Spatial Heterogeneity Analysis of Urban Service Distribution in Tabriz Metropolis Using Geographically Weighted Regression and Spatial Autocorrelation Indices

A B S T R A C T
The spatial distribution of urban services plays an essential role in achieving spatial justice, improving quality of life, and enhancing the efficiency of the urban planning system. Unbalanced physical expansion, concentration of activities, and population growth in the metropolis of Tabriz have led to spatial inequality in the allocation of services and reduced accessibility for residents. This study is applied in terms of objective and descriptive–analytical in nature, employing a spatial–statistical approach to analyze the spatial pattern of urban services and assess its compatibility with population density across the urban districts of Tabriz. Spatial data on services and population were analyzed in a GIS environment using Kernel Density estimation, the Average Nearest Neighbor (ANN) index, Global Moran’s I spatial autocorrelation index, and the Geographically Weighted Regression (GWR) model. The results indicate that most urban services follow a clustered pattern with high concentration in the central core of the city, whereas both the density and diversity of services decrease with increasing distance from the center. ANN values below one and positive, statistically significant Moran’s I values confirm the presence of positive spatial autocorrelation and a structured concentration of services. Results of the GWR model further demonstrate spatial heterogeneity in the relationship between population density and service abundance; the strength of this relationship varies across diverse districts, and no whole alignment between population needs and service provisions is not observed. This situation reflects challenges in attaining both horizontal and vertical equity in the distribution of urban services. Accordingly, strengthening peripheral service centers and revising service location policies are essential to reduce spatial inequality.
Extended Abstract
Introduction
The rapid pace of urbanization, the concentration of population, and economic activities in metropolitan areas have made the spatial reorganization of urban services and the systematic evaluation of their distribution patterns a central concern in urban planning. The spatial distribution of urban services not only influences infrastructure efficiency and transportation systems but is also directly linked to quality of life, equality of opportunities, and the realization of spatial justice. The concentration of services in central areas and their scarcity in peripheral zones contribute to a core–periphery pattern and the reproduction of spatial inequality. International literature indicates that such spatial mismatches result from the interplay of physical structures, demographic dynamics, land market mechanisms, and urban policy decisions, and their analysis requires advanced spatial–statistical frameworks. In recent decade, the utilization of GIS tools, density analysis, spatial autocorrelation indices, neighborhood statistics, and location-based regression models has enabled the identification of service clusters, deficit areas, and spatial heterogeneity in the relationship between population and services. In Iran, numerous studies have examined spatial justice in urban services; however, many have concentrated chiefly on per capita indicators, ranking techniques, and multi-criteria decision-making models, with limited attention to modeling spatial non-stationarity in the population–service relationship. Consequently, data-driven and GIS-based studies that analytically and explanatorily assess the actual distribution of services and their alignment with population structure remain essential. Within this framework, the present study integrates Kernel Density analysis, the Average Nearest Neighbor index, Global Moran’s I, and regression models to investigate the spatial organization of urban services in the metropolitan city of Tabriz.
 
Methodology
This study employs a quantitative, applied approach with a descriptive-analytical design and a spatial-statistical methodology. The unit of analysis consists of 38 urban districts within Tabriz city. Population data were obtained from the 2016 national census, and population density was calculated as the independent variable. Spatial data for 12 types of urban services were collected in point format and analyzed using ArcGIS 10.8.2. Kernel Density, the Average Nearest Neighbor index, and Global Moran’s I were applied to examine spatial distribution patterns. The relationship between population density and the number of services at the district level was first modeled using Ordinary Least Squares (OLS) and subsequently with Geographically Weighted Regression (GWR). In conclusion, spatial autocorrelation of model residuals was assessed to evaluate model adequacy.
 
Results and Discussion
The findings indicate that the spatial distribution of urban services in the metropolis of Tabriz is predominantly concentrated and clustered, significantly reflecting the city’s center–periphery structure. Kernel density analysis and the Average Nearest Neighbor index (ANN < 1) disclose spatial concentration of most services within the central core. Positive and statistically significant Global Moran’s I values confirm the presence of positive spatial autocorrelation and a structured clustered pattern. However, the intensity of concentration varies across service types. Commercial, cultural–artistic, and religious services illustrate the highest density within the historical core, whereas network-based and safety-related services such as metro, BRT, fire stations, and CNG stations exhibit a more dispersed distribution pattern governed by network logic. Comparison of OLS and GWR models demonstrates that, for most services, GWR provides improved model fit through higher R² values and lower AICc scores, confirming spatial non-stationarity in the relationship between population density and service distribution. The variation in Local R² and local coefficients indicates spatial heterogeneity at the district level. In the eastern zones, despite low population density, positive and significant coefficients suggest proactive service development. In contrast, northern high-density districts exhibit weak or negative coefficients for certain services, indicating a mismatch between service provision and demographic demand. In the central core, historical accumulation of services has resulted in their relative independence from the current population structure. Overall, the distribution pattern of urban services in Tabriz reflects a combination of historical concentration, network-based logic, and spatial heterogeneity in the population–service relationship.
 
Conclusion
The results of this study indicate that the urban service distribution system in Tabriz has not developed according to a balanced and needs-based pattern, rather reflects the historical accumulation of investments and development priorities within the central core. The statistically significant concentration of services in the city center and their gradual decline toward peripheral areas demonstrate the persistence of a center–periphery structure in the spatial organization of services. This concentration is merely a function of the functional attractiveness of the historical core but also a consequence of location policies driven by economic efficiency and central accessibility. Spatial non-stationarity analysis reveals that the relationship between population density and service provision is not uniform across the city. In certain high-density areas—particularly in the northern districts—the weak correlation between population and number of services indicates relative shortages and deficiencies in vertical equity. Simultaneously, noticeable differences in service levels among districts with similar population densities reflect shortcomings in horizontal equity. Conversely, proactive service development in eastern areas illustrates that planned interventions can promote spatial balance prior to demographic pressure. Thus, the principal issue in Tabriz is not merely service scarcity, but spatial misalignment between service allocation and demographic dynamics. The Continuation of this pattern may intensify access inequalities and increase functional pressure on the central core. Revising service location policies, strengthening peripheral service centers, and systematically incorporating non-stationary spatial models into urban decision-making are essential steps toward realizing sustainable spatial justice in Tabriz.
 
Funding
There is no funding support.
 
Authors’ Contribution Statements
Mohammad Shali: Supervision, project administration, conceptualization, methodology design, data analysis, writing – original draft, and final approval of the version to be published
Hessam Esmaeili Qezeljeh Meydan: Data collection and updating, literature review, and initial draft preparation
 
Conflict of Interest
Authors declared no conflict of interest.
 
Acknowledgments
We are grateful to all the scientific consultants of this paper.