Areal Unit Research Articles

A zero‐inflated Poisson spatial model with misreporting for wildfire occurrences in southern Italian municipalities

AbstractWe propose a Poisson model for zero‐inflated spatial counts contaminated by measurement error: we accommodate the excess of zeroes in the counts, consider the possible under/over reporting of the response and account for the neighboring structure of spatial areal units. Bayesian inferences are provided by MCMC implementation through the R package NIMBLE. To evaluate the model performance, a simulation study is carried out under configurations that allow for structured and unstructured spatial random effects. The proposed model is applied to investigate the distribution of the counts of wildfire occurrences in the municipal areas of two neighboring Italian regions for the summer season 2021. Fire counts are obtained by processing MODIS satellite data, while several socio‐economic and environmental‐driven potential risk factors are also considered in the model formulation. Data from multiple sources with different spatial support are processed in order to comply with the municipal units. Results suggest the appropriateness of the approach and provide some insights on the features of wildfire occurrences.

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.

Accessibility, Rural depopulation & the Modified Areal Unit Problem: An analysis of mainland Greece

In the realm of new economic geography studies, an ongoing debate centers around the role of transportation costs in redirecting economic activity away from peripheral areas towards urban spaces. This theory gains support from the phenomenon of rural depopulation in developed countries, as it is generally accompanied by improvements in accessibility due to new infrastructure and technology. This study introduces a methodology for analyzing the relationship between accessibility and regional inequality while accounting for rural depopulation. Moreover, it acknowledges the significance of the measurement timeframe, as the dynamics between accessibility components are not always synchronous. The developed methodology is employed for investigation within the geographical region of main-land Greece. The findings reveal that relative accessibility, in contrast to absolute accessibility, exhibits a correlation with rural depopulation in mainland Greece. Finally, the study examines the Modified Areal Unit Problem (MAUP) to address inconsistencies observed in similar spatial studies. The disparities in results among the various geographical administrative levels carry substantial implications for policymakers dealing with issues of urbanization and uneven regional development.

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.

Comparisons of Hounsfield units and volumetric bone density in discriminating vertebral fractures on lumbar CT scans.

To compare the performance of areal Hounsfield units (aHUs), volumetric Hounsfield units (vHUs), and volumetric bone mineral density (vBMD) by quantitative CT (QCT) in discriminating vertebral fractures (VFs) risk. We retrospectively included CT scans of the lumbar spine 101 VFs cases (60 women, mean age: 64 ± 4 years; 41 men, mean age: 73 ± 10 years) and sex- and age-matched 101 control subjects (60 women, mean age: 64 ± 4 years; 41 men, mean age: 72 ± 7 years). In order to assess the discriminatory capability of aHU, vHU, and vBMD measurements at the L1 and L2 levels in identifying VFs, we conducted binary logistic regression and receiver operating characteristic (ROC) curve analyses in men and women. Sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were calculated. In both men and women with and without VFs, aHU, vHU, and vBMD were highly correlated with each other (r2 from 0.832 to 0.957, all P < .001). There was a statistically significant difference in aHU, vHU, and vBMD between subjects with and without VFs (P < .001). When age, gender, and BMI were taken into account as covariances and adjusted simultaneously, odds ratios (ORs) for aHU, vHU, and vBMD values, which represent the risk of VFs, were significant (P < .001). Compared with aHU and vHU, vBMD was more strongly associated with VF risk (vBMD: OR, 6.29; 95% CI, 3.83-10.35 vs vHU: OR, 3.64; 95% CI, 2.43-5.46 vs aHU: OR, 2.56; 95% CI, 1.79-3.67). In both men and women, further, vBMD had higher values for AUC, sensitivity, specificity, PPV, and NPV compared to vHU, with vHU in turn surpassing aHU. The area under the receiver operating characteristic curve (AUC) for discriminating VFs using the average aHU, vHU, and vBMD of 2 vertebrae was 0.72, 0.77, and 0.87 in men and 0.76, 0.79, and 0.86 in women. In both men and women, there exist statistically significant differences in the AUC when employing the 3 measurements-namely, aHU, vHU, and vBMD-to discriminate fractures (P < .05). The QCT-measured vBMD is more associated with acute VFs than vHU and aHU values of the lumbar spine. Although the use of vHU and aHU values for the diagnosis of osteoporosis and discriminating fracture risk is limited to scanner- and imaging protocol-specific, they have great potential for opportunistic osteoporosis screening, particularly vHU. The novelty of this study presents a comparison of the VF discriminative capabilities among aHU, vHU, and vBMD. The vHU values introduced in this study demonstrate a greater capacity to discriminate fractures compared to aHU, presenting an improved clinical choice. Although its discriminatory capability is slightly lower than that of vBMD, it is more convenient to measure and does not require specialized software.

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

Quantitative analysis of fractional vegetation cover in southern Sichuan urban agglomeration using optimal parameter geographic detector model, China

Vegetation is a main part of ecosystems and an essential indicator for monitoring changes in terrestrial ecosystems. It is crucial for us to discover the temporal and spatial features and potential drivers of vegetation change to promote regional ecological environment protection and management. However, it can be difficult to pinpoint the causes of vegetation change when considering both human activity and climate change. We used trend and stability method to study the temporal and spatial patterns of vegetation evolution in the South Sichuan Urban Agglomeration (SSUA) from 2001 to 2021 with the Google Earth Engine (GEE) platform. An optimal parameter-based geographical detector (OPGD) model was applied to optimize the spatial scale and zoning effect of geographic data, effectively solving the problem of spatial data heterogeneity. It compensates for the inadequacies of conventional approaches that neglect the modifiable areal units problem (MAUP), and improving the science and accuracy of quantitative analysis and identification of vegetation drivers. We studied demonstrate that (1) During the last 21 years, Fractional Vegetation Cover (FVC) has generally been in good condition, with a multi-year average FVC greater than 0.4 of 71.74 %, and the vegetation is significantly characterized by a low fluctuation of 78.16 %. However, there is a significant trend of vegetation degradation, accounting for 8.89 %, mainly in the main urban areas of Neijiang and Zizhong County, Lu County of Luzhou City, Gao County of Yibin City, and other areas with rapid urbanization. In general, FVC is low in the built-up areas of towns and along transportation roads, while the mountainous and agricultural areas have a high level of vegetation cover. (2) The OPGD model detection showed the optimal spatial scale of vegetation cover in this study region was 2 km. Optimal discrete parameter combinations for slope, elevation, temperature and GDP are quantile breaks with 9 intervals, which contribute to improved scientific accuracy and precision in studies of vegetation change and its drivers. (3) The explanatory power of urbanization rate, land use type, slope, GDP, population density, and average annual precipitation were all above 20 % and were the main drivers of vegetation change. Moreover, any two factors interacted in a nonlinear enhancement and a bi-variable enhancement, increasing the impact on vegetation spatial variation. When the slope is 26.9°∼87.4°, the elevation is 967 m ∼ 4207 m, the average annual temperature is 0.18 °C ∼ 13.6 °C, the average annual precipitation is 328 mm ∼ 439 mm, the GDP is 4.07 ∼ 5.23 million yuan km−2, the population density is 12.7 ∼ 21.1 people/km2, the urbanization rate is 33.4 %∼37.7 %, and the land-use type is forest land, the FVC value is the highest and suitable for vegetation growth. The study showed that using the OPGD model to detect the zoning effects and spatial scale of the explanatory variables solves for the shortcomings of the previous methods for variable regional units and discrete methods, may more precisely explore the features of temporal and spatial changes in the vegetation and the driving mechanisms, offers scientific references for environmental conservation and long-term economic growth in the region.

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.

Conceptual and Methodological Arguments against the Use of Location Quotient as an Area-Based Measure of Residential Segregation: A Measurement Perspective

Among a wide range of practical applications, the location quotient (LQ) has been used as an area-based measure of residential segregation by race/ethnicity in some studies. However, it does not correspond to any of the five dimensions of residential segregation. Rather, an application of LQ in demographic data analyses brings about an atypical way to quantify the population composition of areal units by race/ethnicity. To clarify misconceptions, the purpose of this study was to demonstrate the relationships between proportions, percentages, and LQs of six racial/ethnic groups in the conterminous United States (US). Since populations change over time, demographic data on race and ethnicity were obtained from the 2000, 2010, and 2020 Census through the US Census Bureau’s website. Using census tracts and counties as the units of analysis, a sequence of scatterplots and associated Pearson’s correlation coefficients (r) was used to display the analytical results of census-tract- and county-based measures at three different time periods. Despite the different levels of aggregation, the relationships between proportions, percentages, and LQs of six racial/ethnic groups consistently showed perfect positive correlations at three different time periods (r = 1.00). These suggest that census-tract- and county-based measures expressed as the proportion, percentage, and LQ of a racial/ethnic group capture the same distributional pattern, but the units of measurement simply differ from one another. Hence, the study of residential segregation and its societal consequences needs to be specific to the dimension under study and to build upon the conceptual and methodological foundations established by sociologists-demographers and geographers.

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.

Computationally efficient localised spatial smoothing of disease rates using anisotropic basis functions and penalised regression fitting

The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to N areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across N=32,754 Lower Super Output Areas in England. The approach is based on a computationally efficient ridge regression framework, where the spatial trend in disease rates is modelled by a set of anisotropic spatial basis functions that can exhibit either smooth or step change transitions in values between neighbouring areal units. The efficacy of this approach is evidenced by simulation, before using it to identify the highest rate areas and the magnitude of the health inequalities in four measures of mental ill health, namely antidepressant usage, benefit claims, depression diagnoses and hospitalisations.

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.

Marginal-Preserving Imputation of Three-Way Array Data in Nested Structures, with Application to Small Areal Units

Geospatial population data are typically organized into nested hierarchies of areal units, in which each unit is a union of units at the next lower level. There is increasing interest in analyses at fine geographic detail, but these lowest rungs of the areal unit hierarchy are often incompletely tabulated because of cost, privacy, or other considerations. Here, the authors introduce a novel algorithm to impute crosstabs of up to three dimensions (e.g., race, ethnicity, and gender) from marginal data combined with data at higher levels of aggregation. This method exactly preserves the observed fine-grained marginals, while approximating higher-order correlations observed in more complete higher level data. The authors show how this approach can be used with U.S. census data via a case study involving differences in exposure to crime across demographic groups, showing that the imputation process introduces very little error into downstream analysis, while depicting social process at the more fine-grained level.

Is prefecture-level city a “city” in China: a critical review

ABSTRACT The definition and boundaries of cities often determine how research is undertaken due to the areal units used to provide geo-located data and thus affect the research findings. Prefecture-level cities are popular city-equivalent statistical units in China, particularly in studies of inter-city mobility. Most prefecture-level cities in China have been delineated as meso-scale administrative divisions for territorial governance through various approaches of administrative annexation. This study takes a critical look at the city definition in China and summarizes two critical challenges that emerge when prefecture-level cities are adopted as city-equivalent statistical units. The first challenge is that the population and other socioeconomic statistics of different prefecture-level cities are incomparable since a large amount of land administered by such cities is functionally rural. The second challenge is that, because prefecture-level cities cannot represent the real functional areas that are based on a daily labor-shed concept, the estimation of inter-city mobility could be largely erroneous by conflating the real inter-city travel with the de facto intra-metropolitan travel such as daily commuting. While the first challenge has long been addressed by scholars and eventually by the national government of China in 2008, the second challenge remains to be solved. These two challenges demand rigorous attempts to delineate cities in China considering integrated economic and social units. This study sheds light on how delineation of administrative boundaries affects our understanding of city hierarchy and spatial interactions. Its implications are not limited to China but applicable to other countries and regions.

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.