Areal Unit Research Articles

A smart and flexible approach for aggregation of adjacent polygons to meet a minimum target area or attribute value

Many geospatial analyses require flexible aggregation of adjacent units to meet a minimum target area or attribute value. This is usually accomplished using several non-automated and complex GIS tasks. We developed an integrated user-friendly approach and algorithm implemented in the ‘GHS-SmartDissolve’ tool, which addresses minimum mapping unit or attribute value requirements, layers resolution mismatch, spatial uncertainty or modifiable areal unit problem in GIScience. This method automatically dissolves adjacent features updating fields’ values to reach a minimum target area or attribute value, using a flexible settings framework to meet user requirements. Also provided as a toolbox for ArcGIS (Esri), the approach is demonstrated by (i) estimating the mean particulate matter concentrations for all municipalities in Italy in 2011 by combining a coarse grid of global PM2.5 concentrations with fine administrative units; (ii) estimating boundaries of Metropolitan areas in Portugal as aggregation of municipalities, by matching their total population.

The relative roles of different land-use types in bike-sharing demand: A machine learning-based multiple interpolation fusion method

Land use plays a crucial role in promoting the bike-sharing demand. Traditionally, studies on bike-sharing demand (BSD) are mainly focused on its prediction through regression methods, but the influence of MAUP (modifiable areal unit problem) in modeling is ignored. This paper aims to model spatial BSD distribution and prove the driving forces of different land use types to BSD through a machine-learning-based multiple interpolation fusion method. The hotspot detection model is employed to establish sample points covering different land use types in urban areas. In order to capture the differences in adaptations among different urban regions and for different data sizes, six machine learning methods are applied and evaluated to improve BSD estimation by fusing five spatial interpolation algorithms, including Inverse Distance Weight, Spline, Kriging, Natural Neighborhood and Trend. The methodological verification of Beijing City shows that the fusion models improve the estimation performance compared with individual interpolation algorithms, and that GRNN (generalized regression neural network) method is superior to all the others. According to fitting results of all POIs based on the GRNN fusion model, we identify which types of facilities correspond to customers that will have a stronger preference for bike-sharing and demonstrate which facility names are more prominent in each land use type. The conclusions presented here enrich our understanding relationships between land-use and BSD, which provide a valuable foundation for the bike-sharing development. Compared with implementing regression in an analysis zone or a square grid, troubles caused by the MAUP are effectively solved through this method.

Performance of the supervised generative classifiers of spatio-temporal areal data using various spatial autocorrelation indexes

This article is concerned with a generative approach to supervised classification of spatio-temporal data collected at fixed areal units and modeled by Gaussian Markov random field. We focused on the classifiers based on Bayes discriminant functions formed by the log-ratio of the class conditional likelihoods. As a novel modeling contribution, we propose to use decision threshold values induced by three popular spatial autocorrelation indexes, i.e., Moran’s I, Geary’s C and Getis–Ord G. The goal of this study is to extend the recent investigations in the context of geostatistical and hidden Markov Gaussian models to one in the context of areal Gaussian Markov models. The classifiers performance measures are chosen to be the average accuracy rate, which shows the percentage of correctly classified test data, balanced accuracy rate specified by the average of sensitivity and specificity and the geometric mean of sensitivity and specificity. The proposed methodology is illustrated using annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 unicipalities in the period from 2001 to 2019. Classification model selection procedure is illustrated on three data sets with class labels specified by the threshold to mortality index due to acute cardiovascular event, malignant neoplasms and diseases of the circulatory system. Presented critical comparison among proposed approach classifiers with various spatial autocorrelation indexes (decision threshold values) and classifier based hidden Markov model can aid in the selection of proper classification techniques for the spatio-temporal areal data.

Exploring the Relative Importance and Interactive Impacts of Explanatory Variables of the Built Environment on Ride-Hailing Ridership by Using the Optimal Parameter-Based Geographical Detector (OPGD) Model

The impact of the built environment on the ridership of ride-hailing results depends on the spatial grid scale. The existing research on the demand model of ride-hailing ignores the modifiable areal unit problem (MAUP). Taking Chengdu as an example, and taking the density of pick-ups and drop-offs as dependent variables, 12 explanatory variables were selected as independent variables according to the “5D” built environment theory. The nugget–sill ratio (NSR) method and optimal parameter-based geographical detector (OPGD) model were used to determine the optimal grid scale for the aggregation of the built environment variables and the ridership of ride-hailing. Based on the optimal grid scale, the optimal data discretization method of the explanatory variables was determined by comparing the results of the geographic detector under different discretization methods (such as the natural break method, k-means clustering method, equidistant method, and quantile method); we utilized the geographic detector model to explore the relative importance and the interactive impacts of the explanatory variables on the ridership of ride-hailing under the optimal grid scale and optimal data discretization method. The results indicated that: (1) the suggested grid scale for the aggregation of the built environment and ride-hailing ridership in Chengdu is 1100 m; (2) the optimal data discretization method is the quantile method; (3) the floor area ratio (FAR), distance from the nearest subway station, and residential POI (point of interest) density resulted in a relatively high importance of the explanatory variable that affects the ridership of ride-hailing; and (4) the interactions of the diversity index of mixed land use ∩ FAR, distance to the nearest subway station ∩ FAR, transportation POI density ∩ FAR, and distance to the central business district (CBD) ∩ FAR made a higher contribution to ride-hailing ridership than the single-factor effect of FAR, which had the highest contribution compared with the other explanatory variables. The proposed grid scale can provide the basis for the partitioning management and scheduling optimization of ride-hailing. In the process of adjusting the ride-hailing demand, the ranking results of the importance and interaction of the built-environment explanatory variables offer valuable references for formulating the priority renewal order and proposing a scientific combination scheme of the built-environment factors.

Spatially Weighted Bayesian Classification of Spatio-Temporal Areal Data Based on Gaussian-Hidden Markov Models

This article is concerned with an original approach to generative classification of spatiotemporal areal (or lattice) data based on implementation of spatial weighting to Hidden Markov Models (HMMs). In the framework of this approach data model at each areal unit is specified by conditionally independent Gaussian observations and first-order Markov chain for labels and call it local HMM. The proposed classification is based on modification of conventional HMM by the implementation of spatially weighted estimators of local HMMs parameters. We focus on classification rules based on Bayes discriminant function (BDF) with plugged in the spatially weighted parameter estimators obtained from the labeled training sample. For each local HMM, the estimators of regression coefficients and variances and two types of transition probabilities are used in two levels (higher and lower) of spatial weighting. The average accuracy rate (ACC) and balanced accuracy rate (BAC), computed from confusion matrices evaluated from a test sample, are used as performance measures of classifiers. The proposed methodology is illustrated for simulated data and for real dataset, i.e., annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 municipalities in the period from 2001 to 2019. Critical comparison of proposed classifiers is done. The experimental results showed that classifiers based on HMM with higher level of spatial weighting in majority cases have advantage in spatial–temporal consistency and classification accuracy over one with lower level of spatial weighting.

Privacy by Projection: Federated Population Density Estimation by Projecting on Random Features.

We consider the problem of population density estimation based on location data crowdsourced from mobile devices, using kernel density estimation (KDE). In a conventional, centralized setting, KDE requires mobile users to upload their location data to a server, thus raising privacy concerns. Here, we propose a Federated KDE framework for estimating the user population density, which not only keeps location data on the devices but also provides probabilistic privacy guarantees against a malicious server that tries to infer users' location. Our approach Federated random Fourier feature (RFF) KDE leverages a random feature representation of the KDE solution, in which each user's information is irreversibly projected onto a small number of spatially delocalized basis functions, making precise localization impossible while still allowing population density estimation. We evaluate our method on both synthetic and real-world datasets, and we show that it achieves a better utility (estimation performance)-vs-privacy (distance between inferred and true locations) tradeoff, compared to state-of-the-art baselines (e.g., GeoInd). We also vary the number of basis functions per user, to further improve the privacy-utility trade-off, and we provide analytical bounds on localization as a function of areal unit size and kernel bandwidth.

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.