, median household income, traffic speed, distance to residential areas, and distance to green spaces. The model could correct bias in crowdsourced data from Strava in Tempe with 86% of road segments being predicted within a margin of &plusmn, 100 average annual bicyclists. Our results indicate that it is possible to map ridership for cities at the street-level by correcting bias in crowdsourced bicycle ridership data, with access to adequate data from official count programs and geographical covariates at a comparable spatial and temporal resolution.

Cross-border studies have recently received increasing attention in many disciplines, stimulated by globalisation, international trade and migration. In this paper, we take the analysis of the determinants of educational attainment on both sides of the international border between Northern Ireland and the Republic of Ireland to demonstrate how the impacts of the changing areal units and extent on social processes can be examined through spatial statistical analysis. A statistical model is constructed to relate the proportion of people with a post-secondary degree in a small area to a series of socio-economic characteristics of that area. We utilise both a traditional ‘global’ regression model and the local technique of Geographically Weighted Regression (GWR). Both models are calibrated on various cross-border data sets. The results also highlight the multi-scalar effects of the Modifiable Areal Unit Problem (MAUP) which are partially relevant in cross-border statistical analysis. They also demonstrate the potential of GWR to highlight cross-border differences in social processes.

GIScience 2016 Short Paper Proceedings A Closer Examination of Spatial-Filter-Based Local Models Taylor Oshan, A. Stewart Fotheringham Arizona State University, Tempe, Arizona 85281 Email: {toshan; stewart.fotheringham}@asu.edu Abstract Local modeling is a spatial analysis technique that explores spatial non-stationarity in data- generating processes. Geographically weighted regression (GWR) is one method that has been widely applied across domains, which has helped uncover local spatial relationships and gener- ally increases model goodness-of-fit. Despite this, some have criticized GWR for being extra susceptible to issues such as multicollinearity and spatial autocorrelation. Spatial-filtering- based local regression (SFLR) has been suggested as a solution. While SFLR is claimed to be approximately equivalent to GWR, it is also touted as superior. Therefore, it is of interest to compare the output from these two techniques. We do this by examining how well both techniques replicate the known coefficient values derived by simulating data that is represen- tative of spatially varying processes. The results indicate that the original SFLR specification is prone to overfitting, while an alternative specification that minimizes the mean square error produces coefficients similar to GWR. Introduction and Background Non-stationarity in data-generating processes goes largely undetected in traditional global models. Hence, local models, which explicitly allow regression coefficients to vary over space, are necessary to capture such heterogenous processes. One local modeling technique that has become particularly popular is geographically weighted regression (GWR) (Fotheringham et al. 2002). Despite its usefulness, GWR has been critiqued as being highly susceptible to multicollinearity (Wheeler & Tiefelsdorf 2005), whereby multicollinearity amongst explana- tory variables causes intolerable levels of correlation amongst GWR coefficients. However, results show that when the sample size is large, GWR is robust to even remarkably high levels of multicollinearity (Paez et al. 2011; Fotheringham & Oshan Submitted). Still, the work of Wheeler and Tiefelsdorf (Wheeler & Tiefelsdorf 2005) sparked much subsequent critiques of GWR. Specifically, spatial-filter-based local regression (SFLR) has been suggested as a supe- rior alternative to GWR (Griffith 2008). While Griffith (2008) posits that SFLR and GWR are approximately equivalent, he also points out that local coefficients produced from GWR and SFLR are minimally correlated, suggesting that the two models are producing much different results, thereby implying a contradiction within the SFLR method. To the knowledge of the authors, the SFLR method has not been applied outside its original conception (Griffith 2008), while GWR has produced agreeable results in many studies. Therefore, the primarily goal of this paper is to employ simulated data in order to test which of the techniques can more reliably estimate the true coefficients of non-stationary processes. Some modifications of the SFLR routine are investigated and several issues of the SFLR framework are highlighted. A basic GWR model may be specified as p y i = b i0 + Â b ik x ik + e i , k=1 i = 1, ..., n

The Irish famine of the 1840s had a dramatic effect both on the population within Ireland and the populations of countries such as the US, the UK and Australia, which received the bulk of the Irish diaspora resulting from the famine (Kenny 2003). As such, the effects of the famine have been examined extensively across a range of disciplines. It is therefore a challenge to provide any new perspective on this well-researched area. However, this paper provides novel insights into the spatial effects of the famine on population in two ways. Firstly, we present the most spatially detailed data recorded to date on population change in the period 1841–51 covering the famine. We are able to do this by, for the first time, linking census data from 1851 (which also records 1841 population) to the boundaries of 3436 Electoral Divisions (EDs) to provide a very detailed description of the uneven nature of population change during the famine decade. Secondly, by collecting data at the same spatial scale for over 100 other variables, we are able to analyse the relationship between population change during this decade and various demographic, locational and land use characteristics of EDs. We do this through not only traditional regression but also by geographically weighted regression (GWR), which allows us to investigate possible spatial variations in the determinants of population change during the famine period. The results of this analysis raise a series of intriguing new questions relating to the effect of the Irish famine on population change and point the way to further detailed historical and geographical research on this important topic. The research also demonstrates the use of GIS and spatial analytical techniques in historical geography as a means of uncovering new questions that can be answered by further qualitative research.

For administration efficiency most countries subdivide their national territory into administrative regions. These regions are used to delineate areas which are internally well connected and relatively cohesive, especially compared with the links between regions. Hence, many countries seek to delineate local labour markets (LLMs): geographical regions where the majority of the local population seeks employment and from which the majority of local employers recruit labour. LLM boundaries are often based on functional regions, which represent the aggregate commuting patterns of the local population. A number of regionalisation procedures for objectivity delineating functional regions have been suggested, though many of these procedures require the use of ad hoc parameters to control the size and number of regions. Recently, a range of network-based alternatives have been developed in the literature. One of the most successful such methods is based on the concept of modularity: the extent to which there are dense connections within functional regions, but only sparse connections between functional regions. In this paper we maximise the modularity of a network of commuting flows to produce a regionalisation that exhibits less interaction than expected between regions. We demonstrate the effectiveness of this type of regionalisation procedure on a simulated geographical network, as well as using commuting data for the Republic of Ireland. We suggest that this new method has specific advantages over existing regionalisation procedures, particularly in the context of disaggregate commuting patterns of socioeconomic subgroups.

Terrestrial laser scanning (TLS) data-sets are seeing increasing use in geology, geomorphology, forestry and urban mapping. The ease of use, affordability and operational flexibility of TLS suggest that demand for it is likely to increase in large-scale mapping studies. However, its advantages may remain restricted to specific environments, because of difficulties in defining bare-ground level in the presence of ground-level vegetation. This paper seeks to clarify the component contributions to TLS elevation error deriving from vegetation occlusion, scan co-registration error, point cloud georeferencing error and target position definition in TLS point cloud data. A multi-scan single-returns TLS point cloud data-set of very high resolution (∼250 points/m2) was acquired for an 11 hectare area of open, substantially flat and 100% vegetated coastal saltmarsh, providing data for the empirical quantification of TLS error. Errors deriving from the sources discussed are quantified, clarifying the potential proportional contribution of vegetation to other error sources. Initial data validation is applied to the TLS point cloud data after application of a local-lowest-point selection process, and repeat validation tests are applied to the resulting filtered point cloud after application of a kriging-based error adjustment and data fusion with GPS. The final results highlight the problem of representing bare ground effectively within TLS data captured in the presence of dense ground vegetation and clarify the component contributions of elevation error deriving from surveying and data processing. Resume Les donnees TLS (laser terrestre a balayage) se voient de plus en plus utilisees en geologie, geomorphologie, ingenierie forestiere et cartographie urbaine. La facilite d’utilisation, la disponibilite et la flexibilite operationnelle du TLS laissent a penser que cette methode va etre de plus en plus demandee pour des etudes cartographiques a grande echelle. Cependant, ses avantages peuvent etre limites a des environnements particuliers, en raison de difficultes liees a la definition du niveau du sol en presence de vegetation. Cet article vise a montrer dans quelle mesure les occlusions dues a la vegetation, les erreurs de recalage relatif et de georeferencement des nuages de points et la definition des positions des cibles, contribuent a l’erreur altimetrique du TLS. Un nuage de points a tres haute resolution (environ 250 points/m2) issu de plusieurs balayages a ete acquis sur un marais cotier de 11 hectares, ouvert et relativement plat, fournissant des donnees pour la quantification empirique de l’erreur du TLS. Les erreur dues aux differentes sources considerees ont ete quantifiees, ce qui permet de clarifier la contribution relative de la vegetation par rapport aux autres sources d’erreurs. Le nuage de points TLS fait l’objet d’une premiere validation apres application d’un processus de selection du point localement le plus bas, et des tests de validation recurrents sont appliques au nuage de point filtre apres application d’un ajustement d’erreur par krigeage et d’une fusion avec les donnees GPS. Les resultats obtenus mettent en evidence la difficulte d’obtenir effectivement le sol a partir de donnees acquises en presence de vegetation dense et permettent de preciser la contribution relative de l’acquisition et du traitement des donnees a l’erreur altimetrique obtenue. Zusammenfassung Terrestrische Laserscanner (TLS) werden zunehmend in Geologie, Geomorphologie, Forstwirtschaft und Stadtplanung genutzt. Die einfache Anwendung, die Erschwinglichkeit und operationelle Flexibilitat von TLS lasst erwarten, dass der Bedarf an dieser Technologie fur grosmasstabige Kartierung weiter zunimmt. Allerdings besteht fur bestimmte Anwendungen das Problem, bei Bodenbewuchs die Gelandeoberflache zu definieren. Dieser Beitrag beschaftigt sich mit der Klarung des Einflusses verschiedener Fehlerkomponenten auf die TLS Hohenbestimmung. Dazu gehoren: der Einfluss der Verdeckung durch Vegetation, die Registrierfehler, Fehler in der Georeferenzierung der Punktwolke und Definition der Position von Referenzmarken in TLS Punktwolken. Zur empirischen Bestimmung der Fehler wurden ein TLS Punktwolkendatensatz mit sehr hoher Auflosung (∼250 Punkte/m2) uber ein 11 ha groses, offenes, nahezu flaches und 100% bewachsenes Kustenmarschgebiet erfasst. Die oben beschriebenen Fehlerkomponenten werden quantifiziert und der Einfluss der Vegetation bestimmt. Ein Datenvalidierung der TLS Punktwolke erfolgt zunachst nach einem lokalen Auswahlprozess des niedrigsten Punktes. Weitere Validierungsschritte folgen fur die gefilterte Punktwolke nach einer Fehlerausgleichung (Kriging) und einer Datenfusion mit GPS. Die Endergebnisse stellen die Probleme der effektiven Modellierung der Gelandeoberflache aus TLS Daten bei dichter Bodenvegetation heraus und klaren die einzelnen Anteile am Hohenfehler aus Erfassung und Datenprozessierung. Resumen Los datos obtenidos mediante escaner laser terrestre (ELT) estan teniendo una aplicacion creciente en geologia, geomorfologia, explotacion forestal y cartografia urbana. La facilidad de uso, la economia y flexibilidad operativa del ELT apuntan a que su demanda se incrementara en las aplicaciones a escalas grandes. Sin embargo sus ventajas pueden quedar restringidas a entornos especificos por la dificultad para definir el nivel del terreno raso en presencia de vegetacion superficial. Este articulo busca identificar la contribucion especifica de los distintos componentes al error de elevacion del ELT debida a la oclusion de la vegetacion, al error de corregistro del escaner, al error de georreferenciacion de la nube de puntos y a la definicion de la posicion de blancos en el conjunto de datos de la nube de puntos obtenida mediante un ELT. Se obtuvo una nube de puntos de retornos simples mediante escaneado multiple de muy alta resolucion (∼250 puntos/m2) de una marisma salina costera practicamente plana de 11 ha de superficie casi toda cubierta de vegetacion, cuyos datos permiten determinar de forma empirica el error del ELT. Se cuantificaron los errores causados por las fuentes citadas, lo que permite aclarar la contribucion proporcional potencial de la vegetacion respecto de otras fuentes de error. La validacion inicial de los datos se aplica a la nube de datos del ELT tras un proceso de seleccion del punto local mas bajo, y se realizaron repetidos tests de validacion a las nubes de puntos filtradas resultantes de la aplicacion de un ajuste de error basado en kriging y la fusion con datos GPS. Los resultados finales destacan la dificultad de representar de forma efectiva el terreno desnudo presente en los datos del ELT obtenidos en presencia de vegetacion densa, asi como aclarar la contribucion de los componentes del error de elevacion debidos al trabajo de campo y procesado de datos.

Ireland has a dramatic and unusual population history, with overall population declining dramatically from 8.2 million to 6.5 million between 1841 and 1851 and then declining gradually and almost continuously to 4.5 million in 1961. However, most attempts to understand long-term population change in Ireland have been made at a national scale. Those that have examined the uneven spatial imprint of long-term population change have tended to do so at crude spatial scales. In an attempt to redress this issue, Irish population change data for 160 years of Irish population history have been assembled in an interactive online atlas through which population change at a consistent set of 3432 electoral divisions (EDs) combining Irish and Northern Irish data can be examined. This article focuses on a description of the atlas paying attention to the manner in which data were collected and assembled; the use of the atlas as a resource that encourages and facilitates greater public engagement with the spatiality of po...

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.