Areal Unit Research Articles

The impacts of the modifiable areal unit problem (MAUP) on social equity analysis of public transit reliability

This study aims to examine the degree to which the results of social equity analysis on public transit reliability are sensitive to the choice of spatial unit of analysis (i.e., modifiable areal unit problem (MAUP)). Using the city of Winnipeg as an example, we investigate the social equity of bus on-time performance (OTP), and pass-up distribution at multiple levels (e.g., stop, route, neighborhood) and compare the results. Neighborhoods are classified as minority vs. non-minority population dominant neighborhoods and transit routes and stops are classified into minority vs. non-minority population serving ones according to the socioeconomics of residents. We conduct an equity assessment by calculating 1) the number of pass-ups, 2) the number of bus deviations (e.g., early arrivals, delays) from the predetermined schedule, and 3) the average deviations time (in seconds) that occurred on minority vs. non-minority serving routes/stops as well as in minority vs. non-minority dominant neighborhoods. We also consider different day types (e.g., weekdays, weekends) and disability status (e.g., wheelchair, regular passengers) in the equity assessment. While the route-level results depict that transit service reliability is equitable, results of the neighborhood and stop-level analysis reveal inequities in the distribution of the OTP and pass-ups in the city. Our findings demonstrate that different levels of spatial aggregation can significantly change the results of social equity analysis of public transit reliability, thereby leading to incomplete conclusions that inadequately capture the inequity due to the existence of MAUP. The results of this paper provide insights to transit authorities, planners, and policymakers for diagnosing the social equity landscape of transit reliability in a more robust manner.

Analysis of Work Participation Rate among Tehsils Level of Ahmednagar District of Maharashtra State

Abstract: India has a large number of primary workers, so the Indian economy is highly unbalanced. Ahmednagar district is an agriculture-oriented district. This research paper is written to explore the changing pattern of work participation rate and the gender gap in the workforce among the tehsils of Ahmednagar district during 2001-2011. In the present study, the tehsils have been taken as the component areal units of the study region for determining the variation in the distribution of the workforce. The present study is entirely based on a secondary source of data collected from the census of the Ahmednagar district between 2001 and 2011. Simple statistical methods are used to process the collected data to calculate work participation rate, decadal variation, and gender gap. This paper has attempted a comprehensive study of the trends in the work participation rate tehsil level in general and male-female.

Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated according to a specific neighboring structure. Incorporating the temporal and spatial dimension into a statistical model poses challenges regarding the underlying theoretical framework as well as the implementation of efficient computational methods. We propose to include spatio-temporal random effects using a conditional autoregressive prior, where the temporal correlation is modeled through an autoregressive mean decomposition and the spatial correlation by the precision matrix inheriting the neighboring structure. Their joint distribution constitutes a Gaussian Markov random field, whose sparse precision matrix enables the usage of efficient sampling algorithms. We cluster the areal units using a nonparametric prior, thereby learning latent partitions of the areal units. The performance of the model is assessed via an application to study regional unemployment patterns in Italy. When compared to other spatial and spatio-temporal competitors, the proposed model shows more precise estimates and the additional information obtained from the clustering allows for an extended economic interpretation of the unemployment rates of the Italian provinces.

A Downsampling Method Addressing the Modifiable Areal Unit Problem in Remote Sensing

Handling multiple scales efficiently is one avenue for processing big remote sensing imagery data. Unfortunately, imagery is also affected by the infamous modifiable areal unit problem, which creates unpredictable errors at different scales. We developed a downsampling method that attempts to keep the data distribution in a downsampled image constant, reducing the modifiable areal unit problem. We tested our method against classic downsampling methods (mean, central pixel selection, random) under a range of typical remote sensing scenarios. Under our experimental conditions, our downsampling method consistently outperformed the classical downsampling methods within a 95% confidence level. The downsampling method can be used in most typical situations where downsampling is needed, but it is likely to shine when used as a pyramid building policy in geocomputing platforms, such as Google Earth Engine.

Influences on Public Transport Utilization: The Case of Auckland

Regression analysis is applied to cross-sectional data for 318 census area units served by the public transportation system in Auckland, New Zealand. The goal is to ascertain the determinants of public transport patronage for the purpose of commuting to work in the region. The analysis addresses both the modifiable areal units problem and spatial autocorrelation. Elasticity estimates are derived for a number of hypothesized drivers of patronage. The paper shows that adjusting for spatial autocorrelation improves the fit of the regression model to the data, a finding that should be of interest to public transportation planners and analysts working with cross-sectional data of a geographic nature.

“Hot street” of crime detection in London borough and lockdown impacts

ABSTRACT In recent years, the police intervention strategy “Hot spots policing” has been effective in combating crimes. However, as cities are under the intense pressure of increasing crime and scarce police resources, police patrols are expected to target more accurately at finer geographic units rather than ballpark “hot spot” areas. This study aims to develop an algorithm using geographic information to detect crime patterns at street level, the so-called “hot street”, to further assist the Criminal Investigation Department (CID) in capturing crime change and transitive moments efficiently. The algorithm applies Kernel Density Estimation (KDE) technique onto street networks, rather than traditional areal units, in one case study borough in London; it then maps the detected crime “hot streets” by crime type. It was found that the algorithm could successfully generate “hot street” maps for Law Enforcement Agencies (LEAs), enabling more effective allocation of police patrolling; and bear enough resilience itself for the Strategic Crime Analysis (SCA) team’s sustainable utilization, by either updating the inputs with latest data or modifying the model parameters (i.e. the kernel function, and the range of spillover). Moreover, this study explores contextual characteristics of crime “hot streets” by applying various regression models, in recognition of the best fitted Geographically Weighted Regression (GWR) model, encompassing eight significant contextual factors with their varied effects on crimes at different streets. Having discussed the impact of lockdown on crime rates, it was apparent that the land-use driven mobility change during lockdown was a fundamental reason for changes in crime. Overall, these research findings have provided evidence and practical suggestions for crime prevention to local governors and policy practitioners, through more optimal urban planning (e.g. Low Traffic Neighborhoods), proactive policing (e.g. in the listed top 10 “Hot Streets” of crime), publicizing of laws and regulations, and installations of security infrastructures (e.g. CCTV cameras and traffic signals).

Associations Between Surface Mining Airsheds and Birth Outcomes in Central Appalachia at Multiple Spatial Scales.

A considerable body of research exists outlining ecological impacts of surface coal mining, but less work has explicitly focused on human health, and few studies have examined potential links between health and surface coal mining at fine spatial scales. In particular, relationships between individual birth outcomes and exposure to air contaminants from coal mining activities has received little attention. Central Appalachia (portions of Virginia, West Virginia, Kentucky, and Tennessee, USA), our study area, has a history of resource extraction, and epidemiologic research notes that the region experiences a greater level of adverse health outcomes compared to the rest of the country that are not fully explained by socioeconomic and behavioral factors. The purpose of this study is to examine associations between surface mining and birth outcomes at four spatial scales: individual, Census tract, county, and across county‐sized grid cells. Notably, this study is among the first to examine these associations at the individual scale, providing a more direct measure of exposure and outcome. Airsheds were constructed for surface mines using an atmospheric trajectory model. We then implemented linear (birthweight) and logistic (preterm birth [PTB]) regression models to examine associations between airsheds and birth outcomes, which were geocoded to home address for individual analyses and then aggregated for areal unit analyses, while controlling for a number of demographic variables. This study found that surface mining airsheds are significantly associated with PTB and decreased birthweight at all four spatial scales, suggesting that surface coal mining activities impact birth outcomes via airborne contaminants.

Nonlinear and threshold effects of the built environment on e-scooter sharing ridership

Understanding the relationship between the built environment and e-scooter sharing (ESS) usage is important because it could help planners determine the high-demand area and design an effective investment plan to promote the use of micromobility. Previous studies usually assume that the relationship is linear, which may lead to inaccurate ridership prediction and ineffective policy. Thus, this study explores the nonlinear and threshold effects of the built environment on ESS ridership in Los Angeles using the gradient boosting decision tree. Fourteen built environment and ten demographic variables are selected as independent variables. We find that the built environment accounts for 91.66% of the total relative importance. The ten most important variables are intersection density, road density, public transit station density, restaurant density, employment density, distance to the center, population density, proportion of park area, parking density, and bike lane density. The nonlinear and threshold effects of the built environment on ESS ridership are determined. By using two spatial analysis units (census tract and census block group) and four temporal analysis units (spring, summer, autumn, and winter), the modifiable areal unit problem and the modifiable temporal unit problem are revealed.

Using the areal unit segregation measure to identify racially “packed” and “cracked” legislative districts

This paper provides a novel and systematic technique for differentiating legislative districts that are “naturally packed” with racial minorities from those that are “unnaturally packed.” Unnaturally packed districts—called segregated districts in this paper—contain greater shares of racial minorities than the share of racial minorities in the geographic regions in which they are located. By contrast, “naturally packed” districts are the ineluctable result of the geographic concentration of large numbers of minorities (often in urban areas) and are thus non-segregated. Differentiating segregated from non-segregated districts requires observing the average share of racial minorities among the nearest N neighbors of a district’s residents (where N is the number of people in a state divided by the number of legislative districts). When the share of minorities in a district exceeds the average share of minorities who are the nearest N neighbors of district residents, the district is segregated. This paper explains how to measure segregation for individual legislative districts, provides a test case by examining Virginia’s State House Districts ruled Unconstitutional in Bethune-Hill v. Virginia Board of Elections, and shows how measuring segregation provides information different from typical ways of detecting gerrymanders.

Understanding the Modifiable Areal Unit Problem and Identifying Appropriate Spatial Units while Studying the Influence of the Built Environment on the Traffic System State

Spatially aggregated data are prone to the effects of the modifiable areal unit problem (MAUP), which applies to built environments and traffic data. Although various studies have been carried out to explore the impact of built environment factors on traffic systems, few have considered MAUPs, which may result in statistical inconsistency. The purpose of this study is to assess the effects of MAUPs on statistical variables and geographically weighted regression results when evaluating the influence of the built environment on the traffic system state. Fifty sets of spatial configurations were created using the different aggregation criteria. The variance inflation factor and spatial autocorrelation of the variables, as well as the R2 and root mean squared error of the GWR model, were used to assess the MAUP effect. The results show that the index variation is more dependent on the scale of the spatial unit than on zoning type. In the case study presented, based on the available dataset, the optimal spatial unit size for analyzing the influence of the built environment on Jinan’s traffic system was 900 m × 900 m.

Virus containment measures and homicide in Mexico: An assessment of community strain theory

ObjectivesThis study examined whether Covid-19 virus containment measures moderated the relationship between community strain and homicide rates in Mexico City neighborhoods and police quadrants. MethodsWe tested the moderation effects hypothesis with the use of a mixed-effects regression to estimate fixed effects with random effects at different levels of aggregation. A sensitivity analysis was used to assess whether results of the moderation effects were affected by changes in the unit of analysis. ResultsWe found no evidence that virus containment measures moderated the relationship between community strain and observed changes in homicide rates. Moreover, although community strain measures were found to be statistically associated with homicide rates, the results were seemingly affected by the Modifiable areal unit problem (MAUP). ConclusionsFirst, the link being made in the literature between the homicide drop and the Covid-19 pandemic based on strain theory premises has no universal empirical basis. Second, although homicide rates dropped on average after containment measures were implemented, these had different effects across places, making arguments based on overall average change inexact. Third, we find evidence that community strain can predict homicide rates, but results are sensitive to the MAUP. Thus, community strain explanations of homicide rates may only apply in some areas of cities and conditional on the unit of analysis.

Developing a methodological framework for capturing regional disparities in social development

AbstractThis paper attempts to develop a methodological framework for capturing regional disparities in social development by adopting the methods suggested by McMeekin et al. (2020). A set of six conditions and their adjoining cases were developed that determined the methodology. A new methodological framework was formulated as an interconnected network of conditions, cases, tools, methods and other aspects. This framework was pilot tested in Kerala, India, to explore the regional inequalities in housing infrastructure and living conditions. Comparison of results with the index of deprivation revealed the importance of adopting multivariate methods and lower areal units of analysis to produce better results.

Spatiotemporal analysis of regional TIA trends.

BackgroundThere has been a decline in the stroke incidence across high income countries but such knowledge exists at Country or State rather than areal unit level such local government area (LGA). In this disease mapping study, we evaluate if there are local hot spots or temporal trends in TIA rate. Such knowledge will be of help in planning healthcare service delivery across regions.MethodsLinked hospital discharge data (Victorian Admitted Episodes Dataset or VAED) was used to collect TIA (defined by ICD-10-AM codes G450-G459) cases from 2001 to 2011. The State of Victoria is the second most populous state in Australia, with a population of 6.7 million and can be divided into 79 administrative units or LGA. The data is anonymized and contains residence of the patient in terms of LGA but not exact location. The date of the TIA event when the patient is admitted to hospital is provided in the dataset. The number of TIAs per year was aggregated for each LGA. Standardized TIA ratios were calculated by dividing actual over expected cases for each LGA per year. We used Integrated Nested Laplace Approximation (INLA) to perform spatial and spatiotemporal regression, adjusting for hypertension, sex and population, age (≥60), and socio-economic status (SES) decile within the LGA. The final model was chosen based on the lowest the Deviance Information Criterion (DIC) and Watanabe-Akaike information criteria (WAIC).ResultsChoropleth maps showed a higher standardized TIA ratios in North-West rural region. Compared to the baseline model (DIC 13,159, WAIC 13,261), adding in a spatial random effect significantly improved the model (DIC 6,463, WAIC 6,667). However, adding a temporal component did not lead to a significant improvement (DIC 6,483, WAIC 6,707).ConclusionOur finding suggests a statically significant spatial component to TIA rate over regional areas but no temporal changes or yearly trends. We propose that such exploratory method should be followed by evaluation of reasons for regional variations and which in turn can identify opportunities in primary prevention of stroke, and stroke care.

Delivering spatially comparable inference on the risks of multiple severities of respiratory disease from spatially misaligned disease count data.

Population-level disease risk varies between communities, and public health professionals are interested in mapping this spatial variation to monitor the locations of high-risk areas and the magnitudes of health inequalities. Almost all of these risk maps relate to a single severity of disease outcome, such as hospitalization, which thus ignores any cases of disease of a different severity, such as a mild case treated in a primary care setting. These spatially-varying risk maps are estimated from spatially aggregated disease count data, but the set of areal units to which these disease counts relate often varies by severity. Thus, the statistical challenge is to provide spatially comparable inference from multiple sets of spatially misaligned disease count data, and an additional complexity is that the spatial extents of the areal units for some severities are partially unknown. This paper thus proposes a novel spatial realignment approach for multivariate misaligned count data, and applies it to the first study delivering spatially comparable inference for multiple severities of the same disease. Inference is via a novel spatially smoothed data augmented MCMC algorithm, and the methods are motivated by a new study of respiratory disease risk in Scotland in2017.

How accurate are WorldPop-Global-Unconstrained gridded population data at the cell-level?: A simulation analysis in urban Namibia.

Disaggregated population counts are needed to calculate health, economic, and development indicators in Low- and Middle-Income Countries (LMICs), especially in settings of rapid urbanisation. Censuses are often outdated and inaccurate in LMIC settings, and rarely disaggregated at fine geographic scale. Modelled gridded population datasets derived from census data have become widely used by development researchers and practitioners; however, accuracy in these datasets are evaluated at the spatial scale of model input data which is generally courser than the neighbourhood or cell-level scale of many applications. We simulate a realistic synthetic 2016 population in Khomas, Namibia, a majority urban region, and introduce several realistic levels of outdatedness (over 15 years) and inaccuracy in slum, non-slum, and rural areas. We aggregate the synthetic populations by census and administrative boundaries (to mimic census data), resulting in 32 gridded population datasets that are typical of LMIC settings using the WorldPop-Global-Unconstrained gridded population approach. We evaluate the cell-level accuracy of these gridded population datasets using the original synthetic population as a reference. In our simulation, we found large cell-level errors, particularly in slum cells. These were driven by the averaging of population densities in large areal units before model training. Age, accuracy, and aggregation of the input data also played a role in these errors. We suggest incorporating finer-scale training data into gridded population models generally, and WorldPop-Global-Unconstrained in particular (e.g., from routine household surveys or slum community population counts), and use of new building footprint datasets as a covariate to improve cell-level accuracy (as done in some new WorldPop-Global-Constrained datasets). It is important to measure accuracy of gridded population datasets at spatial scales more consistent with how the data are being applied, especially if they are to be used for monitoring key development indicators at neighbourhood scales within cities.

The modifiable areal unit problem in the analysis of the demand for urban freight transport

This document diagnoses the effects of the Modifiable Areal Unit Problem (MAUP) in the study of the demand for urban freight transport, by means of a comparison of different analysis scales to determine the relevance of working with different levels of detail. It is recommended to analyze the number of retail businesses, because they are the ones that mainly attract urban freight transport, and other variables of a socio-territorial type, considering three different spatial units: basic geostatistical area, electoral section, and regular 500-by-500-meter grids. For each scale, descriptive statistics parameters, correlation between variables, as well as global and local spatial autocorrelation (Moran-LISA’s I) were obtained to determine the impact of the MAUP. The results obtained show that the electoral sections do not result in an adequate scale, unless it is used as a complementary scale, since the statistical results indicate a greater variation. However, its cartographic representation allows seeing spatial groupings that are not observed in the other scales, which can be a valuable contribution. In the case of the Basic Geostatistical Area (BGA) scale and the 500-by-500-meter grids, data show less dispersion. The variables analyzed show a greater correlation and present a greater global spatial autocorrelation, which is why it is determined that they may be the most appropriate scales to model the transport of merchandise in the study area. The site that had no discrepancy, regardless of the scale of analysis, was the historic downtown of the city of Toluca, so it can be considered a priority site based on its demand for merchandise and territorial characteristics, where regulation and transport control alternatives can be incorporated, as well as the creation of infrastructure to make deliv-eries more efficient and to mitigate its negative impacts.

A Bayesian shared-effects modeling framework to quantify the modifiable areal unit problem

The modifiable areal unit problem (MAUP) refers to the effects caused by modifying the units of analysis in the context of spatial statistical analyses on areal data. The problem was formulated decades ago, but it is still of interest due to its complexity. Usually, studies on the MAUP are experimental, focusing mainly on analyzing the variation of model estimates or statistical properties as a consequence of varying the units of analysis. Indeed, the theoretical advances in this research line are scarce, leaving the MAUP as an issue to be considered in practice if spatial analyses are carried out at different scales or with multiple zonations of the study area. In this paper, a Bayesian shared-effects modeling framework is proposed for quantifying the MAUP, both globally and locally. In a global sense, the model described allows measuring the discrepancy in a covariate effect between two different spatial scales. If a global MAUP effect is identified, posterior predictive checks can be computed to detect those spatial units that contribute the most to such discrepancies. The methodology proposed is applied first to a traffic accident dataset recorded in Valencia, Spain, including multiple environmental and sociodemographic covariates. Five different partitions of the city based on the structure of census tracts are considered to analyze MAUP effects. A second application is also shown, considering a dataset about COVID-19 death counts in the Greater London area at two different aggregation levels. This second dataset includes multiple socioeconomic and health indicators as well.

A fully automated and generic spatial discretization procedure for cultivated landscapes with human-made landscape elements

Abstract Landscape discretization is an essential hydrological modeling pre-processing step that comprises the numerical representation of different geographical objects considered in the modeling process and the connections between these objects within a graph structure. GROOV'Scape is a new landscape discretization procedure that (i) produces an oriented tree of a wide range of human-made landscape elements, such as plots, hedges, benches, grass stripes, and ditches, (ii) is fully automated to avoid local drainage anomalies that require user corrections, and (iii) is fast enough to enable sensitivity analysis and the interactive production of mediated modeling landscape management scenarios. GROOV'Scape was tested on a small agricultural catchment in south-west France (Doazit catchment, 9.05 km2). The results show good agreement between the connections of areal units computed by GROOV'Scape and those observed in the field. The system exhibited substantial sensitivity to the user's choice of minimum area unit size and of digital elevation model (DEM) resolution, suggesting trial-and-error approaches are needed to reach the best landscape discretization for any given modeling purpose. Finally, we demonstrated the feasibility of using GROOV'Scape to find an optimum configuration of an infrastructure network with respect to a given ecosystem function.

ClockBoard: A zoning system for urban analysis

Zones are the building blocks of urban analysis. Fields ranging from demographics to transport planning routinely use zones - spatially contiguous areal units that break-up continuous space into discrete chunks - as the foundation for diverse analysis techniques. Key methods such as origin-destination analysis and choropleth mapping rely on zones with appropriate sizes, shapes and coverage. However, existing zoning systems are sub-optimal in many urban analysis contexts, for three main reasons: 1) administrative zoning systems are often based on somewhat arbitrary factors; 2) zoning systems that are evidence-based (e.g., based on equal population size) are often highly variable in size and shape, reducing their utility for inter-city comparison; and 3) official zoning systems in many places simply do not exist or are unavailable. We set out to develop a flexible, open and scalable solution to these problems. The result is the zonebuilder project (with R, Rust and Python implementations), which was used to create the ClockBoard zoning system. ClockBoard consists of 12 segments emanating from a central place and divided by concentric rings with radii that increase in line with the triangular number sequence (1, 3, 6 km etc). 'ClockBoards' thus create a consistent visual frame of reference for monocentric cities that is reminiscent of clocks and a dartboard. This paper outlines the design and potential uses of the ClockBoard zoning system in the historical context, and discusses future avenues for research into the design and assessment of zoning systems.

Characterizing mobility patterns of private electric vehicle users with trajectory data

Human mobility pattern analysis has received rising attention. However, little is known about the mobility patterns of private Electric Vehicle (EV) users. In response, this paper characterized mobility patterns of private EV users using a unique one-month dataset containing moving trajectories of 76,774 actual private EVs in January 2018 in Beijing. Specifically, we first explored the diversity, regularity, spatial extent, and uniqueness of EV users’ mobility patterns. The results suggested that most EV users had both regular travel and activity patterns (the mean travel and activity entropies were 2.17 and 1.83, respectively) with special preferences towards some specific activity locations relative to all the locations they visited (the mean number of activity locations visited was 13.57 in one month). Furthermore, they tended to perform activities within a small geographical area (the mean radius of gyration was 7.60 km) and have a short daily travel distance (the mean value was 37.35 km) relative to their electric driving range. Further, we associated EV users’ mobility patterns with the built environment through ordinary least squares and geographically weighted regression models, particularly considering the so-called modifiable areal unit problem (MAUP). Due to the MAUP, most of the statistically significant built environment variables varied across spatial analysis units (SAUs). Gymnasia was the only variable statistically associated with the mobility patterns for all SAUs; while the variables related to residence and workplace were not statistically associated.