Modifiable Areal Unit Problem Research Articles

A framework for analyzing the effects of modifiable areal unit problem on ecological security pattern

Ecological security pattern (ESP) provide a solution to balance ecosystems and urban development. The modifiable areal unit problem (MAUP) is a well-known geographical issue that affects the understanding of ecological processes and the results of spatial modeling. However, only a few studies have explicitly clarified the effects of MAUP on ESP. Herein, we propose new methods for identifying ecological sources and mapping the resistance surface, as well as a framework for analyzing the effects of MAUP on ESP. Our results indicate that (1) the datasets used for identifying ecological sources should possess a grain size of smaller than 300 × 300 m2. (2) The resistance surface directly influenced the results of the ecological corridors and nodes. (3) MAUP could generate uncertainties in ESP policymaking. Additionally, this study developed comprehensive network analysis tools based on graph machine learning to analyze the effect of MAUP on ESP policymaking, which can provide important landscape planning. The network analysis approaches may help policymakers gain a comprehensive understanding of the ESP network to improve the credibility of policies.

Does flood risk funding protect the most vulnerable? A case study of England

Not only has the frequency and severity of flooding increased under climate change, but which communities are at-risk and how those risks are distributed within communities has changed too. This realisation points to an important interplay between exposure (risk) and social vulnerability. Who is vulnerable? Answering this question is far from straightforward as different vulnerability indicators identify different groups across different scales. This paper addresses this issue. Using the empirical case of England, the spatial distribution of flood risk at different administrative scales is analysed in relation to the Environment Agency (EA) allocation of flood funding between 2015 and 2021. We find that Upper-tier Local Authority Districts with higher levels of both flood risk and social vulnerability received more funding in the period considered. Yet, that is not the scale at which flood scheme funding decisions are made. Flood schemes are decided at the local level, but funding data for smaller administrative scales is not available. Different understandings of vulnerability, the Modifiable Areal Unit Problem (MAUP), and issues around data transparency and availability in flood risk management, need to be urgently addressed.

Does 2D and 3D built environment matter for the spreading of COVID-19 at early stages in Wuhan, China: A spatial and multi-scale analysis

Evidence for the impacts of urban physical attributes on the spread of COVID-19 remains weak due to few investigations into the modifiable areal unit problem (MAUP) and spatial autocorrelation, as well as the lack of fine-grained COVID-19 case data. This study presents a spatial and multi-scale approach to examine the relationships between two-dimensional (2D) and three-dimensional (3D) urban parameters and accumulative confirmed infection cases. The spatial distributions of COVID-19 infections are mapped using anonymized neighborhood-level report data with nearly 50,000 confirmed cases at the early stages of the epidemic in Wuhan, China, and the 2D and 3D built environment factors at multiple spatial scales are characterized. Next, geographical detector model is used to examine the MAUP in the spread of COVID-19 and effects of urban parameters, and spatial regression models are then used to address spatial autocorrelation in the results at the identified appropriate spatial scales. Results reveal that the influences of most urban parameters are sensitive to the scale and areal unit used, and 3D urban parameters, such as building height, have a greater influence than 2D parameters. The estimates from both spatial and non-spatial models suggest the presence of spatial dependence and unobserved autocorrelated factors, and the overestimation of the effects of most urban parameters.

Ecosystem services to support sustainable development: The modifiable areal unit problem in the transition between evaluation and management units

AbstractUnderstanding the role of ecosystem services (ES) and their interactions at different spatial scales in territorial space governance is crucial for sustainable development. However, a unified analysis of scale and zoning effects on ES supporting sustainable development remains a theoretical and practical gap. Therefore, this study utilized the traditional concept of the modifiable areal unit problem (MAUP) to establish the ES‐MAUP framework. Additionally, the highly urbanized region of Southern Jiangsu, China, was selected as a case study area to quantitatively evaluate four typical regulating ecosystem services in 2020: urban cooling (UC), flood mitigation (FM), soil conservation (SC), and net primary productivity (NPP). The spatial characteristic information of these four ES was effectively preserved with increasing spatial scale. Significant differences existed in the hotspot patterns of NPP, UC, and SC among different zoning units. Across the three zoning units, the correlations between NPP‐UC, NPP‐SC, and UC‐SC exhibited consistent positive trends, while notable differences in correlations between other ES pairs, such as NPP‐FM and UC‐FM.

Understanding the impact of modifiable areal unit problem on urban vitality and its built environment factors

ABSTRACT Urban vitality is an essential reference for formulating urban planning and urban development policies, while the Modifiable Areal Unit Problem (MAUP) is a crucial issue that affects the accurate assessment of urban vitality and the understanding of its driving factors. Currently, MAUP in urban vitality studies has not received sufficient attention, and there are limited investigations on whether MAUP significantly affects the spatial autocorrelation of urban vitality. Moreover, existing studies have mainly focused on the impact of individual factors on urban vitality, with minor consideration of the interactions between factors and their effects on urban vitality at different spatial scales. This study takes the Pearl River Delta Core (PRDC) region as the research area. It used the Optimal Parameters-based Geographic Detector (OPGD) model and spatial autocorrelation to analyze the impact of the MAUP on urban vitality and its Built Environment (BE) factors. The results indicated that (1) the five types of BE driving factors, including work, living, rest, traffic, and Points of Interest (POI) diversity, were spatially sensitive and exhibited scale threshold effects. (2) The zoning schemes demonstrated the ability to alter the explanatory power (q-value) of driving factors and their trends. The spatial granularity and aggregation level of the grid-based zoning scheme, NPP-VIIRS nighttime light zoning scheme, and land surface temperature zoning scheme exhibited a logarithmic relationship, where spatial autocorrelation levels decreased with increasing aggregation level. (3) Compared to single-factor effects, the interactive effects of BE factors exhibited a higher q-value for urban vitality. Additionally, the q-values for factor interactions were more stable in multiple spatial scales than those q-values for individual factors. This study provides decision-making references for urban planners and policymakers to accurately assess urban vitality and find balanced, improved paths to enhance it.

Abstract MP04: Socioeconomic Spatial Social Polarization and Blood Pressure at Three Spatial Levels

Spatial social polarization (SSP) indices measure how a population is distributed at extremes of privilege and deprivation. The choice of spatial level for analysis impacts the results of studies of SSP, resulting in a bias known as the Modifiable Areal Unit Problem (MAUP). The objective of this study is to examine the association between participant SSP with systolic and high blood pressure among Black and White adults in the CHS and REGARDS studies across three spatial levels: ZCTA, census tract, and county. We used the Index of Concentration at the Extremes (ICE) to measure SSP across socioeconomic domains including race/ethnicity, income, joint race/ethnicity with income, and home ownership using ZCTA-, census tract-, and county-level data. We computed quintiles for each geographic level, with quintile 1 representing the most deprived area and quintile 5 representing the most privileged for each SSP domain measured. High BP was defined as a treated or untreated blood pressure >140/90 mmHg. Multilevel mixed-effects regression models were adjusted for source study and a priori defined covariates with a random intercept for spatial level. The magnitude of the association between spatial privilege and blood pressure was higher at more local levels. We found that study participants who resided in the most polarized and disadvantaged quintile for race/ethnicity had an odds ratio of 1.01 (95% CI: 0.87, 1.16), 1.20 (95% CI: 1.06, 1.35), and 1.24 (95% CI: 1.09, 1.40) at the county, ZCTA, and tract level respectively for high blood pressure compared to those in the most polarized privileged groups for race/ethnicity. Similar results were found for systolic blood pressure, though results varied by the ICE domain examined. These varying effects as a result of MAUP may be functions of the larger area units not capturing the underlying granular SSP distributions of deprivation and privilege and washing out the total effects of spatial polarization on blood pressure.

Assessing the role of spatial externalities in the survival of Italian innovative startups

The paper provides novel empirical evidence about the effects of spatial externalities on the survival of innovative startups in Italy. Using geocoded firm‐level data, we build micro‐geographic measures of specialization and diversity that are robust to the modifiable areal unit problem. Estimates of spatial externalities are obtained through survival regression models that assess the relationship between these measures and firms' survival time. The main findings are that the nature and strength of agglomeration externalities depend on the firm's life cycle. In particular, an interesting stylized fact can be deduced: these kinds of external economies have a negative effect on innovative startups' survival at the beginning of their activity, which then reverses to be positive when innovative startups reach a certain maturity.

A simulated ‘sandbox’ for exploring the modifiable areal unit problem in aggregation and disaggregation

We present a spatial testbed of simulated boundary data based on a set of very high-resolution census-based areal units surrounding Guadalajara, Mexico. From these input areal units, we simulated 10 levels of spatial resolutions, ranging from levels with 5,515–52,388 units and 100 simulated zonal configurations for each level – totalling 1,000 simulated sets of areal units. These data facilitate interrogating various realizations of the data and the effects of the spatial coarseness and zonal configurations, the Modifiable Areal Unit Problem (MAUP), on applications such as model training, model prediction, disaggregation, and aggregation processes. Further, these data can facilitate the production of spatially explicit, non-parametric estimates of confidence intervals via bootstrapping. We provide a pre-processed version of these 1,000 simulated sets of areal units, meta- and summary data to assist in their use, and a code notebook with the means to alter and/or reproduce these data.

Application of the local colocation quotient method in jobs-housing balance measurement based on mobile phone data: A case study of Nanjing City

The issue of jobs-housing balance concerns the sustainable development of cities and the well-being of residents. Conventional measurement approaches, however, often fall short due to the zoning problem (as a subproblem of the modifiable areal unit problem), leading to inconsistent and inaccurate results depending on the spatial partitioning scheme applied. This paper discusses the application and advantages of the local colocation quotient method in jobs-housing balance measurement. A case study of Nanjing, China, is selected, and mobile location data are used to obtain the jobs and housing locations of workers. Then, the adjusted jobs-workers ratio and the local colocation quotient values that reflect the degree of jobs-housing balance are calculated and compared by category. The results show that on the one hand, due to the zoning effect, when points are aggregated into spatial units, some points with different spatial characteristics are masked by the dominant value of the units; on the other hand, the local colocation quotient method can solve the zoning problem and obtain more fine-scale and accurate results, thus providing a new analytical tool and perspective for this field.

Addressing the Boundary and Modifiable Areal Unit Problems Simultaneously when Measuring Landscape Fragmentation Using Patch-Based Metrics: a Case Study of Effective Mesh Size in Nova Scotia, Canada

Addressing the Boundary and Modifiable Areal Unit Problems Simultaneously when Measuring Landscape Fragmentation Using Patch-Based Metrics: a Case Study of Effective Mesh Size in Nova Scotia, Canada

Exploring the spatial relationship of e-bike and motorcycle crashes: Implications for risk reduction

Introduction: Electric bicycles, or e-bikes, have become very popular over the past decade. In order to reduce the risk of crashes, it is necessary to understand the contributing factors. While several researchers have examined these elements, few have considered the spatial heterogeneity between crashes and environmental variables, such as Points of Interest (POI). In addition, there is a scarcity of studies comparing the crash-related factors of e-bikes and motorcycles. Despite their differing speed and range capabilities, different POIs also tend to impact area/bandwidths differently because e-bikes cannot cover the same range that motorcycles can. Method: In this study, we compared e-bike and motorcycle crashes at 11 different types of POIs in Taipei from 2016 to 2020. Since crashes are sparse events and easily affected by the Modifiable Areal Unit Problem (MAUP), Kernel Density Estimation (KDE) was employed to transform crash points (count data) to crash risk surfaces (continuous data). Additionally, an advanced variant of Geographical Weighted Regression (GWR), Multiscale Geographically Weighted Regression (MGWR) utilized to predict crash risk because each predictor is allowed to have a different bandwidth. Results: The results showed: (a) For e-bike crashes, the MGWR model outperformed the GWR and OLS models in terms of AIC values, while the MGWR and GWR performed similarly with regard to motorcycle crashes; (b) The analysis revealed e-bike and motorcycle crash risk to be associated with various types of POIs. E-bike crashes tended to occur more frequently in areas with more schools, supermarkets, intersections, and elderly people. Meanwhile, motorcycle crashes were more likely to occur in areas with a high number of restaurants and intersections. The search bandwidths of e-bikes are inconsistent and narrower than those of motorcycles.

Multiscale Analysis of Spatial Accessibility to Acute Hospitals in Carinthia, Austria

Health care accessibility studies are well established in the US but lacking in Austria, even though both experience high costs and have hospital care as the largest contributor to health care spending. This study aims to examine multiscale spatial accessibility to acute hospitals in Carinthia, Austria. Using the most recent data at census block and 250 meter grid levels, we refine proximity and generalized two-step floating catchment area (G2SFCA) methods while accounting for the modifiable areal unit problem (MAUP) and edge effects. For census blocks and 250 meter grids, the mean travel times to the nearest acute hospitals are 16 and 21 min, respectively, covering 58.8% and 76.2% of the population, which, however, increases to 25 and 31 min to the three nearest hospitals with similar populations. People bypassing the nearest hospital to seek hospitals at a longer distance, termed “bypass behavior”, is more influential, as 20% more of the population living in mountainous or rural areas need to travel 30 min longer. The G2SFCA method with a more pronounced distance decay results in a more decentralized polycentric structure of accessibility and identifies poorer access areas. While urban advantage is most evident in Klagenfurt and Villach, not all areas near hospitals enjoy the highest accessibility. A combination of the proximity and G2SFCA methods identifies less accessible areas. The MAUP overestimates accessibility at a coarse level and in less populous areas. Edge effects occur at the border when using proximity only, but they are more sensitive when considering bypass behavior or a weak distance decay effect. This study contributes to our understanding of acute hospitals’ accessibility in Carinthia and highlights the need to improve low-accessible areas in addition to universal health coverage. Cautions need to be exercised when using different geographic units or considering edge effects for health care planning and management.

Mapping Gross Domestic Product Distribution at 1 km Resolution across Thailand Using the Random Forest Area-to-Area Regression Kriging Model

Accurate spatial distribution of gridded gross domestic product (GDP) data is crucial for revealing regional disparities within administrative units, thus facilitating a deeper understanding of regional economic dynamics, industrial distribution, and urbanization trends. The existing GDP spatial models often rely on prediction residuals for model evaluation or utilize residual distribution to improve the final accuracy, frequently overlooking the modifiable areal unit problem within residual distribution. This paper introduces a hybrid downscaling model that combines random forest and area-to-area kriging to map gridded GDP. Employing Thailand as a case study, GDP distribution maps were generated at a 1 km spatial resolution for the year 2015 and compared with five alternative downscaling methods and an existing GDP product. The results demonstrate that the proposed approach yields higher accuracy and greater precision in detailing GDP distribution, as evidenced by the smallest mean absolute error and root mean squared error values, which stand at USD 256.458 and 699.348 ten million, respectively. Among the four different sets of auxiliary variables considered, one consistently exhibited a higher prediction accuracy. This particular set of auxiliary variables integrated classification-based variables, illustrating the advantages of incorporating such integrated variables into modeling while accounting for classification characteristics.

Influence of the built environment on taxi travel demand based on the optimal spatial analysis unit.

When discussing the influence of the built environment on taxi travel demand, few studies have considered the effect of the modifiable areal unit problem (MAUP) or the influence of the "5D" dimensions of the built environment (It refers to the consideration of the built environment from five dimensions of density, diversity, design, destination accessibility and distance to transit.) on taxi travel demand. Moreover, discussion of the nonlinear and linear relationships between taxi demand and environment variables is also lacking. To address these gaps, we constructed a "5D" dimension index system of built environment variables. The influence of the MAUP on the model results was discussed using the optimal parameter-based geographical detector (OPGD) model, and the optimal spatial analysis unit was selected. The OPGD and multiscale geographically weighted regression (MGWR) models were used to reveal the influence of different dimensions of the built environment on taxi travel demand from global and local perspectives, respectively. Finally, the central urban area of Xi'an was analyzed as an example. The results show the following: (1) Most built environment variables are sensitive to the influence of MAUP. (2) It is better to divide the space into regular hexagons than squares, and the optimal spatial analysis unit in this study is a regular hexagon grid with sides of 900m. (3) From a global perspective, the distance to the city center, commercial residence POI density, transportation facility POI density, and population density have the greatest influence on the demand for taxi travel. (4) From a local perspective, the MGWR model considering spatial heterogeneity and scale differences is superior to the GWR model, and the influence of built environment variables exhibited spatial heterogeneity. The proposed optimal spatial analysis unit can provide a basis for taxi demand forecasting and scheduling. This study provides a reference for urban planners and traffic managers to offer optimization strategies related to the built environment, promote healthy development of the taxi industry, and solve the problems of the urban transportation system.

Spatial stratified heterogeneity and driving mechanism of urban development level in China under different urban growth patterns with optimal parameter-based geographic detector model mining

The rapid urbanization leads to the dynamic changes of the urban external landscape and forms different urban growth patterns (UGP), which in turn affects the development level of the urban internal functions as well. However, few studies have quantitatively examined the spatial stratified heterogeneity (SSH) and driving mechanism of the urban development level (UDL) under different UGPs. Based on the multi-source geographic data of 368 Chinese cities, this study identified the UGP at the patch scale from 2010 to 2020. It furthermore quantified the UDL of newly added construction land. In order to reveal the SSH pattern, motivating factors, and interaction mechanism of the UDL under different UGPs, this paper chose to use the optimal parameter-based geographic detector (OPGD) model, which accounts for the modifiable areal unit problem (MAUP). The results indicate that: 1) There are significant spatial differences in the UDL among different UGPs. Namely, the infilling pattern exhibits the highest UDL, followed by the edge pattern, and the outlying pattern, which has the worst UDL; 2) The SSH of the UDL is defined by the interaction of multiple factors. Different UGPs have both differences and similarities in their motivating factors, thus affecting the spatial distribution of UDL. GDP density and road network density are the two factors with the strongest driving force for all UGPs. Specifically, the UDL of infilling-expansion areas is more sensitive to the industrial structure and infrastructure conditions. On the other hand, factors such as residential density and socio-economic activities are more important to the UDL of edge-expansion areas, while population, topography, and location factors have a stronger influence on the UDL of outlying-expansion; 3) A change of spatial scale will result in the heterogeneity of the influence of motivating factors in each UGP. In general, the systematic comparison of the SSH and driving mechanism of UDL under different UGPs helps us explore high-quality and sustainable urbanization paths. As a result, this scientific field is given theoretical basis for urban planners and managers to rationally regulate external urban forms and optimize the internal structure layout.

Modifiable Areal Unit Problem on Grided Mobile Crowd Sensing: Analysis and Restoration

Aggregating crowd density in grids from big mobile datasets is a basic but critical work in urban computing and mobile computing. The error of position estimation in raw mobile data, including spatial deviation and temporal deviation, is inevitable and directly impacts the accuracy of aggregated crowd density results. In this case, a key modifiable areal unit problem is raised to understand the relationship among the crowd density accuracy, raw mobile data error, grid shape, and size, but few studies focused on it. This paper analyzes this modifiable areal unit problem of the error in crowd density estimation from big mobility data. By regarding the error as the result of a convolution operation, an optimization model based restoration method was proposed to fix the error of the estimated result, and we analyzed the restoration effect under different circumstances by several simulation experiments. A real application for grided population distribution map construction and restoration from Call Detail Record was conducted to prove the reliability of the whole analysis, which demonstrates the restoration method can reduce the error by nearly 40% under certain conditions.

Seasonal variance in electric vehicle charging demand and its impacts on infrastructure deployment: A big data approach

Electric vehicle (EV) charging demand is an essential input of charging facility location models. However, charging demand may vary across seasons. In response, this paper first provided insights into the seasonal variance in charging demand using a unique GPS trajectory dataset which contained travel, parking, and charging information of 2,658 private EVs in Beijing. The dataset was collected in January, April, July, and October 2018, which were representative months in winter, spring, summer, and autumn, respectively. Through statistical and spatiotemporal analyses, we found that in winter, EVs got recharged when their state of charge (SOC) was lower: the average SOCs on working days were 51.96%, 48.39%, 50.86%, and 43.50%, in spring, summer, autumn, and winter, respectively. Furthermore, the central urban areas tended to have a higher charging demand in winter. To further explore how the seasonal variance in charging demand may influence infrastructure deployment, we used the classical p-median model to deploy charging facilities with the charging demands in the four seasons, considering the modifiable areal unit problem (MAUP). The results suggested that the seasonal variance did influence the layout of charging facilities under different spatial analysis units (SAUs). The deployment of charging facilities in the central urban areas and outer suburbs tended to be more sensitive to seasonal variance in charging demand. The findings are expected to be useful for charging infrastructure planning in both the transport and power sectors.

Social and environmental vulnerability to flooding: Investigating cross-scale hypotheses

Flooding is a natural hazard that touches nearly all facets of the globe and is expected to become more frequent and intensified due to climate and land-use change. However, flooding does not impact all individuals equally. Therefore, understanding how flooding impacts distribute across populations of different socioeconomic and demographic backgrounds is vital. One approach to reducing flood risk on people is using indicators, such as social vulnerability indices and flood exposure metrics, to inform decision-making for flood risk management. However, such indicators can face the scale and zonal effect produced by the Modifiable Areal Unit Problem (MAUP). This study investigates how the U.S. Census block group, tract, and county scale selection impacts social vulnerability and flood exposure outcomes within coastal Virginia, USA. Here we show how (1) scale selection can obstruct our understanding of drivers of vulnerability, (2) increasingly aggregated scales significantly undercount highly vulnerable populations, and (3) hotspot clusters of social vulnerability and flood exposure can identify variable priority areas for current and future flood risk reduction. Study results present considerations about using such indicators, given the real-life consequences that can occur due to the MAUP. The results of this work warrant understanding the implications of scale selection on research methodological approaches and what this means for practitioners and policymakers that utilize such information to help guide flood mitigation strategies.

Investigating local variation in disease rates within high-rate regions identified using smoothing.

Exploratory disease maps are designed to identify risk factors of disease and guide appropriate responses to disease and helpseeking behaviour. However, when produced using aggregatelevel administrative units, as is standard practice, disease maps may mislead users due to the Modifiable Areal Unit Problem (MAUP). Smoothed maps of fine-resolution data mitigate the MAUP but may still obscure spatial patterns and features. To investigate these issues, we mapped rates of Mental Health- Related Emergency Department (MHED) presentations in Perth, Western Australia, in 2018/19 using Australian Bureau of Statistics (ABS) Statistical Areas Level 2 (SA2) boundaries and a recent spatial smoothing technique: the Overlay Aggregation Method (OAM). Then, we investigated local variation in rates within high-rate regions delineated using both approaches. The SA2- and OAM-based maps identified two and five high-rate regions, respectively, with the latter not conforming to SA2 boundaries. Meanwhile, both sets of high-rate regions were found to comprise a select number of localised areas with exceptionally high rates. These results demonstrate how, due to the MAUP, disease maps that are produced using aggregate-level administrative units are unreliable as a basis for delineating geographic regions of interest for targeted interventions. Instead, reliance on such maps to guide responses may compromise the efficient and equitable delivery of healthcare. Detailed investigation of local variation in rates within high-rate regions identified using both administrative units and smoothing is required to improve hypothesis generation and the design of healthcare responses.

A Geographical Perspective on Simpson's Paradox

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?