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The Modifiable Aerial Unit Problem (MAUP) influences the interpretation of spatial data in that forms of spatial aggregation creates scale and segmentation ecological fallacies. This paper explores the extent to which similar scalar and segmentation issues affect the analysis of temporal data. The analogy of gerrymandering in spatial data, which is the purposeful segmentation of space such that the underlying aggregations prove a specific point, is used to demonstrate segmentation and aggregation effects on time series data. To do so, the paper evaluates real-time sound monitoring data for Dublin, Ireland at multiple aggregation scales and segmentations to determine their effects with respect to compliance with European Union regulations concerning acceptable decibel levels. Like the MAUP, increasing scales of temporal aggregation remove extremes at more local scales, which has the effect of reducing measurements of non-compliance. Similarly, and unlike the spatial equivalent, because of circadian human social patterns, segmentation of temporal measurements also has a predictable, and gerrymander-able, effect on the measurement of compliance with ambient sound limits. The effect is computed as the Temporal Aggregation Bias and strategies which could justify gerrymandering of sound monitoring data are presented.

There is growing evidence that psychological characteristics are spatially clustered across geographic regions and that regionally aggregated psychological characteristics are related to important outcomes. However, much of the evidence comes from research that relied on methods that are theoretically ill-suited for working with spatial data. The validity and generalizability of this work are thus unclear. Here we address two main challenges of working with spatial data (i.e., modifiable areal unit problem and spatial dependencies) and evaluate data-analysis techniques designed to tackle those challenges. To illustrate these issues, we investigate the robustness of regional Big Five personality differences and their correlates within the United States (Study 1; N = 3,387,303) and Germany (Study 2; N = 110,029). First, we display regional personality differences using a spatial smoothing approach. Second, we account for the modifiable areal unit problem by examining the correlates of regional personality scores across multiple spatial levels. Third, we account for spatial dependencies using spatial regression models. Our results suggest that regional psychological differences are robust and can reliably be studied across countries and spatial levels. The results also show that ignoring the methodological challenges of spatial data can have serious consequences for research concerned with regional psychological differences.

Understanding the relationships between commuting demand and built environment (BE) features is advantageous in alleviating travel pressure during the commuting period. Numerous works have explored these relationships under either a single spatial unit or travel modes. However, few efforts have attempted to examine how variations in both spatial units and transport modes affect the relationships. To address the above issues, we investigate the impact of the modifiable areal unit problem (MAUP) on the modeling results across three partitioning schemes (i.e., hexagonal-based, square-based, and administrative boundary) and nine spatial units under four commuting modes (i.e., taxi, bike-sharing, ride-hailing, and bus). A geographically weighted regression is applied to estimate commuting demands considering spatial autocorrelation and heterogeneity. The experiment is conducted using smart card data and vehicle GPS trajectories collected in Shenzhen City, China. The contributions of this study include the following three parts. First, it evaluates the pros and cons of different spatial units for commuting demand modeling. Second, it summarizes the effects of the MAUP on relationships among land use, demographic, and traffic network characteristics and commuting demand according to the partitioning scale and schemes. Third, it examines the similarities and differences in the effect of the MAUP on commuting demand modeling among four travel modes. The findings of this study contribute to the division of traffic analysis zones and the allocation of commuting trips.

This paper investigates how important measurement issues such as the modifiable areal unit problem (MAUP), random unevenness and spatial autocorrelation affect cross-sectional studies of ethnic segregation. We use geocoded data for German cities to investigate the impact of these measurement problems on the average level of segregation and on the ranking of cities. The findings on the average level of residential segregation turn out to be rather robust. The ranking of cities is, however, sensitive to the assumptions regarding reallocation of population across neighbourhoods that the use of different segregation measures involves. Moreover, the results suggest that standard aspatial approaches tend to underrate the degree of segregation because they ignore the spatial clustering of ethnic groups. In contrast, non-consideration of random unevenness gives rise to a moderate upward bias of the mean segregation level and involves minor changes in the ranking of cities if the minority group is large. However, the importance of random segregation significantly increases as the size of the minority group declines. If the size of specific ethnic groups differs across regions, this may also affect the ranking of regions. Thus, the necessity to properly account for measurement issues increases as segregation analyses become more detailed and consider specific (small) minority groups.

Urban segregation is a widespread phenomenon with profound social implications, and one that presents difficult measurement challenges. Segregation indexes may be affected by scale or zoning biases of the modifiable areal unit problem (MAUP). In this article, we develop a methodology that relies on spatial clustering algorithms to simultaneously cope with both kinds of MAUP biases, and we test it with complete census data for most Chilean cities. We find a robust correlation between segregation and city size, contesting previous claims about the spuriousness of this relationship. We also show that socioeconomic polarization is a widespread phenomenon in Chile and that it is not just a problem of disadvantaged groups’ concentration. Based on these results, we suggest that area-based desegregation policies should be generally reinforced, and complemented in big Chilean cities with housing-mix policies. We argue that using spatially unbiased segregation indexes could improve comparative urban studies.

To assess spatial heterogeneity in geographic data, geographically weighted regression (GWR) has been widely used. This study used an advanced version of GWR, multiscale geographically weighted regression (MGWR), which provides a unique extension that allows each predictor to be associated with a distinct bandwidth in predicting traffic fatalities in Texas. Traffic data from fatality analysis reporting system (FARS) between 2010 and 2015, aggregated at the census tract level (N = 5265), were used to examine different scales at which selected economic variables explain the traffic road fatality rate per 100,000 population. Twelve economic variables were initially selected and reduced to four factors (ride-sharing to work, driving alone, mean travel time to work, and work commuting) using the varimax rotation technique. The spatial pattern of the four factors in the GWR model differs significantly from MGWR in spatial patterns, signs, and values relative to the traffic fatality rate. The diagnostic results showed that traditional GWR over fitted the predictors compared to MGWR (max. condition number in GWR = 28.3 versus MGWR = 9.6; adjusted R2 GWR = 61.8% versus MGWR = 44.5%). The application of the MGWR technique is a robust technique in ensuring the correct process scale or bandwidth in modeling spatial data such as road traffic fatality for place and scale-specific intervention purposes. We discussed the three levels of scale identified in the MGWR model for traffic planning intervention and policymaking. Lastly, we concluded with how MGWR mitigates the common problem of aggregated data such as MAUP.

Spatial data brings an important dimension to AI’s quest for algorithmic transparency. For example, data driven computer-aided policy-decisions use measures of segregation (e.g., dissimilarity index) or income-inequality (e.g., Gini index), and these measures are affected by space partitioning choice. This may lead policymakers to underestimate the level of inequality or segregation within a region. The problem stems from the fact that many segregation based analyses use aggregated census data but do not report result sensitivity to choice of spatial partitioning (e.g., census block, tract). Beyond the well-known Modifiable Areal Unit Problem, this paper shows (via mathematical proofs as well as case studies with census data and census based synthetic micro-population data) that values of many measures (e.g., Gini index, dissimilarity index) diminish monotonically with increasing spatial-unit size in a hierarchical space partitioning (e.g., block, block-group, tract), however the ranking based on spatially aggregated measures remain sensitive to the scale of spatial partitions (e.g., block, block group). This paper highlights the need for social scientists to report how rankings of inequality are affected by the choice of spatial partitions.

The importance of spatial data science and Geo-AI is growing with the rise of spatial and spatiotemporal big data (e.g., trajectories, remote-sensing images, census and geo-social media) [1-2]. Societal use cases include Agriculture (global crop monitoring, precision agriculture), Location-based services (e.g., navigation, ride-sharing), Public Health (e.g., monitoring disease spread), Environment and Climate (change detection, land-cover classification), Smart Cities (e.g., mapping buildings), etc. [1-2] Classical data science and AI (e.g., machine learning) often perform poorly when applied to spatial data sets because of the many reasons [1-5]. First, spatial data is embedded in a continuous space and classical statistics (e.g., correlation) are not robust to the modifiable areal unit problem. Second, spatial data-items have extended footprints (e.g., line strings, polygons) and implicit relationships (e.g., distance, touch). Third, high cost of spurious patterns requires guardrails (e.g., statistical significance tests) to reduce false positives. Furthermore, spatial autocorrelation and variability violate the classical assumption of data samples being generated independently from identical distributions, which risk models that are either inaccurate or inconsistent with the data. Thus, new methods are needed to analyze spatial data [1-5]. This talk surveys common and emerging methods for spatial classification and prediction (e.g., spatial autoregression, spatial decision trees [6], spatial variability aware neural networks [7]), as well as techniques for discovering interesting, useful and non-trivial patterns such as hotspots (e.g., circular, linear, arbitrary shapes [8]), interactions (e.g., co-locations [9], tele-connections), spatial outliers [10], and their spatio-temporal counterparts [3].

The classical travel demand modelling overlooks an important factor normally found in the interest variables: spatial autocorrelation. Recent research recognises and includes this characteristic in travel demand forecasting, but there are limitations regarding the basic aggregation spatial units used in the approaches, for example, the modifiable areal unit problem, error variance, and high randomness. In order to overcome these problems, the present study relied on spatial dependence between boarding and alighting observations, per bus stop, and loading on sections, along a public transport line, to calculate estimates of these variables in stops and sections that would not be sampled during the passenger boarding and alighting survey. This estimation was made by applying ordinary kriging with Euclidean distances to two bus lines in the city of Sao Paulo, Brazil. Afterwards, this method was compared to the estimates obtained using network distances along the same bus lines. The results, from cross-validation, showed a considerable adjustment of the estimated values to those observed for both types of distances. Thus, this article presents two main contributions. The first one is related to applying geostatistics to public transport demand data, which overcomes constraints found in previous studies. The last one is a practical contribution, considering the support to public transport planning provided by the kriging continuous surface of estimated values, since it covers points that lacks the observed boarding, alighting, and loading information. This last contribution is also related to possible resource savings of boarding/alighting survey, especially in cities where automatic counters are not available.

Introduction: The Need for Spatial Statistics, D.A. Griffith Components of Geographic Information and Analysis Background: The Importance of Locational Information Background: Statistical Estimator Properties Organization of the Book Summary References Visualization of Spatial Dependence: An Elementary View of Spatial Autocorrelation, I.R. Vasiliev Editorial Note Introduction The Spatial Mean and Other Basic Concepts Spatial Autocorrelation Map Complexity Map Representations of Changes in Space and Time Summary: Rules-of-Thumb for Spatial Autocorrelation References Spatial Sampling, S.V. Stehman and W.S. Overton Introduction Spatial Universes and Populations Sampling Fundamentals Sampling a Continuous Universe Sampling Spatially Distributed Objects via Areal Samples of the Continuous Universe Inference in Spatial Sampling Applications of Spatial Sampling Empirical Evaluation of Sampling Strategies Summary References Some Guidelines for Specifying the Geopraphic Weights Matrix Contained in Spatial Statistical Models, D.A. Griffith Introduction Background Evaluation Criteria Rules-of-Thumb Implications References Aggregation Effects in Geo-Referenced Data, D.W.S. Wong Spatial Dependency of Spatial Data Analysis Source of the MAUP: Spatial Dependence and the Averaging Process General Impacts of the MAUP on Spatial Data Approaches to "Solving" the MAUP Guidelines for Analyzing Data From Different Scales Conclusions References Implementing Spatial Statistics on Parallel Computers, B. Li Introduction A Brief Introduction to Parallel Processing Software Models for Parallel Processing Parallel Implementations Performance Summary References Appendix I: Test Statistics for Spatial Autocorrelation Coefficients Appendix II: Source Code Spatial Statistics and GIS Applied to Internal Migration in Rwanda, Central Africa, D.G. Brown Introduction Study Area Database Description GIS Data Management Traditional Regression Analysis Mapping Residuals Spatial Statistical Model Conclusions References Spatial Statistical Modeling of Regional Fertility Rates: A Case Study of He-Nan Province, China, H.M. Feng Introduction Preliminary Considerations of the Spatial Statistical Application The Dataset and the Model Specification Explicit Variables A Classical Linear Regression Model of Explicit Variables In Search of a Spatial Pattern Interpretation and Conclusions References Appendix I: Description of Data Set Appendix II: Maps Appendix III: Scatter-Plots Spatial Statistical/Econometric Versions of Simple Urban Population Density Models, D.A. Griffith and A. Can Introduction and Background The Selected Metropolitan Landscapes Preliminaries for Estimating the Autoregressive Model The Estimated Population Density Models Implementation Findings References Spatial Statistics for Analysis of Variance of Agronomic Field Trials, D.S. Long The Example Data Set Goals of the Case Study The Autoregressive Response Model Calculating the Moran Coefficient Calculating the Necessary Eigenvalues Estimating the Jacobian Term Estimating an Autoregressive Response Model Comparison of AR-based ANOVA and Conventional ANOVA Conclusions Acknowledgments References Index

Several recent studies have explored the association between environmental factors, such as temperature, humidity, and air pollution, and the severity of the COVID-19 outbreak by analyzing the statistical association at the district level. However, we argue that the modifiable areal unit problem (MAUP) arises when aggregating disease and environmental data into districts, leading to bias in such studies. Therefore, in this study, we analyzed the association between environmental factors and the number of COVID-19 death cases under different aggregation strategies to illustrate the presence of MAUP. We used real-world COVID-19 outbreak data from the Hubei and Henan Provinces and studied their association with atmospheric NO2 levels. By fitting linear regression models with penalized splines on NO2, we found that the association between COVID-19 mortality and NO2 varies when data were aggregated (1) at the city level, (2) under two different aggregation strategies, and (3) at the provincial level, indicating the presence of MAUP. Therefore, this study reminds researchers of the presence of MAUP and the necessity to minimize this problem while exploring the environmental determinants of the COVID-19 outbreak., Graphical abstract Unlabelled Image, Highlights • Modifiable areal unit problem (MAUP) arises when aggregating data into districts, leading to statistical bias. • Real data of atmospheric NO2 and COVID-19 outbreak in China is analyzed to illustrate the presence of MAUP. • Atmospheric NO2 is found to have different directions of association with COVID-19 mortality under different data aggregation strategies.

Background The modifiable areal unit problem (MAUP) arises when the support size of a spatial variable affects the relationship between prevalence and environmental risk factors. Its effect on schistosomiasis modelling studies could lead to unreliable parameter estimates. The present research aims to quantify MAUP effects on environmental drivers of Schistosoma japonicum infection by (i) bringing all covariates to the same spatial support, (ii) estimating individual-level regression parameters at 30 m, 90 m, 250 m, 500 m and 1 km spatial supports, and (iii) quantifying the differences between parameter estimates using five models. Methods We modelled the prevalence of Schistosoma japonicum using sub-provinces health outcome data and pixel-level environmental data. We estimated and compared regression coefficients from convolution models using Bayesian statistics. Results Increasing the spatial support to 500 m gradually increased the parameter estimates and their associated uncertainties. Abrupt changes in the parameter estimates occur at 1 km spatial support, resulting in loss of significance of almost all the covariates. No significant differences were found between the predicted values and their uncertainties from the five models. We provide suggestions to define an appropriate spatial data structure for modelling that gives more reliable parameter estimates and a clear relationship between risk factors and the disease. Conclusions Inclusion of quantified MAUP effects was important in this study on schistosomiasis. This will support helminth control programmes by providing reliable parameter estimates at the same spatial support and suggesting the use of an adequate spatial data structure, to generate reliable maps that could guide efficient mass drug administration campaigns.

This paper reflects on a number of trends towards a more open and reproducible approach to geographic and spatial data science over recent years. In particular it considers trends towards Big Data, and the impacts this is having on spatial data analysis and modelling. It identifies a turn in academia towards coding as a core analytic tool, and away from proprietary software tools offering 'black boxes' where the internal workings of the analysis are not revealed. It is argued that this closed form software is problematic, and considers a number of ways in which issues identified in spatial data analysis (such as the MAUP) could be overlooked when working with closed tools, leading to problems of interpretation and possibly inappropriate actions and policies based on these. In addition, this paper and considers the role that reproducible and open spatial science may play in such an approach, taking into account the issues raised. It highlights the dangers of failing to account for the geographical properties of data, now that all data are spatial (they are collected somewhere), the problems of a desire for n=all observations in data science and it identifies the need for a critical approach. This is one in which openness, transparency, sharing and reproducibility provide a mantra for defensible and robust spatial data science., Comment: 19 pages, 1 figure

The objective of this paper is to investigate uncertainties surrounding relationships between spatial autocorrelation (SA) and the modifiable areal unit problem (MAUP) with an extensive simulation ...

We estimate the cultural heritage amenity impact on the residential real estate market of Lisbon, Portugal, paying particular attention to heterogeneity of types and capturing spatial dependencies through a spatial error model. Our heritage amenities include conservation areas, listed historic buildings, and designated heritage which includes churches, palaces, historic buildings and lithic structures. We construct gridded spatial fixed effects which mitigate biases from the modifiable areal unit problem, and further employ a geographic regression discontinuity ensuring the robustness of results. The analysis is complemented with spatial interactions and mixed geographically weighted regressions (MGWR) to explore spatial heterogeneity of impacts. Conservation areas yield 4.1% premiums with spillover benefits of 3.3%, while proximity to designated heritage has a positive price elasticity of 0.0075. This impact is equivalent to an additional designated heritage within 100 m. Ten additional listed buildings within 500 m on the other hand yield 0.5% premiums. We find spatial variation in heritage amenity impacts with MGWR and spatial interactions highlighting common patterns whereby positive price impacts are strongest for the closest properties, and the biggest for landmark amenities. We compare these two manners to evaluate spatial non-stationarity of impacts and highlight the benefits of high-level GIS techniques which are commonly lacking in hedonic studies with urban spatial data.

Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis.

BackgroundAccurate disease mapping based on spatiotemporal data is an important aspect of public health surveillance, targeting interventions, and health service planning. This is achieved by public health surveillance organisations around the world through the construction of choropleth maps based on single spatiotemporal aggregations of finer resolution data. However, such maps are undermined by their dependence on the spatiotemporal units used. This dependence is described by the related modifiable areal and temporal unit problems (MAUP; MTUP), also known as change of support problems (COSPs). AimTo accurately map disease. MethodsUsing ischaemic stroke admissions and mental health-related ED presentations in metropolitan Perth between 2013 and 2016 as exemplars, we present a novel zonation overlay approach for disease mapping. This method involves aggregating fine resolution spatial data numerous times instead of just once, using the automated zonation construction software AZTool. Results Through implementing the zonation overlay method in combination with a rolling window of time, both the MAUP and the MTUP may be overcome in the context of disease mapping. Furthermore, the AZTool zonations act as a geographical encryption key, allowing fine resolution, precise maps to be constructed while protecting the privacy of individuals. ConclusionHealth surveillance organisations continue to produce single aggregation choropleth maps of disease, without acknowledging their limitations except in rare cases. Producing such maps and suggesting they should guide policy makers, while being aware of but not acknowledging the impact of COSPs, could be described as scientific malfeasance. However, assuming that most researchers producing such maps are not intending to mislead, we must conclude that COSPs are poorly understood and their impact underestimated. The zonation overlay method we describe can help alleviate the consequences of this continued practice.

The introduction of apartheid in 1948 resulted in racial residential segregation that has influenced the spatial distribution of the population in South Africa. Apartheid laws, which were mainly based on race, brought about the exclusion of the non-white population from urban areas and the mainstream economy of South Africa, as well as the benefits that come with it. In the early 1990’s, apartheid was abolished and the South African government set to bring about social and spatial justice, address inequalities and promote social cohesion. This also meant doing away with racial residential segregation that had been entrenched into the urban morphology of the country. Despite this, in the post-apartheid era, racial-residential segregation still exists (Parry and Van Eeden 2015).Figure 1 shows the density (kernel) distribution of each of the four population groups in Gauteng in 2011: Indian/Asian (IA), white (W), black African (BA) and coloured (C). It is a reflection of the legacy of apartheid town planning which isolated non-whites to the peripheral areas of urban economic centers. Densely populated areas are coloured in red while less populated areas are coloured in green. As it can be seen in the map (Figure 1), the white population group densely occupies areas close to the business centers of the province in places such as Pretoria and northern parts of Johannesburg, while non-whites densely occupy peripheral areas in former townships designated to non-whites, such as Soweto (black African), Mabopane (black African) and Lenasia (Indian/Asians). This observed pattern is more pronounced for black Africans.To study the pattern of racial residential segregation in South Africa, non-spatial indices of segregation are widely employed despite their shortcomings. Parry and Van Eeden (2015) are among the few authors who have acknowledged the importance of employing spatial indices of segregation, even though they did not explicitly use one due to the lack of ready to use GIS software. Massey and Denton (1988) define residential segregation as “the degree to which two or more groups live separately from one another, in different parts of the urban environment”, i.e. racial residential segregation manifests itself across space. Hence, in order to assess the extent to which the levels of racial residential segregation have subsided, adequate empirical studies that employ spatial segregation indices on socio-economic data are necessary. The purpose of this research is to study the pattern of racial residential segregation by employing a spatial index of segregation namely the ‘spatial information theory index (H)’ for Gauteng province, the economic hub and most populated province of South Africa.Some of the shortcomings of existing non-spatial indices of segregation (and also of some of the spatial ones) include the Modifiable Areal Unit Problem (MAUP) which refers to how such indices are sensitive to the size of the areal units (i.e. administrative or political boundaries) of analysis that might be arbitrarily chosen or might not accurately reflect the actual racial composition of the local neighbourhoods. This introduces possibilities of obtaining inaccurate measures of racial residential segregation and also being unable to compare the results at various scales of analysis (Reardon et al. 2004; Weir-Smith 2016). One of the major challenges that impedes the use of spatial segregation indices is the lack of ready to use software that has implemented spatial segregation indices which have attempted to address the MAUP. To address such a challenge, Hong et al. 2014 implemented a series of spatial equivalences of existing segregation measures in R under the package ‘seg’ based on Reardon et al. (2004)’s formulation of spatial segregation indices. Reardon et al. (2004) emphasise the computation of spatial indices of segregation based on the racial composition of the population as reflected by their immediate local environment instead of relying on arbitrary or fixed administrative boundaries. The ‘spatial information theory index (H)’ as implemented by Reardon et al. (2004) is experimented in this study.This study explores existing literature related to racial residential segregation in order to further complement and supplement existing theories on segregation in South Africa by adopting a spatial analytical approach. The authors take advantage of the R implementation of spatial measures of segregation (Hong et al. 2014), namely the spatial information theory index (H), to study the patterns of residential segregation in Gauteng province (South Africa).

To measure the equity of urban park green space, spatial matching between service supply and user group demand should be taken into consideration. However, if the demographic data, with the administrative division as the basic unit, are directly applied to characterize the spatial distribution of a user group, it may introduce inevitable deviation into the evaluation results due to the low-resolution nature and modifiable areal unit problem of such data. Taking the central area of Wuhan as an example, the population data spatialization method based on land use modeling was used to build a geographically weighted regression (GWR) model of land cover type and demographic data, and the spatial distribution of the population of the 150 m grid was obtained by inversion. Then, the equity of park green space in Wuhan central city was evaluated by population spatial data and network accessibility. The results showed that (1) the range of park green space in the central urban area of Wuhan was within a walking distance of 15 min, accounting for 25.8% of the total study area and covering 54.2% of the population in the study area, (2) the equity of park green space in Hongshan District was the worst, (3) and the use of population spatial data can measure equity on a more precise scale.

Traffic safety analysis at the macroscopic level usually relies on previously defined areal traffic analysis zones (TAZs) that are used as the units of investigation. Hence, statistical inference is made on the basis of such units, implying that the consideration of a certain TAZ configuration may influence the results and conclusions achieved. Regarding this, the modifiable areal unit problem (MAUP) is a well-known issue in the field of spatial statistics, which refers to the effects that arise in statistical properties and estimations when there is a change in areal units of analysis. In this paper, the consequences of MAUP have been investigated through a dataset of traffic crashes that occurred in Valencia within the years 2014 and 2015 and two common statistical models: a conditional autoregressive model and a geographically weighted regression. In the absence of an established TAZ scheme for the city, four classes of basic spatial units (BSUs) were considered: census tracts, hexagonal units and two types with construction based on the structure of main roads and intersections of the city. Each of these BSU types was specified at different levels of spatial aggregation. The main research objective was to investigate the final effects that changes in BSU type and scale have on model parameter estimations, but also the specific alterations that MAUP causes to data in terms of the distributional characteristics of the response, multicollinearity among the covariates and covariates’ spatial autocorrelation. The results showed the presence and severity of MAUP for the dataset and area that were analysed. Although effects from scale variations were more moderate, changing the BSU type affected the results severely. The joint use of hexagonal units and a conditional autoregressive model achieved the best performance among all the possibilities explored, but the choice of a proper BSU unit should rely on more factors. Despite MAUP effects, educational centres showed a consistent (and negative) association with traffic crashes, a fact possibly related to their distribution across the whole city. Other covariates revealed a positive correlation with crash counts, but these findings were more uncertain given the discrepancies found at different scales and zonings.

In this review we examine the past 5 years of landscape ecology research examining the effects of both spatial and thematic resolution on ecological analysis. While spatial resolution has been a topic of research for many decades, scale effects from thematic resolution have only recently been studied. Recent multi-scale analyses have demonstrated that the effects of thematic resolution on ecological analysis are comparable to spatial resolution and both spatial and thematic resolution interact. Additionally, spatial and thematic resolution can impact on multi-scale methods that are commonly used to identify the intrinsic scale—the scale at which ecological phenomena interact with the environment. A key aim of multi-scale analysis in landscape ecology is to characterise the scale-dependency of ecological processes, however, the interdisciplinary nature of landscape ecology means that research on scale has incorporated methods from a range of disciplines. These methods and concepts include: 1) multi-scale methods which characterise the sensitivity of an analysis to the modifiable areal unit problem, 2) spatial statistics for characterising the scale dependency of landscape patterns and identifying the optimal scale and 3) ecological theory describing intrinsic scales/domains of scales. We conclude by drawing on the existing literature to describe potential future areas of research to address the impacts of spatial and thematic resolution. We suggest further research on the effects of thematic resolution and conceptualising the scale continuum as multi-dimensional. We also identify mechanistic models and spatial statistics as a promising direction for future research.

Areal crash modeling has gained increased attention in the past decade because of initiatives to incorporate safety performance–based decision making in transportation planning. Particularly in urban multimodal transportation systems, safety outcomes may be influenced by long-term planning decisions at the area and network levels. How multimodal facilities are layered and prioritized eventually affects conflicts that may result between modes, influencing expected crash frequencies and severities for various road user types. The emphasis on areal crash modeling has opened the door for various innovative statistical methods, applied to explain factors that contribute to crashes, as well as to address issues that arise in spatially aggregated count data. These issues include spatial autocorrelation, ecological fallacy, and the modifiable areal unit problem. Previous studies used generalized linear models with fixed and random effects to address these issues, while the Bayesian framework has become a dominant approach in areal crash analysis—particularly at the county level—in the past decade. This paper explores an alternative frequentist approach to areal crash modeling with generalized additive models with smooth functions across the location and compares these models to negative binomial and Bayesian hierarchical models. The results, based on data from Chicago, Illinois, show that generalized additive models can account for spatial autocorrelation in the data, particularly when autocorrelation is lower and more data are available to reduce the number of potentially omitted variables.

In the last few decades extreme heat events have led to substantial excess mortality, most dramatically in Central Europe in 2003, in Russia in 2010, and even in typically cool locations such as Vancouver, Canada, in 2009. Heat-related morbidity and mortality is expected to increase over the coming centuries as the result of climate-driven global increases in the severity and frequency of extreme heat events. Spatial information on heat exposure and population vulnerability may be combined to map the areas of highest risk and focus mitigation efforts there. However, a mismatch in spatial resolution between heat exposure and vulnerability data can cause spatial scale issues such as the Modifiable Areal Unit Problem (MAUP). We used a raster-based model to integrate heat exposure and vulnerability data in a multi-criteria decision analysis, and compared it to the traditional vector-based model. We then used the Getis-Ord G(i) index to generate spatially smoothed heat risk hotspot maps from fine to coarse spatial scales. The raster-based model allowed production of maps at spatial resolution, more description of local-scale heat risk variability, and identification of heat-risk areas not identified with the vector-based approach. Spatial smoothing with the Getis-Ord G(i) index produced heat risk hotspots from local to regional spatial scale. The approach is a framework for reducing spatial scale issues in future heat risk mapping, and for identifying heat risk hotspots at spatial scales ranging from the block-level to the municipality level.

Spatial analyses of crashes have been adopted in road safety for decades in order to determine how crashes are affected by neighboring locations, how the influence of parameters varies spatially and which locations warrant interventions more urgently. The aim of the present research is to critically review the existing literature on different spatial approaches through which researchers handle the dimension of space in its various aspects in their studies and analyses. Specifically, the use of different areal unit levels in spatial road safety studies is investigated, different modelling approaches are discussed, and the corresponding study design characteristics are summarized in respective tables including traffic, road environment and area parameters and spatial aggregation approaches. Developments in famous issues in spatial analysis such as the boundary problem, the modifiable areal unit problem and spatial proximity structures are also discussed. Studies focusing on spatially analyzing vulnerable road users are reviewed as well. Regarding spatial models, the application, advantages and disadvantages of various functional/econometric approaches, Bayesian models and machine learning methods are discussed. Based on the reviewed studies, present challenges and future research directions are determined.

This paper presents a new approach to deal with spatial inequalities in risk adjustment between health insurances. The shortcomings of non-spatial and spatial fixed effects in risk adjustment models are analysed and opposed against spatial kernel estimators. Theoretical and empirical evidence suggests that a reasonable choice of the spatial kernel could limit the spatial uncertainty of the modifiable area unit problem under heavy-tailed claims data, leading to more precise predictions and economically positive incentives on the healthcare market. A case study of the German risk adjustment shows a spatial risk spread of 86 Euro p.c., leading to incentives for spatial risk selection. The proposed estimator eliminates this issue and conserves incentives for services optimisation.

As Ecosystem Services (ES) are the products of complex socio-ecological systems, their mapping requires a deep understanding of the spatial relationships and pattern that underpin ES provision. Upscaling ES maps is often carried out to avoid mismatches between the scale of ES assessment and that of their level of management. However, so far only a few efforts have been made to quantify how information loss occurs as data are aggregated to coarser scales. In the present study this was analyzed for three distinct case studies in the eastern Alps by comparing ES maps of outdoor recreation at the municipality level and at finer scales, i.e. high-resolution grids. Specifically, we adopt an innovative and flexible methodology based on Exploratory Spatial Data Analysis (ESDA), to disentangle the problem of the scale from the perspective of different levels of jurisdiction, by assessing in an iterative process how ES patterns change when upscaling high-resolution maps. Furthermore, we assess the sensitivity to the modifiable areal unit problem (MAUP) by calculating global statistics over three grid displacements. Our results demonstrate that spatial clusters tend to disappear when their extent becomes smaller than the features to which values are upscaled, leading to substantial information loss. Moreover, cross-comparison among grids and the municipality level highlights local anomalies that global spatial autocorrelation indicators fail to detect, revealing hidden clusters and inconsistencies among multiple scales. We conclude that, whenever ES maps are aggregated to a coarser scale, our methodology represents a suitable and flexible approach to explore clustering trends, shape and position of upscaling units, through graphs and maps showing spatial autocorrelation statistics. This can be crucial to finding the best compromise among scale mismatches, information loss and statistical bias that can directly affect the targeted ES mapping.

This work presents a nonparametric statistical test, $S$-maup, to measure the sensitivity of a spatially intensive variable to the effects of the Modifiable Areal Unit Problem (MAUP). $S$-maup is the first statistic of its type and focuses on determining how much the distribution of the variable, at its highest level of spatial disaggregation, will change when it is spatially aggregated. Through a computational experiment, we obtain the basis for the design of the statistical test under the null hypothesis of non-sensitivity to MAUP. We performed a simulation study for approaching the empirical distribution of the statistical test, obtaining its critical values, and computing its power and size. The results indicate that the power of the statistic is good if the sample (number of areas) grows, and in general, the size decreases with increasing sample number. Finally, an empirical application is made using the Mincer equation in South Africa., Paper with 10 pages and 11 figures

Considerable research has been conducted to advance our understanding of how environmental factors influence people’s health behaviors (e.g., leisure-time physical inactivity) at the neighborhood level. However, different environmental factors may operate differently at different geographic locations. This study explores the inconsistent findings regarding the associations between environmental exposures and physical inactivity. To address spatial autocorrelation and explore the impact of spatial non-stationarity on research results which may lead to biased estimators, this study uses spatial regression models to examine the associations between leisure-time physical inactivity and different social and physical environmental factors for all counties in the conterminous U.S. By comparing the results with the conventional ordinary least squares regression and spatial lag model, the geographically weighted regression model adequately addresses the problem of spatial autocorrelation (Moran’s I of the residual = 0.0293) and highlights the spatial non-stationarity of the associations. The existence of spatial non-stationarity that leads to biased estimators, which were often ignored in past research, may be another reason for the inconsistent findings in previous studies besides the modifiable areal unit problem and the uncertain geographic context problem. Also, the observed associations between environmental variables and leisure-time physical inactivity are helpful for developing location-based policies and interventions to encourage people to undertake more physical activity.

Uncertainty is an attendant characteristic of all spatial data. Spatial data are complex, as are the phenomena and processes we use these data to represent, model, and understand. Although not exhaustive, this article reviews fundamental concepts related to spatial data uncertainty and methods the geospatial research communities have developed to understand and represent uncertainty. Addressing uncertainty is an ongoing creative exploration and challenge. Especially in the era of big geospatial data, spatial analyses and spatial datasets evolve with technological advances; therefore, new methods for studying uncertainty will be required. In the meantime, existing methods reviewed here should be more widely integrated into standard geospatial practice.

This study attempted to test the scale effect of MAUP, particularly focusing on the spatial autocorrelation of sex crime, correlations among neighborhood structural variables, and causal mechanism leading to sex crime. Analysis results of nation-wide Eup-Myon-Dong and Si-Gun-Gu data discovered that the spatial autocorrelation, correlations among independent variables, and determinant coefficient of multiple regression of Si-Gun-Gu level were generally bigger and stronger than those of Eup-Myon-Dong, which appeared to be due to the averaging effect. Regarding the causal effect to sex crime, two interesting results were found: First, the ratio of non-apartment residency lowered sex crime at both levels contrary to the hypothesis. Second, the ratio of food and lodging increased sex crime only at Eup-Myon-Dong level. These suggested that future research need to perform more detailed analyses dividing data into subsets such as urban vs. rural and/or economically advantaged vs. disadvantaged areas.

Socioeconomic and health analysts commonly rely on areally aggregated data, in part because government regulations on confidentiality prohibit data release at the individual level. Analytical results from areally aggregated data, however, are sensitive to the modifiable areal unit problem (MAUP). Levels of aggregation as well as the arbitrary and modifiable sizes, shapes, and arrangements of zones affect the validity and reliability of findings from analyses of areally aggregated data. MAUP, long acknowledged, remains unresolved. We present an exploratory spatial data analytical approach (ESDA) to understand the scalar effects of MAUP. To characterize relationships between data aggregation structures and spatial scales, we develop a method for statistically and visually exploring the local indicators of spatial association (LISA) exhibited between a variable and itself across varying levels of aggregation. We demonstrate our approach by analyzing the across-scale relationships of aggregated 2010 m...

When geographically aggregated data are included in hedonic models, the resulting coefficients are biased by the spatial scale and spatial configuration of variable measurement. We explore the effects of this modifiable areal unit problem (MAUP) within the context of hedonic price models with an individual-level dependent variable. Specifically, we developed standard and spatial hedonic regression models in order to examine the effects of the MAUP on model fit and coefficient estimates. Our empirical analysis documents several significant scale and zoning effects in the hedonic modeling framework. First, neighborhood characteristics are clearly important in efforts to improve model fit—and they are more significant contributors in the standard model than in the spatial hedonic model. For aggregation scale, the model fit change of the standard model is relatively large, whereas the change is more modest for spatial models. The patterns of change in model fit for standard and spatial hedonic models clearly ...

The modifiable areal unit problem (MAUP) is a problem by which aggregated units of data influence the results of spatial data analysis. Standard GWR, which ignores aggregation mechanisms, cannot be considered to serve as an efficient countermeasure of MAUP. Accordingly, this study proposes a type of GWR with aggregation mechanisms, termed area-to-point (ATP) GWR herein. ATP GWR, which is closely related to geostatistical approaches, estimates the disaggregate-level local trend parameters by using aggregated variables. We examine the effectiveness of ATP GWR for mitigating MAUP through a simulation study and an empirical study. The simulation study indicates that the method proposed herein is robust to the MAUP when the spatial scales of aggregation are not too global compared with the scale of the underlying spatial variations. The empirical studies demonstrate that the method provides intuitively consistent estimates.

Socio-demographic data are typically collected at various levels of aggregation, leading to the modifiable areal unit problem. Spatial non-stationarity of statistical associations between variables further influences the demographic analyses. This study investigates the implications of these two phenomena within the context of migration-environment associations. Global and local statistical models are fit across increasing levels of aggregation using household level survey data from rural South Africa. We raise the issue of operational scale sensitivity, which describes how the explanatory power of certain variables depends on the aggregation level. We find that as units of analysis (households) are aggregated, some variables become non-significant in the global models, while others are less sensitive to aggregation. Local model results show that aggregation reduces spatial variation in migration-related local associations but also affects variables differently. Spatial non-stationarity appears to be the driving force behind this phenomenon as the results from the global model mask this relationship. Operational scale sensitivity appears related to the underlying spatial autocorrelation of the non-aggregated variables but also to the way a variable is constructed. Understanding operational scale sensitivity can help to refine the process of selecting variables related to the scale of analysis and better understand the effects of spatial non-stationarity on statistical relationships.

Understanding the patterns and dynamics of spatial origin-destination flow data has been a long-standing goal of spatial scientists. This study aims at developing a new flow clustering method called flowHDBSCAN, which has the potential to be applied to various urban dynamics issues such as spatial movement analysis and intelligent transportation systems. Flows entail origin and destinations pairs, at the exclusion of the actual path in-between. The method combines density-based clustering and hierarchical clustering approaches and extends them to the context of spatial flows. Not only can it extract flow clusters from various situations including varying flow densities, lengths, directions, and hierarchies, but it also provides an effective way to reveal the potentially hierarchical data structure of the clusters. Common issues such as the modifiable areal unit problem (MAUP) of flow endpoints, false positive errors on short flows, and loss of spatial information are well handled. Moreover, the sole-parameter design guarantees its ease of use and practicality. Experiments are conducted with both a synthetic dataset and an eBay online trade flow dataset in the contiguous U.S.