Modeling Urban Green Access: Combining Zone-Based Proximity and Demand-Weighted Metrics in a Medium-Sized U.S. City

Abstract

Urban green space (UGS) accessibility is a cornerstone of equitable and sustainable city planning. However, existing studies focus on large metropolitan areas and rely on limited spatial models that overlook the complexity of urban morphology and socio-demographic diversity. This study shifts the focus to East Lansing, a medium-sized U.S. city that exhibits neither the spatial concentration of major metropolises nor the uniformity of small towns, thereby offering a distinctive context to examine urban green space equity. To this end, we develop a composite accessibility index by integrating four complementary spatial models: Euclidean distance, gravity-based access, two-step floating catchment area (2SFCA), and zone-based analysis. Utilizing high-resolution spatial, demographic, and environmental datasets, the study applies both Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) to uncover global patterns and local variations in accessibility determinants. The results reveal pronounced neighborhood-level disparities, with variables such as green coverage, park provision, and commercial density emerging as significant but spatially uneven predictors. The composite index yields a more robust and equitable representation of UGS accessibility than any individual model. This multi-model, spatially explicit framework contributes to methodological advances in accessibility assessment and offers actionable insights for place-based urban greening strategies.

1. Introduction

Urban green spaces (UGSs) are an essential component of sustainable cities, encompassing parks, gardens, greenways, and street trees that bring ecological, social, and health benefits to urban residents. These enable biodiversity and microclimate regulation, while also providing public health benefits, opportunities for social interaction, and enhanced well-being. Recent research has further highlighted that the spatial and temporal patterns of UGS significantly contribute to mitigating urban heat island (UHI) effects, particularly in the context of urban densification, thereby enriching the theoretical understanding of their ecosystem service functions [1]. With accelerated urbanization in the world, access to UGS has been a central part of urban environmental justice [2,3]. Although green infrastructure has been increasingly in vogue worldwide, the equitable allocation and accessibility of UGS continues to be extremely uneven, mirroring and sustaining larger socio-economic disparities within the urban system.

Inequalities in access manifest not only through spatial distance or usage patterns of UGSs, but also through deeper structural and social concerns tied to urban form and social hierarchy. Numerous studies have shown that marginalized groups such as poor families, ethnic minorities, immigrants, and the elderly are deprived of quality UGSs [4]. This has been further supported by practice-based research on urban green equity in multicultural contexts, which highlights distributional and recognitional inequities in cities such as New York, Phoenix, and Portland, and offers practical models for addressing these disparities [5]. Empirical studies also reveal that such inequities are not coincidental but structurally embedded: for instance, Dai [6] found that neighborhoods with higher concentrations of African Americans and socioeconomically disadvantaged populations in Atlanta had significantly poorer access to green spaces, while similar inequities were observed in Chicago, where spatial analyses revealed systematic mismatches between green space distribution and the needs of low-income and minority residents. This disparity contributes to unequal access to clean air, reduced mitigation of urban heat island effects, and fewer opportunities for physical activity, thereby exacerbating health inequalities. For example, residents of socioeconomically deprived communities are more vulnerable to air pollution and urban heat islands due to insufficient vegetation cover and limited opportunities for engaging in daily activities provided by UGSs [7]. In addition to physical health, inadequate access to UGSs has also been associated with adverse mental health outcomes, including elevated risks of depression and anxiety disorders. Recent evidence further demonstrates that inequitable distribution of green spaces undermines residents’ subjective well-being: disparities in accessibility create a spatial mismatch between green equity and happiness, particularly among vulnerable groups such as the elderly, low-income, and immigrant populations [8]. Therefore, UGS accessibility serves as a valuable indicator for assessing social equity in urban environments.

Accessibility is widely acknowledged as a central dimension of equity in UGS, determining who benefits from environmental and social resources in cities. However, measuring accessibility involves significant methodological complexity. For instance, Euclidean distance and buffer analysis are straightforward to implement and provide intuitive measures of proximity, but they ignore variations in service capacity and user demand. Gravity models enhance proximity-based approaches by incorporating distance decay functions and attraction effects, but they are highly sensitive to parameter settings and may oversimplify behavioral assumptions. The two-step floating catchment area (2SFCA) method addresses demand–supply balance more explicitly, but it relies on fixed catchment thresholds and may overlook dynamic mobility patterns [9]. In addition, actual accessibility is influenced not only by spatial configuration but also by behavioral and contextual factors, such as transportation modes, park typologies, and temporal patterns of use [10]. While advances in geospatial analytics and machine learning have expanded technical capabilities, existing studies often apply these models in isolation rather than in combination, thereby limiting their capacity to capture the multifaceted nature of accessibility.

Although attention to UGS accessibility has grown, most studies remain concentrated on megacities such as Beijing, London, or New York, with limited examination of medium-sized cities, particularly at the neighborhood scale where spatial heterogeneity is most evident [2,11]. Furthermore, conventional approaches frequently rely on static models and formal parkland, while paying insufficient attention to the combined influence of environmental heterogeneity and socio-demographic diversity. While issues such as informal UGS or subjective experiences are important, they fall outside the focus of this study. Instead, our work emphasizes the methodological limitations of existing models and addresses them through an integrated multi-model approach [3,12]. Safety, comfort, and cultural appropriateness are also relevant factors, though they are less frequently integrated into accessibility evaluations [12]. These limitations require cross-scale, multi-variable modeling platforms that integrate both behavioral and spatial dimensions.

Beyond methodological innovation, this integration also provides practical value for urban planning: it enables more equitable prioritization of green investment, supports neighborhood-level comparisons in medium-sized cities, and informs strategies to mitigate health inequalities linked to environmental exposures. To address the gaps in research, the present research examines the spatial accessibility of UGS in East Lansing, Michigan, a medium-sized city that typifies many understudied urban contexts in the United States. It serves as an illustrative case for analyzing UGS accessibility in medium-sized U.S. cities. Although global cities like New York or Beijing may not be strictly centralized in spatial structure, East Lansing cannot be equated with small towns due to its population scale and spatial diversity. The coexistence of a large student population, long-term residents, and suburban areas generates heterogeneous demand for green spaces within a compact urban footprint. These characteristics position East Lansing as a significant test case for determining how rival ac-accessibility models capture neighborhood-level inequities in a context that is neither hyper-urban nor homogeneous. Findings from this case can inform broader debates on equitable urban greening by highlighting challenges and possibilities in medium-sized cities collectively hosting a disproportionate share of the U.S. population yet rarely represented in the accessibility literature.

This study aims to address the following research questions:

• How is UGS accessibility different across urban neighborhoods when estimated by different spatial models?
• Which environmental, land use, and demographic factors are highly associated with variability in accessibility?
• How do spatial regression models help to reveal spatial heterogeneity and inequality in access to UGS?

Building on these questions, we advance the following expectations:

H1: 

Composite measures that integrate multiple spatial models will capture neighborhood-level disparities in UGS accessibility compared to any single model.

H2: 

Environmental and land use factors (e.g., canopy cover, park provision) will be stronger predictors of accessibility in some neighborhoods, while socio-demographic variables (e.g., income, age structure) will play a larger role in others.

H3: 

Geographically Weighted Regression (GWR) will reveal non-stationary effects, demonstrating that the relationships between accessibility and its determinants vary significantly across space.

To achieve this, the study adopts a multi-method approach by applying a variety of commonly used accessibility measures, including Euclidean distance, gravity-based models, and the 2SFCA method. The independent variables include land use composition, park typologies, canopy cover, and demographic characteristics derived from the American Community Survey. Both geographically weighted regression (GWR) and ordinary least squares (OLS) regression are used to contrast associations between UGS accessibility and the said variables. This approach enables a comprehensive exploration of contextual inequalities and spatial variations in the availability of UGS, facilitating richer insights into urban planning and spatial justice.

The paper is structured as follows. Section 2 reviews the literature on UGS equity and spatial accessibility modeling. Section 3 introduces the study area, data, and the construction of a composite index based on four spatial models. Section 4 presents the results of accessibility comparisons and regression analyses using OLS and GWR. Section 5 discusses the implications for spatial equity and green planning in medium-sized cities. Section 6 concludes with a summary of contributions and future directions. This study contributes to the emerging body of literature through the application of a multi-model, multi-variable spatial strategy to the analysis of UGS accessibility in a medium-sized city, incorporating high-resolution data and spatially responsive techniques to address both methodological and contextual gaps.

2. Literature Review

2.1. Conceptualizing Accessibility

Urban green space (UGS) accessibility has now been recognized as a multifaceted concept extending far beyond physical proximity [2,13,14]. Earlier indicators often conflated accessibility with availability, focusing primarily on the overall extent or presence of UGS within administrative boundaries [15]. This does not indicate whether individuals can reach, access, or safely use such UGS. Current research emphasized the critical distinction between availability (provision of green infrastructure) and accessibility (operational capability for use), particularly for spatial justice and environmental equity [3]. Accessibility is guided by a synergy between spatial forces (e.g., geographical location, travel barriers), social attributes (e.g., household income, age, ethnicity), and behavioral attributes (e.g., mobility profiles, personal likes/dislikes). Scholars have complemented this analysis by integrating network-based travel behavior with users’ cultural and perceptual dimensions to enhance the representation of differential access [16,17]. Such developments point out that accessibility transcends the subject matter of spatial measurement but is instead a socially embedded, context-sensitive issue that continues to be at the forefront of just green infrastructure planning.

2.2. Measurement Approaches of Accessibility

Several spatial models have been developed to measure access to UGS, differing in assumptions, computational requirements, and planning relevance [18,19,20]. The most straightforward approaches, such as Euclidean distance and buffer analysis, rely on straight-line proximity or fixed-radius buffers to estimate access. While computationally efficient, these methods oversimplify urban mobility by assuming uniform terrain and ignoring barriers such as fragmented land use or irregular street grids [21]. As a result, they often inflate accessibility estimates in auto-oriented or spatially segregated contexts.

More advanced approaches, including gravity-based models, improve upon these limitations by integrating distance decay and UGS attractiveness. However, they are highly sensitive to parameter specification, such as the choice of decay function or catchment threshold, potentially altering results significantly and undermining cross-study comparability [22]. The two-step floating catchment area (2SFCA) method has been widely adopted in health and equity research because it simultaneously accounts for supply and demand, yet it also inherits a strong dependence on predefined catchment sizes. Enhancements like generalized 2SFCA and variable catchment models attempt to address this rigidity, but they introduce additional assumptions about behavioral sensitivity and travel thresholds that are rarely validated empirically [23,24].

Comparison studies further demonstrate that model selection is not merely a technical consideration but a substantive determinant shaping the interpretation of spatial equity [25,26,27]. For instance, buffer models may suggest universally high access in dense urban centers, while gravity or 2SFCA models reveal acute disparities once competition for resources is considered. This study responds to such concerns by adopting a multi-model strategy, which enables a more robust comparison of access outcomes under different assumptions and allows equity patterns to be interpreted with greater contextual sensitivity.

2.3. Socio-Spatial Inequalities in UGS

UGS is not a homogeneous category but a composite of heterogeneous typologies with varying appearance, purpose, size, and accessibility. Official UGSs such as public parks, botanical gardens, and sports grounds are often planned and managed by municipal authorities, while unofficial UGSs, such as derelict lots, roadside vegetation, or unbuilt parcels emerge spontaneously and may play important social or ecological roles despite lacking official status [22,28]. These differences in function and type substantially influence how easily a UGS is reached by various groups of users. Bigger destination parks can have additional amenities but are usually more remote from housing locations, while small community parks or linear greenways are often more closely integrated into daily activity spaces and hence closer to pedestrian users and the physically vulnerable [29]. Land use type also has significant potential to influence both UGS distribution and the corridors along which people encounter UGS. Resettlement areas of high density, mixed use, and transit areas are likely to have UGS networks integrated within them, while automobile-oriented or industrial areas are more likely to experience UGS fragmentation or absence. Multiple pieces of research indicated that failing to account for typological diversity within UGSs may result in misinterpretation of outcomes on accessibility as well as lessen the relevance of policies, particularly research based upon the boundaries of parks or ratio measures of greenspaces [30,31]. Incorporating land use data and differentiating among UGS types allows more advanced analysis that considers actual potential for participation, environmental accessibility, and ecosystem service provision [32,33]. Typological variation is especially important in analyses of spatial equity because marginalized groups may be more reliant on informal or smaller-scale UGSs that are often excluded from official planning records.

UGS access is generally disproportionally allocated to socio-demographic groups, exacerbating general structural patterns of environmental injustice and inequality. Much of the research has shown that the low-income population, racial and ethnic minorities, older adults, children, and people with disabilities frequently face both physical and social barriers to quality UGSs [34]. These disparities are driven largely by long-standing disinvestment dynamics, exclusionary zoning ordinances, and racially discriminatory urban planning that have generated uneven spatial patterns of green infrastructure [35]. Empirical studies indicate that the percentage of minority or low-income communities is often located further away from big or well-cared-for parks and face higher obstacles related to safety, upkeep, and access [34,36]. In addition, gender and age also shape how individuals perceive and use UGSs, such as women and older people can avoid certain areas due to mobility and safety concerns [35]. These variations are also intensified by unequal mobility resource access, such as car ownership or pedestrian facilities [37], which determine whether UGSs are not just physically accessible but also functionally usable [38]. Recent research emphasizes how such socio-spatial inequalities are written into urban form and embedded in urban morphology and reflected in policy implementation [19]. Solving such issues requires incorporating equity-oriented indicators in accessibility analysis to promote environmental justice and public health equity in UGS planning.

2.4. Spatial Statistical Approaches

Spatial statistical models are now an essential instrument for analyzing the geographically varying and complex relations between accessibility to UGS and its determinants [22,39]. Ordinary Least Squares (OLS) regression has long served as a standard method for examining associations between socio-environmental predictors and accessibility indices. Nevertheless, OLS assumes spatial stationarity, i.e., it does not account for the potential that varying relations between variables may vary across geographic space [40]. This deficiency is particularly problematic in urban studies, as the influences of land use patterns, socio-economic conditions, or park typologies on accessibility usually have local variations due to spatial heterogeneity. When such variation is ignored, statistical results may suggest a misleading sense of uniformity, obscuring the fact that disadvantaged neighborhoods often face distinctly different barriers compared to affluent ones. In practice, global coefficients estimated by OLS can understate inequities in some areas while overstating them in others, thereby limiting the effectiveness of targeted policy interventions.

In response, Geographically Weighted Regression (GWR) has emerged as a stronger option where coefficients may vary by location and thus identify spatially dependent relationships. Applications in GWR have shown significant increases in model goodness-of-fit and explanation, particularly where accessibility varies in response to complex and disjointed metropolitan structures [41]. Yet the method is also sensitive to bandwidth choices and can generate results that are harder to interpret across contexts, which limits its direct transferability to policy.

Advances lately have extended the case of GWR to multiscale forms with potential for finer-scale identification of how variable effects differ across spatial scales [33]. These models are not only beneficial for where inequities do exist but also for why and under what conditions they do occur. Moreover, spatial regression techniques offer opportunities to integrate planning-relevant factors such as housing markets, land cover, and population trends, and yield findings that are critical to equity-focused urban design and policy [38].

2.5. Research Gaps and Emerging Directions

Despite heightened interest in UGS availability, several conceptual and methodological lacunae remain. For one, the majority of research has focused on large metropolitan cities, whereas medium-sized cities characterized by different urban morphologies, land use structures, and UGS governance institutions have been comparatively under researched [37,40]. This limits the generalizability of research to date to a wider range of urban contexts. Second, most existing studies use a single accessibility model or spatial scale alone, potentially oversimplifying the complexity of accessibility and obscuring model-dependent variability in results [28,32,37]. Third, informal green UGSs, dynamic behavioral patterns, and subjective experiences such as safety and usability are often excluded from spatial analyses, even though growing evidence suggests they significantly influence how UGSs are experienced, especially for vulnerable groups [35]. Additionally, many studies fail to simultaneously account for spatial and social heterogeneity simultaneously, either by relying solely on aggregate indicators or by overlooking interactions between demographic and environmental variables at the local level [41]. In response to these limitations, scholars have increasingly called for integrated frameworks incorporating multiple accessibility indicators, multivariate spatial modeling techniques, and socially differentiated variables. These approaches offer a more nuanced, context-specific understanding of UGS equity and yield planning intervention insights that are both spatially equitable and demographically inclusive [40,42].

3. Materials and Methods

To guide the empirical process, this study adopts an integrated framework that links the three research questions with multi-source data collection, accessibility modeling techniques, and spatial-statistical methods (Figure 1).

3.1. Study Areas

This study focuses on East Lansing, Michigan (USA) as the research site (Figure 2). East Lansing is located in central Michigan, approximately at 42.73698° N latitude and 84.48387° W longitude. It is a representative mid-sized college town with a population of about 48,000 and an area of 35.2 km², exhibits diverse land use types, socio-demographic compositions, and various forms of urban green spaces (UGSs). The city is home to Michigan State University and exhibits a mixed urban morphology that supports spatial heterogeneity analysis. Datasets including land use, tree canopy, and green space layers were obtained from the City of East Lansing GIS portal, the State of Michigan Open Data platform, and publicly available satellite imagery. With high data availability and a spatially diverse urban fabric, East Lansing offers an ideal case for assessing UGS accessibility, its socio-environmental determinants, and implications for equitable urban planning.

East Lansing is analytically relevant for investigating UGS accessibility for several reasons. First, its demographic structure combines long-term residents with a large and transient university population, offering a unique setting to explore how different social groups experience access to green infrastructure. Second, as a mid-sized city, East Lansing lacks both the extreme spatial concentration of large metropolitan areas and the homogeneity of small towns, making it a critical bridge case for understanding equity patterns in cities of intermediate scale. Third, its urban morphology—characterized by fragmented residential neighborhoods, mixed land us-es, and campus-centered development—creates spatial heterogeneity that directly re-lates to our research questions on variability in accessibility and spatial equity. These features make East Lansing not only a meaningful empirical case but also a representative example of many medium-sized U.S. cities, enhancing the generalizability of the findings.

3.2. Data Collection

This study adopts a multi-source data integration approach, incorporating spatial, remote sensing, and statistical datasets to construct both independent variables and the dependent variable for analyzing UGS accessibility (

Table 1. Summary of Multi-source Datasets for UGS Accessibility Modeling.

Data	Reference Year	Resolution	Usage	Data Source
Land Use Data	2023	Vector	Classification of urban functional zones	City of East Lansing GIS Portal
Urban Green Space Boundary Data	2023	Vector	Identification of park types and sizes	Michigan Statewide GIS Database
Tree Canopy Coverage (NDVI)	2022–2023	Raster	Measurement of vegetation density and green coverage	USGS Landsat 8 and Sentinel-2 (via Google Earth Engine)
Demographic and Socio-economic Data	2020–2022	Tabular	Analysis of income, education level, age distribution, and ethnicity	U.S. Census Bureau—American Community Survey (ACS)
Housing Price Data	2023	Tabular/Point	Representation of neighborhood-level economic conditions	Zillow, Redfin
Weather and Climate Data	2022–2023	Tabular	Control variable for environmental influences on outdoor space usage	NOAA National Centers for Environmental Information
Street Network and Road Data	2023	Vector	Construction of network-based accessibility models and service areas	OpenStreetMap, City of East Lansing GIS Portal

). Spatial data, including land use and UGS boundaries, were obtained from the City of East Lansing GIS portal and the Michigan Statewide GIS database. Tree canopy coverage was derived from high-resolution satellite imagery (e.g., Landsat 8 and Sentinel-2), processed using remote sensing classification techniques. Socio-demographic variables such as population density, income level, age distribution, and education attainment were collected from the U.S. Census Bureau’s American Community Survey (ACS). Housing price data were retrieved from online real estate platforms such as Zillow (https://www.zillow.com) and Redfin (https://www.redfin.com). Additionally, local weather data were acquired from the National Oceanic and Atmospheric Administration (NOAA) to control for potential environmental influences. This diverse set of data sources provides a robust and comprehensive foundation for spatial analysis and statistical modeling of UGS accessibility.

To investigate the multifaceted determinants of UGS accessibility, this study incorporates a range of independent variables derived from spatial, socio-economic, and environmental data. Land use pattern was considered a key factor, with data obtained from city planning maps, OpenStreetMap (https://www.openstreetmap.org), and remote sensing imagery. These datasets were used to classify urban areas into residential, commercial, industrial, educational, and mixed-use zones, allowing the study to assess how the spatial configuration of land use influences accessibility to UGSs.

In addition, the classification and size of UGSs were included as important variables. Urban parks were categorized into community parks, regional parks, special-purpose green areas (e.g., university campuses and cemeteries), and linear UGSs like greenways. These classifications were derived from official UGS databases and satellite image interpretation, capturing the functional and spatial diversity of UGSs within the study area. Tree canopy coverage, representing vegetation density and ecological quality, was measured using high-resolution satellite imagery from Landsat 8/9 and Sentinel-2. The Normalized Difference Vegetation Index (NDVI) and machine learning algorithms (e.g., random forest classification) were applied to quantify the spatial distribution of canopy cover across the city. Demographic and socioeconomic characteristics were also included as explanatory variables. Data from the U.S. Census Bureau’s ACS provided information on population density, income levels, age distribution, educational attainment, and racial or ethnic composition. These indicators are essential for understanding social disparities in access to UGSs. Housing prices, gathered from online real estate platforms such as Zillow and Redfin, were used as proxies for neighborhood-level socioeconomic status. This variable helps capture spatial inequalities that may affect both the availability of and access to UGS. Lastly, weather data from the National Oceanic and Atmospheric Administration (NOAA) and local meteorological stations were used as control variables to control for potential variations in UGS usage due to seasonal changes or extreme weather events. Collectively, these independent variables offer a comprehensive framework for analyzing the spatial, social, and environmental dimensions of UGS accessibility in East Lansing.

3.3. Multi-Model Framework for Accessibility Measurement

This study analyzed UGS accessibility across 46 residential blocks in East Lansing, using a combination of four spatial accessibility models. To provide a comprehensive assessment of spatial access to UGS in East Lansing, we integrated four models that capturing both proximity and potential availability, including: zone-level statistical assessment (Zone-based), Euclidean-based spatial distance calculation (Distance-based), gravity-based accessibility (Gravity-based), and the Two-Step Floating Catchment Area model (2SFCA) (

Table 2. Summary of UGS accessibility models.

Model	Conceptual Assumption	Strengths	Limitations	References
Zone-based	Accessibility determined by internal supply only	Straightforward; widely used in policy and monitoring	Sensitive to boundary effects; ignores cross-boundary access	[5,6]
Distance-based	Closest park distance represents accessibility	Intuitive; easily replicable across contexts	Oversimplifies access; neglects cumulative opportunities	[43,44]
Gravity-based	Larger and nearer parks exert stronger influence	Incorporates supply–demand balance; sensitive to park size	Dependent on parameter choice; may privilege large facilities	[3,45]
2SFCA	Accessibility as supply–demand balance within a catchment	Accounts for population competition and service distribution	Sensitive to catchment threshold and decay function; more complex to implement	[23,46]

).

3.3.1. Zone-Level Statistical Assessment

The zone-based approach measures UGS availability within the administrative boundaries of each residential blocks and calculates several basic indicators reflecting internal green resource distribution. Four indicators were calculated: (1) Total UGS area, (2) Number of parks, (3) Proportion of green coverage, and (4) Per capita green area. These indicators serve as a baseline to provide a representation of supply within administrative boundaries, independent of spatial impedance. Although straightforward and policy-relevant, this method fails to capture accessibility beyond block boundaries or inter-neighborhood flows [5,6].

3.3.2. Euclidean-Based Spatial Distance Calculation

The distance-based approach assumes that accessibility primarily depends on spatial proximity. We calculated the Euclidean distance from the centroid of each residential block i to the centroid of the nearest park j:

$$D_i = \min \left(d_{ij}\right)$$

(1)

where $d_{ij}$ denotes the straight-line distance between block i and park j. This method provides a baseline measure of minimum access cost, commonly used in spatial equity assessments due to its replicability and computational efficiency. It is widely used because it is easy to implement and replicate, but it oversimplifies real-world accessibility by ignoring cumulative opportunities and network-based travel constraints [43,44].

3.3.3. Gravity-Based Accessibility

The gravity model integrates both supply and demand, assuming that larger parks and shorter distances enhance accessibility. It estimates potential accessibility by considering the supply capacity of UGSs and population demand at each block, using an inverse-square distance decay function. The accessibility score $A_i$ for each block i is calculated using:

$$A_i=\sum _j {\displaystyle \frac{S_j^{\alpha }}{d_{ij}^{\beta }}}$$

(2)

where $S_j$ is the service capacity of park (measured as area), $d_{ij}$ is the Euclidean distance from block i to park j, $\alpha$ is the supply exponent, and $\beta$ is the distance decay parameter. Following Zhang et al. [47], a value of 1.91 was adopted as the distance decay coefficient for urban green spaces. However, its performance is sensitive to parameter selection and may overemphasize larger facilities at the expense of smaller, local green spaces [3,45].

3.3.4. The Two-Step Floating Catchment Area Model

The 2SFCA method measures accessibility by considering both the supply of green space and the population demand within a catchment area, adjusted by a Gaussian distance decay function. It assumes that accessibility to a park diminishes gradually as travel distance increases, and that effective availability also depends on how many people compete for the same park resources.

In the first stage, the model evaluates each park’s service capacity relative to the population that can potentially access it. For every park $j$, a supply-to-demand ratio ($R_j$) is calculated as:

$$R_j={\displaystyle \frac{S_j}{\sum _{k\in d_{kj}\le d_0} G(d_{kj},d_0)D_k}}$$

(3)

where $S_j$ denotes the area of park j, representing its service capacity; $D_k$ is the population of demand location k, $d_{kj}$ refers to the distance between demand location k and j, $d_0$ is the catchment threshold, set to 1000 m in this study to approximate a reasonable walking distance; and $G\left(d_{kj,\mathrm{ }}{d}_0\right)$ is the Gaussian distance decay function that discounts the influence of populations located farther from the park. This formulation reflects how much effective green space each park can provide per person within its service area, after accounting for both distance decay and competition among nearby residents.

In the second step, the accessibility score of each residential block i is obtained by aggregating the weighted supply ratios of all parks within its catchment:

$$A_i=\sum _{j\in d_{ij}\le d_0} G(d_{ij},d_0)R_j$$

(4)

where $d_{ij}$ is the distance between block i and park j. This means that the accessibility of a block depends on the cumulative contribution of nearby parks, with each contribution discounted by distance [23,46].

The results derived from the four accessibility measurement approaches were compiled into an index table (

Table 3. Summary of UGS Accessibility Indicators.

Measure	Code	Indicator	Unit
Zone-based	ZB-1	Total area of green space in each block	m2
	ZB-2	Number of green spaces in each block	Count
	ZB-3	Proportion of green coverage in block	%
	ZB-4	Per capita green space in each block	m2/person
Distance-based	DB-1	Euclidean distance to nearest park	m
Gravity-based	GR-1	Gravity-based accessibility index	Index
2SFCA	SFCA-1	Two-step floating catchment area index	Index

), in which each method is represented as an independent variable. This multi-indicator framework allows for comparative analysis of UGS accessibility under different spatial assumptions and measurement logics, without applying any weighting or normalization across methods. Together, these indicators provide a multi-dimensional perspective on spatial access to UGS, capturing different aspects of spatial behavior, administrative boundaries, and urban morphology [43,48].

3.4. Modeling Approaches

While the four single-model approaches provide valuable but distinct perspectives on UGS accessibility, relying on any one model risks bias due to its inherent assumptions. To overcome this limitation, we constructed a composite index (“Four access”) that integrates the outputs of all four models into a unified measure of neighborhood-level accessibility.

Each model was assigned an equal weight of 25%, following the principle of methodological neutrality. Equal weighting has been widely used in composite index construction as a baseline strategy when indicators are theoretically relevant but no strong a priori justification exists for privileging one over another [49]. In this context, the four models reflect complementary logics of accessibility: institutional supply (Zone-based), minimum spatial cost (Distance-based), supply–demand balance (Gravity-based), and demand competition (2SFCA). Assigning equal weights ensures that the composite measure captures all these dimensions without disproportionately amplifying any single perspective. In addition to the baseline equal-weighting scheme, we conducted robustness checks by slightly varying the weights assigned to each model (±10–20%). The results were consistent with the main analysis, confirming that the composite index is not overly sensitive to modest changes in weighting.

To better understand the distribution of UGS accessibility and related spatial characteristics in East Lansing, we computed descriptive statistics for each key variable (

Table 4. Descriptive Statistics of Accessibility Variables.

Variable	Mean	Std. Dev.	Min	Max	Unit
Population	1021.53	760.31	0.00	3318.00	persons
Block Area	770,859.84	1,320,331.98	49,020.82	7,197,807.44	m2
Total Green Space Area	45,866.54	115,177.70	0.00	682,948.51	m2
Number of Parks	0.91	1.47	0.00	8.00	count
Green Coverage Ratio	0.06	0.12	0.00	0.52	ratio from 0 to 1
Park Area per Capita	44.40	98.82	0.00	387.82	m2 per person
Nearest Park Distance	2192.32	701.89	1346.66	4417.42	m
Average Distance to 30 Parks	459.37	364.93	29.63	2022.34	m
Gravity Index	1.82	5.44	0.00	24.84	unitless index
2SFCA Index	937.74	709.30	2.34	3046.27	unitless index
Combined Accessibility Index	3499.63	7214.05	294.50	43,501.98	unitless index

). These include demographic indicators, UGS features, and multiple accessibility metrics. The results are summarized in Table 1, showing the mean, standard deviation, and value ranges across all 46 census blocks. The average population per block was 1021.53, ranging from 0 to 3318, indicating wide variation in residential density. The mean block area was approximately 770,859.84 m², with the largest reaching over 7.1 million m², reflecting considerable differences in spatial unit size. In terms of UGS availability, the total UGS area per block averaged 45,866.54 m², but some blocks had no UGS. The number of parks per block averaged 0.91, with a maximum of 8 parks, suggesting a highly uneven spatial distribution. The green coverage ratio, calculated as the proportion of green area to block area, averaged 0.06 but ranged up to 0.52, revealing a significant disparity in greenness across blocks. The per capita park area was 44.4 m²/person on average, varying widely depending on both park distribution and population size. Regarding proximity, the Euclidean distance to the nearest park centroid averaged 2192.32 meters, with some residents living over 4.4 km from the closest UGS. In contrast, the average distance to the 30 nearest parks was significantly lower at 459.37 meters, suggesting denser UGS availability in certain areas despite distant nearest parks in others.

The gravity-based and 2SFCA indices both serve to quantify accessibility to urban green spaces, albeit through distinct methodological frameworks. The gravity-based index, which yielded values between 0 and 24.84 in this study, represents the cumulative accessibility of a location to surrounding parks, weighted by park size and inversely by distance. Higher values indicate that a block is situated near larger parks and experiences lower spatial impedance, whereas lower values reflect limited access due to greater distances or smaller park sizes. In contrast, the 2SFCA index incorporates both supply and demand by assessing the amount of green space available per capita within a defined catchment, adjusted by a distance decay function. The resulting values ranged from 2.34 to 3046.27, with higher scores indicating greater green space availability relative to local population density. Although the absolute scales of the two indices differ, primarily due to differences in unit structure and normalization procedures, both are interpreted such that higher values correspond to greater levels of accessibility. These indices, when analyzed together, provide a more comprehensive understanding of spatial variability in urban green space provision.

Model-based accessibility measures showed further disparity. The gravity-based index had a mean value of 1.82, ranging up to 24.84, indicating high concentration of access in a few locations. The 2SFCA index, incorporating both supply and distance-decay effects, averaged 937.74 (min: 2.34, max: 3046.27), again demonstrating uneven accessibility. Finally, the combined accessibility index, calculated as the unweighted average of the four core measures, revealed a highly skewed distribution, with a mean of 3499.63 and a maximum exceeding 43,500. These descriptive results confirm the presence of substantial spatial inequality in UGS access and form the foundation for the following spatial equity and statistical correlation analyses.

3.5. Linear Regression Model

Prior to conducting the correlation analysis, normality tests were performed on both the dependent variable (UGS accessibility index) and the independent variables to determine the suitability of parametric statistical methods. The Shapiro–Wilk test indicated that the majority of variables approximate a normal distribution (p > 0.05), thereby supporting the assumption of normality. As a result, Pearson’s correlation coefficient was employed to assess the strength and direction of linear relationships between each independent variable and the UGS accessibility index. This initial step served to identify statistically significant bivariate relationships and provides the basis for the subsequent regression modeling. The confirmation of linearity and normality also justified the application of applying Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) in later stages of analysis.

To examine the global-level associations between UGS accessibility and its influencing factors, this study applied OLS regression. As a standard parametric technique, OLS is used to estimate the linear relationship between the UGS accessibility index and a set of independent variables that include land use composition, park typologies, tree canopy coverage, and key demographic attributes (e.g., population density, income, age, education, and ethnicity).

The general form of the OLS regression model used in this study is expressed as:

Y_i = β₀ + β₁X_1i + β₂X_2i + ⋯ + β_kX_ki + ε_i

(5)

where Y_i is the UGS accessibility index for block i, X_1i to X_ki represent the values of k independent variables, β₀ is the intercept, β_k are the regression coefficients, and ε_i is the random error term. This model assumes that the relationship between the predictors and the response variable is spatially stationary across the entire study area.

These variables were selected on the basis of prior empirical studies and theoretical frameworks emphasizing the role of environmental and socio-spatial inequality in shaping UGS access. OLS regression serves as a baseline model for understanding how these factors collectively influence accessibility across the entire study area. It assumes spatial stationarity, meaning that the relationship between the predictors and the outcome is constant throughout the city. The OLS model not only identifies statistically significant predictors of UGS accessibility but also offers insight into the direction and magnitude of their effects. Diagnostic tests, such as multicollinearity checks (e.g., Variance Inflation Factor, VIF) and residual analysis, are conducted to ensure the robustness and validity of the model. By serving as a global model, OLS allows for comparison with more localized approaches, such as GWR, which further reveals spatial non-stationarity. Together, these models help uncover both general and place-specific drivers of accessibility disparities, advancing a more comprehensive understanding of spatial equity in urban green infrastructure.

3.6. Spatial Regression for Heterogeneity and Inequality

While the OLS regression provides a global understanding of the relationship between UGS accessibility and its potential determinants, it assumes spatial stationarity, that is, the effects of independent variables are constant across all locations. GWR extends the traditional linear regression framework by allowing the estimation of local coefficients for each independent variable at each spatial location. The general form of the GWR model is expressed as:

Y_i = β₀(u_i,v_i) + β₁(u_i,v_i)X_1i + β₂(u_i,v_i)X_2i + ⋯ + β_k(u_i,v_i)X_ki + ε_i

(6)

where (u_i, v_i) are the spatial coordinates of observation i, β_k(u_i, v_i) represents the spatially varying local coefficient for variable k at location i, and ε_i is the residual term. This formulation allows GWR to capture spatial non-stationarity by estimating a separate regression equation at each location, weighted by a spatial kernel function.

Before conducting the GWR analysis, independent variables were selected through correlation testing and multicollinearity diagnostics by clusters, ensuring each conceptual domain was represented by one statistically robust indicator. Only the variables with the highest coefficients or strong statistical significance within each cluster were retained for the final GWR model.

4. Result

4.1. Descriptive Analysis of UGS Accessibility

To examine how estimates of urban green space (UGS) accessibility vary across neighborhoods depending on the choice of spatial model, we applied four widely recognized analytical approaches: Zone-based, Distance-based, Gravity-based, and 2SFCA. Due to their distinct theoretical assumptions regarding spatial access, the accessibility estimates differ across the study area, as visualized in the spatial distribution maps generated by each model (Figure 3).

The results reveal substantial discrepancies in accessibility across models, confirming that no single method provides a fully reliable representation of equity. For instance, neighborhoods in the northern part of the study area, near the intersection of E Saginaw St and N US Highway 27, show high accessibility under the Zone-based and Distance-based models but much lower values under the 2SFCA and Gravity-based models. By contrast, the composite ‘four access’ index delivers a smoother and more balanced distribution, mitigating extreme values and aligning more closely with observed land use and demographic patterns. This highlights the value of integration in capturing accessibility more equitably across neighborhoods (Figure 4). The composite index balances local distance effects with broader considerations such as UGS distribution, service scale, and potential competition, but also produces more consistent accessibility patterns across neighborhoods. For example, the composite index assigns higher accessibility values to neighborhoods located south of E Michigan Ave and west of Haslett Rd. These areas are underestimated by proximity-based models. In contrast, northern neighborhoods near E Saginaw St, which are overrepresented in the Zone-based model, receive more moderate scores. This indicates the composite index’s capacity to reduce extreme variation and provide a more realistic spatial representation. Furthermore, as will be shown in the next section, it also exhibits superior performance in statistical modeling.

The accessibility score generated by all models is presented in Figure 5. Among them, the Distance-based model yields the highest overall values, while the Gravity-based model displays the lowest and exhibits the widest range. In contrast, the “Four Access” index exhibits a more centralized distribution, indicating a balanced and stable representation across neighborhoods. Robustness checks were conducted by varying the weighting scheme across the four models. These tests indicated that the distributional patterns of accessibility and the regression results remained consistent, suggesting that our findings are robust to reasonable variations in weight specification.

4.2. Correlation Analysis

To explore the relationships among different accessibility models and key urban indicators, a correlation analysis was performed prior to regression modeling. Figure 6 presents a correlation matrix that displays the pairwise associations between four spatial accessibility measures and a set of environmental and demographic variables. As shown, the gravity-based and composite indices show positive correlations with greening-related variables such as the proportion of parks, total green space area, and percentage of green land cover. This pattern indicates that these models are more sensitive to ecological supply characteristics. In contrast, proximity-based measures such as the nearest-distance index exhibit weaker or even negative correlations with those variables. Moreover, total population is negatively associated with proximity-based accessibility but demonstrates a modest positive correlation with the composite index.

To systematically evaluate which factors are significantly associated with variations in urban green space (UGS) accessibility, we conducted ordinary least squares (OLS) regression analyses using five dependent variables: four derived from individual spatial accessibility models, and one composite measure labeled “four access”. Explanatory variables were drawn from seven thematic categories, including population density, greening indicators, housing market characteristics, age distribution, gender ratio, racial and ethnic composition, and socio-economic status. Prior to analysis, all independent variables were tested for multicollinearity using variance inflation factors (VIF); variables with excessive collinearity, such as the percentage of white residents and proportion of highly educated individuals, were excluded to enhance model interpretability and stability.

The single-model regressions exhibited weak explanatory power (adjusted R² ranging from –0.282 to 0.209) (

Table 5. OLS Regression for Four Accessibility Models.

Variable	NEARest_DICoef	p-Value	MEAN_NEAR_Coef	p-Value	Gravity-baCoef	p-Value	Ga2SFCACoef	p-Value
Population	0.176	0.028	0.652	0.006	0.849	0.045	0.733	0.069
% Greencover	0.795	0.008	−0.687	0.07	0.162	0.045	−0.538	0.077
Area	0.783	0.077	0.469	0.031	0.547	0.07	−0.789	0.045
Avg. Sale Price	0.632	0.049	−0.183	0.017	−0.155	0.073	0.486	0.095
Avg. Listing Duration	−0.928	0.034	0.557	0.034	0.651	0.074	−0.05	0.054
Median Sale Price	0.384	0.052	0.608	0.017	−0.229	0.039	0.519	0.032
Recent Sales	−0.243	0.027	0.572	0.092	−0.291	0.095	−0.028	0.021
% Age 0–14	0.037	0.032	0.185	0.029	−0.144	0.08	−0.448	0.099
% Age 65+	0.316	0.063	0.329	0.012	−0.21	0.027	−0.236	0.047
Female Ratio	−0.612	0.056	0.293	0.013	0.689	0.064	0.352	0.071
% African American	−0.455	0.033	−0.149	0.076	−0.252	0.085	0.473	0.016
% Asian	0.437	0.04	0.027	0.084	−0.257	0.002	0.941	0.073
% Multiracial	0.566	0.027	0.003	0.005	−0.168	0.009	0.363	0.066
% Other Races	0.701	0.059	−0.926	0.013	−0.151	0.099	−0.019	0.074
Median Income	0.55	0.017	0.416	0.089	0.326	0.079	−0.743	0.091
Commercial Listings	−0.927	0.06	0.241	0.052	−0.62	0.074	0.008	0.08
R2		0.196		0.209		0.105		−0.282

), confirming that no individual approach adequately explains variation in accessibility. While the Gravity-based model was somewhat sensitive to greening variables such as park size, the others produced inconsistent or even contradictory associations with demographic factors. These findings underscore the methodological limitations of relying on a single metric. By contrast, the composite ‘four access’ index yielded substantially higher explanatory power (adjusted R² = 0.821), demonstrating that integrating multiple models yields a more robust and interpretable assessment of urban green space accessibility.

A visual summary of the OLS regression coefficients across the four accessibility models is provided in Figure 7. The figure illustrates both the magnitude and direction of estimated effects for each urban variable, along with their 95% confidence intervals.

In contrast, the composite “four access” index constructed by equally weighting the four individual models produced substantially stronger results (

Table 6. OLS Regression for Composite Model.

Variable	Coefficient	Std. Error	t	P > |t|	[0.025	0.975]
Population	0.1504	0.088	1.709	0.099	−0.03	0.331
% Greencover	0.265	0.109	2.431	0.022	0.041	0.489
Area	0.3812	0.114	3.355	0.002	0.148	0.614
Avg. Sale Price	−0.0241	0.074	−0.325	0.748	−0.176	0.128
Avg. Listing Duration	−0.0231	0.061	−0.38	0.706	−0.143	0.097
Median Sale Price	0.0122	0.068	0.18	0.859	−0.127	0.152
Recent Sales	0.0429	0.12	0.358	0.723	−0.203	0.289
% Age 0–14	0.0676	0.098	0.692	0.495	−0.133	0.268
% Age 65+	0.0153	0.098	0.156	0.877	−0.186	0.216
Female Ratio	−0.104	0.102	−1.005	0.324	−0.303	0.1
% African American	0.0745	0.105	0.711	0.483	−0.141	0.289
% Asian	0.0784	0.078	1.005	0.324	−0.082	0.238
% Multiracial	−0.074	0.087	−0.849	0.404	−0.262	0.109
% Other Races	0.061	0.088	0.692	0.495	−0.12	0.242
Median Income	0.0038	0.1	0.038	0.97	−0.201	0.208
Commercial Listings	0.4605	0.084	5.495	0.0	0.289	0.633
R2	0.888

). The OLS regression using this index achieved an adjusted R² of 0.821, indicating high explanatory power and a well-specified model. This outcome underscores the effectiveness of combining Zone-based, Distance-based, Gravity-based, and 2SFCA approaches to capture multidimensional nature of accessibility. In this model, several variables emerged as significant predictors in the composite model. Green space per capita exhibited a strong positive association with accessibility, indicating that neighborhoods with more generous park provision relative to population experience better access. Similarly, the percentage of green land cover was positively associated with accessibility, highlighting the importance of vegetation density and landscape continuity in shaping access conditions. Additionally, the number of commercial listings in an area was positively linked to accessibility, suggesting that green space is more available or better integrated in commercially active neighborhoods.

Most demographic and housing-related variables, including age structure, racial composition, and recent housing sales, did not display consistent or statistically significant associations. These results indicate that the composite index may smooth out localized variations captured by simpler models and point to the need for further spatially explicit analysis to explore localized inequalities.

Overall, the OLS regression results highlight that the most robust predictors of urban green space accessibility are indicators of physical provision and greening conditions, specifically green space per capita and the percentage of green land cover. Among all models, “four access” index proved particularly effective in capturing these associations, yielding a stable and interpretable outcome that mitigates the methodological limitations of individual models. Owing to its integrative nature and stability, we adopt “four access” as the primary dependent variable for subsequent regression and spatial analyses.

4.3. Spatial Heterogeneity of UGS Accessibility

To capture spatial variation in the relationship between neighborhood characteristics and urban green space (UGS) accessibility, this study employed a Geographically Weighted Regression (GWR) model using the composite “four access” index as the dependent variable. To mitigate multicollinearity, the GWR model only included population density, green land cover percentage, green space area per capita, number of commercial land listings, average housing listing duration, volume of recent home sales, and the proportion of African American residents.

The GWR results reveal substantial spatial heterogeneity in the determinants of accessibility (Figure 8).

For example, green space per capita exhibited stronger positive effects in central and southern neighborhoods but showed weaker effects in northern areas. Similarly, commercial activity enhanced accessibility in peripheral zones but had limited influence in denser urban cores. Importantly, using the composite index as the dependent variable enabled GWR to reveal these localized inequities more clearly than any single model, reinforcing its value as a diagnostic tool for equity-oriented planning.

In sum, the GWR analysis highlights substantial spatial heterogeneity in the determinants of UGS accessibility. These findings underscore the importance of the need for spatially responsive green infrastructure planning that considers local demographic, environmental, and economic contexts. The composite index further facilitates clearer detection of localized inequities (

Table 7. Comparative performance of accessibility models.

Model	Key Predictors (Significant)	Adjusted R2	Strengths	Limitations	Model	Key Predictors (Significant)
Zone-based	% African American, Median Income, Property Sales	0.196	Simple, intuitive, highlights proximity	Sensitive to boundary effects; inconsistent demographic associations	Zone-based	% African American, Median Income, Property Sales
Distance-based	% Minority Residents, Property Sales	0.209	Captures nearest distance to parks	Ignores park size and demand; unstable results	Distance-based	% Minority Residents, Property Sales
Gravity-based	Green space per capita, Park size	0.105	Sensitive to park area and distribution	Still limited explanatory power; ignores demand	Gravity-based	Green space per capita, Park size
2SFCA	None stable	–0.282	Accounts for supply–demand balance	Very weak fit, high residual error	2SFCA	None stable
Composite (“Four Access”)	Green space per capita, % Green land cover	0.821	Integrates multiple perspectives; robust explanatory power	Requires additional computation, but offers stable and interpretable results	Composite (“Four Access”)	Green space per capita, % Green land cover

). By integrating multiple perspectives, the composite approach mitigates the weaknesses of in-dividual models and yields a more stable and interpretable tool for diagnosing inequity ties in green space accessibility.

5. Discussion

5.1. Socio-Spatial Inequality in Green Space Accessibility

RQ1 asked how UGS accessibility differs across urban neighborhoods when estimated by different models. The findings reveal clear socio-spatial disparities in access to urban green space (UGS) in East Lansing, echoing patterns identified in larger urban areas. These disparities in per capita park area, green coverage, and composite accessibility are not incidental but are embedded within broader systemic inequalities shaped by land use patterns and neighborhood demographics. Our results suggest that access to green infrastructure is shaped by more than just how close people live to a park. It is tied to broader patterns of land use and neighborhood composition. In many cases, communities with higher incomes, lower population density, or a higher percentage of white residents tend to have more green space or better access to it. This reflects the kind of environmental inequalities that scholars of environmental justice have long pointed out where some groups consistently benefit more from public amenities than others. In this sense, green spaces often function as spatial advantages that not everyone share equally.

Although East Lansing is a mid-sized city, the patterns seen here reinforce findings from both large cities and suburban settings. Spatial inequality in UGS access is not confined to big metros but shows up in smaller urban systems. Traditional planning approaches often assumed that being physically close to a park meant having meaningful access. But our findings point to the limitations of that view. Metrics of access must go beyond distance to include park quality, neighborhood context, and how well green infrastructure serves diverse users. This perspective aligns with various international case studies: Jin et al. [33] conducted a supply–demand accessibility analysis in a mountainous city in China, showing that small-scale, high-quality green spaces near low-density neighborhoods can significantly improve access—even when average distances are similar. Additionally, a comparative European study across five medium-sized cities (Birmingham, Brussels, Milan, Prague, Stockholm) by Buckland et al. [50] revealed significant disparities in accessibility patterns that cannot be explained by distance alone, reflecting unique historical planning contexts and highlighting that access involves more than mere proximity. Taken together, these findings push both scholarship and planning practice toward a more grounded and inclusive understanding of spatial equity.

5.2. Locating Inequality Through Localized Accessibility Modeling

RQ2 focuses on which environmental, land use, and demographic factors are highly associated with variability in accessibility. At the global level, OLS regression identifies key predictors, such as population density, median household income, tree canopy coverage, and racial composition, as significant correlates of the composite accessibility index. These findings align with longstanding theoretical and empirical evidence suggesting that green infrastructure is unequally distributed along socio-economic lines. For instance, higher-income neighborhoods often enjoy greater proximity to parks as well as better quality green amenities, a pattern observed in multiple U.S. urban contexts [30]. Likewise, dense urban cores may exhibit lower accessibility due to land scarcity and zoning restrictions, despite having high residential concentrations, as seen in European cities such as Stockholm, Milan, and Brussels [50]. The significance of tree canopy coverage supports ecological planning perspectives that emphasize the dual benefits of greening not only for accessibility but also for microclimate regulation and social well-being. Meanwhile, the negative association between racial minority concentration and accessibility underscores how environmental racism persists through urban planning regimes, producing unequal exposures to environmental benefits, a phenomenon documented not only in U.S. cases such as Baltimore and Chicago but also in Southern European contexts like Porto, Portugal [51,52]. Collectively, these patterns indicate that socio-economic and demographic disparities in UGS access are not unique to East Lansing but represent a broader international phenomenon.

RQ3 further examined how spatial regression models reveal spatial heterogeneity and inequality in UGS access. However, these global findings, while statistically robust, assume spatial stationarity that the relationship between predictors and outcomes is consistent across space. This assumption is rarely met in real urban settings, where demographic, infrastructural, and historical conditions vary significantly across neighborhoods. The application of GWR relaxes this assumption and reveals substantial spatial heterogeneity in the determinants of UGS accessibility. Specifically, GWR coefficients show that the strength and direction of associations differ across East Lansing: for example, income is a stronger positive predictor of accessibility in certain high-income western blocks, while in older, more central neighborhoods, its effect weakens or even reverses. Similarly, tree canopy coverage contributes more substantially to accessibility in low-density residential zones but has a diminished role in apartment-heavy areas where green space is disconnected from pedestrian access routes. These spatially varying relationships indicate that green space access is not only a matter of physical distribution but is fundamentally shaped by the local land use context, mobility infrastructure, and neighborhood socio-political history. Comparable spatial heterogeneity has been identified in other international contexts. In Wuhan, China, Yang et al. [53] applied GWR to analyze urban greenness patterns and found that the impact of factors such as road density and urbanization varied significantly across the city, highlighting local tailoring needs. Additionally, studies from Berlin show that accessibility to green spaces is uneven across social groups, shaped by historical housing typologies and uneven service provision, reflecting deep socio-environmental inequalities [4].

Understanding why such heterogeneity exists requires engaging with broader theories of urban political ecology and spatial governance. UGS is not randomly located, but is historically produced through processes such as discriminatory zoning, racialized disinvestment, suburban expansion, and targeted capital investment. In East Lansing, spatial disparities may reflect legacies of institutional planning choices such as exclusionary land use designations or infrastructure prioritization favoring certain districts. For example, areas near the university may have received sustained investments in green amenities to support student and faculty quality of life, while peripheral or historically marginalized neighborhoods may have lacked such sustained infrastructural provision. These place-specific dynamics explain why the same predictor may exert different effects in different contexts, as GWR reveals. In this sense, spatial heterogeneity in the accessibility model reflects not merely analytical nuance but structural inequalities embedded in urban land regimes. The comparative value of GWR lies not only in improved statistical fit but in its epistemological potential. It foregrounds difference over average, local knowledge over metropolitan abstraction, and allows urban scholars to trace the contingent mechanisms that drive accessibility inequalities. Methodologically, the value of GWR lies not only in improving statistical fit but also in its epistemological potential: it foregrounds local difference over metropolitan averages and enables scholars to trace contingent mechanisms driving accessibility inequalities. Practically, this implies that equity-oriented planning cannot rely solely on citywide standards but must adopt neighborhood-sensitive interventions—for example, prioritizing pedestrian infrastructure in dense central districts while expanding canopy cover in suburban residential areas.

5.3. Comparing Accessibility Measures: Integrating Multi-Model Approaches for Enhanced Spatial Equity Assessment

While Section 5.1 highlighted socio-spatial disparities in UGS accessibility, RQ1 further requires examining how these disparities vary when different accessibility models are applied. Much of the literature on urban green space (UGS) accessibility relies on single-method measures such as Euclidean distance or zone-based statistics, this study demonstrates the value of a multi-model approach by integrating four distinct but complementary measures: administrative zone-level indicators, distance-to-nearest-park metrics, gravity-based accessibility, and the Two-Step Floating Catchment Area (2SFCA) method. These models differ not only in their mathematical formulation but also in the behavioral and spatial assumptions they embody. For instance, the zone-based method reflects internal supply availability without accounting for cross-boundary access, while the distance-based approach measures the minimal spatial cost of reaching the nearest park. In contrast, gravity and 2SFCA models provide more dynamic assessments by incorporating both supply and demand, modulated by distance decay functions.

The results indicate substantial variation in performance and sensitivity among these methods. The gravity-based index, which balances park area against population size and applies an inverse-square decay function, produced a more normally distributed set of accessibility values highlighted stronger differentiation across the study area. This suggests it may be more sensitive to local heterogeneity in both green space supply and population demand. The 2SFCA model, incorporating a Gaussian decay kernel within a 1000-m catchment, also captured nuanced variations in accessibility but tended to produce more extreme values in neighborhoods adjacent to large parks with relatively sparse surrounding populations. Meanwhile, the distance-to-nearest-park method underestimated accessibility in areas surrounded by multiple small parks, highlighting its limitations in capturing cumulative opportunities.

Crucially, this study did not simply compare the models in isolation but compiled them into a composite accessibility index, unweighted to preserve the interpretability of individual indicators. This approach represents a methodological contribution to the field of spatial equity assessment by avoiding reliance on a single measurement logic. The use of composite modeling allows for cross-validation of spatial patterns, revealing where different metrics converge or diverge in diagnosing accessibility inequity. For example, blocks with low per capita green space but high 2SFCA values indicate neighborhoods with small populations located near large parks. This triangulation not only increases the robustness of accessibility modeling but also responds to emerging calls for pluralistic, behaviorally informed measures of spatial equity in urban studies.

By integrating zone-based, distance-based, and demand-weighted methods within a unified framework, the study captures both institutional logic and behavioral geographies. This multi-model strategy addresses a key gap in existing literature, where accessibility assessments are often driven by data convenience rather than theoretical coherence. It also provides a foundation for adaptive planning tools that can flexibly prioritize different indicators depending on planning goals, e.g., using gravity-based models for equity audits, or zone-based statistics for service coverage reports. Ultimately, this methodological innovation advances a more comprehensive and just evaluation of urban green infrastructure systems.

A comparative perspective further supports our findings. Research from other medium-sized cities—such as Ghent in Belgium [4], Malmö in Sweden [41], and U.S. cases including Madison, WI [3] and Austin, TX [54]—reveals similar disparities in the distribution and accessibility of green space. Across these contexts, ecological supply indicators (e.g., park provision, vegetation cover) consistently emerge as strong predictors of accessibility, while demographic and housing-market variables show weaker or inconsistent effects. This suggests that East Lansing’s patterns are not unique but reflect broader structural dynamics of mid-sized urban systems. At the same time, local features—such as the university-driven land use and fragmented residential morphology—introduce spatial heterogeneity less evident in European cases, highlighting the need for context-sensitive analysis. These comparisons underscore both the universality and the specificity of our results, strengthening East Lansing’s representativeness as a case study and broadening the policy relevance of the proposed multi-model framework.

5.4. Policy Implications, Limitations, and Future Directions

These findings have clear implications for urban planning and environmental justice. The spatial differences we observed, especially in the local models, demonstrate that citywide standards alone are insufficient to guarantee equitable access. Planners need to focus on neighborhood-level disparities and design responses that fit local conditions. To be specific, low-density western neighborhoods, where green space is abundant but dispersed, policies should emphasize improving connectivity and pedestrian access through green corridors and street-level greening. In contrast, older high-density central neighborhoods with limited per capita green space and low canopy coverage would benefit from small-scale interventions such as pocket parks, greening of vacant lots, or planting street trees to improve everyday exposure to greenery. Around the university district, where substantial investments in green amenities already exist, the priority should be to alleviate usage pressure and diversify services—for example, by introducing multifunctional open spaces or programming activities that serve both students and permanent residents.

At the same time, several limitations should be acknowledged. First, the analysis is based on cross-sectional data from East Lansing, which constrains the ability to assess long-term changes or causal dynamics. Second, the study focused on objective measures of accessibility and did not incorporate residents’ perceptions of safety, satisfaction, or cultural attachment to green spaces. Third, while OLS and GWR models capture important associations, they do not account for multilevel dependencies or spatial error structures that may influence results. Finally, as a single case study, East Lansing cannot represent all mid-sized cities, though its patterns resonate with international findings.

These limitations point toward fruitful directions for future research. First, integrating subjective measures such as perceived accessibility, safety, and quality would enrich the understanding of spatial justice. Second, comparative studies across multiple mid-sized cities, both in the U.S. and internationally, could identify structural determinants of inequality beyond a single local context. Third, longitudinal designs would enable evaluation of whether greening interventions effectively reduce disparities over time. Finally, advanced spatial approaches, including multilevel models, spatial error models, or agent-based simulations, could provide deeper insights into the nested and dynamic nature of green infrastructure planning. By addressing these areas, future work can strengthen both the empirical and practical dimensions of spatial equity research.

6. Conclusions

This study developed a comprehensive, multi-model framework to evaluate neighborhood-level accessibility to urban green spaces (UGSs) in the medium-sized city of East Lansing, Michigan. By comparing four widely used spatial accessibility models and synthesizing them into a composite “four access” index, we demonstrated that methodological choices significantly shape how spatial equity is portrayed.

The study provided categorical answers to the three research questions. For RQ1, the results showed that UGS accessibility differs substantially across neighborhoods, and these disparities appear differently depending on the measurement approach. No single model provides a stable or complete representation; rather, multi-model comparison and composite indices offer a more robust diagnosis. For RQ2, environmental and socio-demographic factors, particularly green space per capita, tree canopy coverage, income, and racial composition, emerged as significant predictors of accessibility. These patterns are not unique to East Lansing but resonate with evidence from other U.S. cities and European cases such as Berlin and Porto, underscoring their international generality. For RQ3, spatial regression revealed that these relationships vary across neighborhoods, with GWR uncovering local heterogeneity shaped by land use history, mobility infrastructure, and socio-political context. This demonstrates that inequality in green access is not evenly distributed but contingent on place-specific dynamics.

The contributions of this study are threefold. Methodologically, it advances spatial equity assessment by integrating diverse accessibility models into a unified composite framework. Empirically, it documents socio-spatial inequalities in a mid-sized U.S. city and situates them within an international comparative perspective. Practically, it provides planners with a flexible and interpretable tool to guide equitable green investment and policy evaluation.

Taken together, the results underscore that equitable access to green infrastructure requires context-sensitive approaches that recognize both physical and social diversity. As mid-sized cities worldwide grapple with uneven green provision, composite modeling and spatially explicit diagnostics provide valuable pathways for developing more inclusive and just urban greening strategies.