Horizontal and Vertical Spatial Equity Analysis Based on Accessibility to Living Service Amenities: A Case Study of Xi’an, China

Abstract

Accessibility is closely related to residents’ well-being and quality of life and is a potential indicator of social equity. This study aims to present a methodology for assessing the combined equity of living service amenities (LSAs) based on accessibility. This study focuses on fourteen types of LSAs in six dimensions and improves the three-step floating catchment area (3SFCA) model by considering the behavioral demand characteristics of different age groups. Taking the main built-up area of Xi’an as an example, the modified 3SFCA model is applied to assess the accessibility of LSAs, and the supply–demand index is used to measure the supply and demand level of the horizontal dimension. Furthermore, random forest regression was used to screen the key socioeconomic indicators affecting the accessibility of LSAs, and then the binary spatial correlation local index was used to reveal the spatial distribution characteristics between LSA accessibility and key socioeconomic indicators in the vertical dimension. Finally, the comprehensive equity of LSAs is evaluated by space superposition. The results showed that there was a serious imbalance between the supply and demand of LSAs in Xi’an’s main built-up area, with polarized oversupply and weak supply areas, especially for accessibility to low-grade LSAs. Accessibility is relatively low for children and young and middle-aged groups, and intergenerational inequalities were particularly pronounced among them. The lower-income group was generally at a disadvantage in accessing the high-demand amenities, and those who resided in affordable housing in the periphery of the city were more likely to face social exclusion. This study emphasizes the importance of distributing urban resources equitably among different social groups, which can help decision makers achieve a balance between horizontal equity and vertical equity in the allocation of urban LSAs and promote spatial equity and sustainable social development.

1. Introduction

According to the Sustainable Development Goals (SDGs) report, nearly half of the urban residents worldwide do not have convenient access to public transportation, and almost 70% are not within easy walking distance to open public spaces [1]. As urbanization accelerates globally, the urban population is growing dramatically, and by 2050, about 70% of the population will live in cities [2]. Meanwhile, China is experiencing the largest and fastest urbanization in the world, with the urban population already reaching 902 million, accounting for 63.89% of the total population [3]. Rapid urbanization has greatly promoted China’s economic development and social progress, but it has also exacerbated the scarcity of urban public resources and widened the wealth gap, leading to a serious structural imbalance between public resources and population growth [4]. Current urban planning policies show a significant spatial tendency, with high-quality public service resources always concentrated in city centers or new urban areas [5]. Residents in suburban areas usually face the inconvenience of long-distance commuting and suffer from relative accessibility deprivation [6]. The renovation and renewal of old urban centers are also sometimes neglected, where there is a concentration of older neighborhoods with age, low construction standards, and poor maintenance, making it difficult for residents to have access to quality amenities [7]. In addition, vulnerable groups such as low-income families, kids, the elderly, and the unemployed often face greater challenges in accessing services and resources [8]. For example, studies have shown that the elderly and low-income groups not only need more time to reach urban parks but the parks they are able to access are often of low quality [9]. As China enters the mid-to-late stages of urbanization, urban planning shifts from “land-oriented” to “people-oriented”, and improving the residents’ quality of life and social equity have become the core goals of sustainable urban development. The New Urban Agenda adopted by the United Nations emphasizes the centrality of amenities in achieving the SDGs [10]. The rational allocation of amenities has become a key factor affecting the issue of social equity and plays a crucial role in improving the quality of life of residents [11].

Various living service amenities (LSAs) provide necessary resources and services for the daily life of residents. In recent years, the spatial equity of public services and other resource allocations in the process of urban development have received extensive and in-depth attention from scholars. Spatial equity emphasizes the level of spatial matching between population and resources [12], which can be categorized into horizontal and vertical equities. Horizontal equity requires equal treatment to all groups [13], focusing on comparing equity among geospatial units to identify which units need to improve public services; for example, the study of the coverage of park services in different spatial units [14] and the study of the spatial distribution characteristics of the accessibility to health resources [15]. Vertical equity emphasizes the differentiate demands with different socioeconomic characteristics [16], aiming at comparing equity between social groups in order to identify which groups’ public services need to be improved. The goals of the 2030 Agenda for Sustainable Development, released in 2015, aim to ensure equal access to public services for all groups, particularly for different genders and disadvantaged groups. Scholars in various countries have begun to focus on spatial equity research on different socioeconomic characteristics. European scholars have paid attention to the gender factor; for example, Martin et al. considered the impact of gender in their study of equitable shared cities [17]. Scholars in North America have also focused on factors such as race and income. Kim et al. considered race and wealth when conducting a study of spatial intersectional pathways for urban park accessibility equity [18], and Wenting et al. paid special attention to the poor and minors when assessing spatial accessibility and equity in public libraries in four major U.S. cities [19]. Studies have shown that age [20], economic status [21], gender, and ethnicity [22] all affect residents’ access to public services, and some studies presented that age and economic status play a more important role [23,24]. Current spatial equity studies typically focus on a single dimension of either horizontal or vertical equity, but the core idea of SDG 11.7 is to guarantee that everyone has access to public services, especially socially vulnerable groups (e.g., children, the elderly, low-income groups, or people with disabilities) [25]. Therefore, to expand the scientific content of SDG 11.7 from the perspective of spatial equity, it is required to consider the comprehensive equity measure of LSAs from both horizontal and vertical perspectives [9].

The accessibility to different amenities in the built environment for all individuals and social groups is the critical component for addressing spatial equity [26,27]. A variety of methods have been developed to assess the accessibility to amenities [28], including the gravity model [29], kernel density estimation [30], network analysis [31], and the two-step floating catchment area (2SFCA) model [32]. Dewulf et al. emphasized that in diverse geographic settings, different methods should be applied to the measurement of medical service accessibility [33]. The provider-to-population method effectively compares supply across large geopolitical units or service areas and is commonly utilized in policy analysis to establish minimum supply standards and identify underserved areas [34]. However, this method presents certain limitations, such as excluding patient border crossings at small geographic scales and lacking in measurements of distance or travel impedance [35]. The method of distance to the nearest provider usually measures the distance from a residence or a population center to the medical facility and is particularly suitable for rural areas, but it proves less effective in high-density urban areas [36]. The gravity model, which combines indicators of accessibility and availability to reflect the decreasing attraction between supply and demand as distance increases, is applicable across both urban and rural regions [37,38]. The 2SFCA model incorporates residents’ demand, amenity supply, and supply–demand distance into the accessibility index, which can reflect the balance between supply and demand on a macroscale while revealing differences in spatial distribution on a microscale, making it a widely used accessibility method among researchers. Due to the original 2SFCA model’s limits, such as using a single search radius and being strongly influenced by distance [15], subsequent studies have proposed various improvements, such as setting various extensions to the search radius [39] and introducing a distance decay function [40] and a three-step floating catchment area (3SFCA) model to take into account competition between amenities [41]. Previous studies have also explored multiple modes of travel. For example, Boisjoly et al. [42] and Liu et al. [32] assessed the accessibility of residents using public transit and driving modes to seek medical care, respectively. Li and Wang [20] proposed a modified 2SFCA method to explore how the walkability of urban parks affects the equity of accessibility. Liang et al. [41] measured residents’ accessibility to urban green spaces by considering multiple modes of travel, including walking, biking, driving, and public transportation. The Chinese government advocates the construction of community life circles, aiming to provide basic public services within a 15 min walk to meet the daily needs of residents [43], emphasizing the importance of walking accessibility in sustainable community development. Within community life circles, accessibility is affected not only by travel mode but also by individual travel behavior [44]. Zhang et al. [45] first proposed a Gaussian-based 2SCFCA method based on travel behavior, which evaluates the accessibility of LSAs by considering residents’ behavioral information, such as travel speed and travel time. A recent study incorporated behavioral demand characteristics of different groups into accessibility measures, bridging the disparities in accessibility due to differentiated demands [46]. However, the quantification of differentiated demands is still an attempt based on general social surveys and lacks questionnaire surveys for specific areas [46]. In addition, traditional studies usually explore spatial disparities in accessibility at the census tract level and fail to meet people’s particular demands affected by daily activity spaces and community life circles [9].

In summary, despite extensive research on the spatial equity of LSAs, most studies have focused on either horizontal or vertical equity from a single dimension, lacking a comprehensive perspective that fully explores the differentiated demands of different socioeconomic groups for LSA accessibility. Furthermore, existing studies tend to rely on general social surveys when quantifying these differentiated demands, neglecting in-depth questionnaires for specific regions, resulting in less refined assessments. Additionally, traditional research often overlooks the actual impact of daily activity spaces and community life circles on accessibility when selecting spatial units, failing to fully address residents’ practical needs.

This study carried out a comprehensive equity assessment based on the accessibility of 14 types of LSAs. By integrating an expert questionnaire that can accurately reflect local residents’ differentiated demands, this study improves the 3SFCA method, resulting in a more refined and personalized accessibility assessment of LSAs. In order to explore the correlation between accessibility and socioeconomic characteristics, this study employs a random forest regression model to filter key socioeconomic indicators affecting the accessibility of LSAs and then uses the bivariate local Moran’s I to analyze the spatial relationship between accessibility and selected indicators to identify spatial hotspots and inequality outliers. In addition, this study combines the horizontal and vertical dimensions to study the spatial equity of LSAs and comprehensively analyzes the spatial mismatch of LSAs. Finally, this study takes fine residential complexes as spatial geographic units and focuses on walking accessibility, responding to the community life circle initiative, which helps to reveal the subtle differences within social groups and provides the possibility for more precise public service and resource allocations.

This study systematically analyzes the horizontal and vertical spatial equity of LSAs in the main urban area of Xi’an by clarifying the study area, data collection, and processing methods, adopting a modified M3SFCA model to evaluate the accessibility of LSAs, and combining methods such as the supply–demand index, random forest regression, and the binary spatial correlation local index. The research results reveal a serious imbalance in the supply and demand of LSAs, differences in accessibility among different social groups, and intergenerational inequality, emphasizing the importance of equitable distribution of urban resources. Finally, the paper summarizes the research findings and puts forward suggestions for urban planning and policies to improve residents’ quality of life and promote spatial equity and socially sustainable development. Meanwhile, it points out the innovations and limitations of the research, providing directions for subsequent research.

This study conducts an in-depth analysis and comprehensive assessment of the accessibility and equity of urban LSAs, aiming to guide the construction and updating of LSAs with the goal of equity so as to alleviate the imbalance of urban development and optimize the urban spatial structure. It would assist in the establishment of a supervision and feedback mechanism for public management to serve the maintenance of public interests and guide the planning and construction of community life circles to ensure that the basic needs of residents’ daily lives are met. Moreover, this study will support the development of equity-oriented housing policies to improve the livability of cities and promote sustainable community development.

2. Materials and Methods

2.1. Study Area and Data Collection

2.1.1. Study Area

Xi’an, the capital of Shaanxi Province and an important central city in western China, is located in the heart of the Guanzhong Plain. The city covers an area of about 5146 square kilometers, with six urban districts and eighty-one sub-districts. As the core urban areas of Xi’an, the six urban districts mainly demonstrate and represent the current urban development status and resource allocation of residential spaces in Xi’an. They have been developed rapidly in the process of urbanization, and have relatively complete infrastructure, but at the same time, they are also facing challenges, such as uneven resource allocation and spatial layout optimization. According to the development goals of improving the coverage and equalization level of infrastructure and promoting the balanced allocation of public resources proposed in the Xi’an Territorial Spatial Master Plan (2021–2035) [47], it is particularly important to conduct a comprehensive equity assessment of the accessibility of LSAs in these six districts. The main urban area of Xi’an, surrounded by the Xi’an Ring Expressway and the Ba River, is designated as the study area for this study. Taking the 2499 representative residential complexes in the study area as the basic assessment units, the study area and the basic units are shown in Figure 1.

2.1.2. Data Collection and Processing

In this study, multi-source urban spatial and big data with high accuracy were selected and applied, including spatial and non-spatial data. Among them, we selected six dimensions of POIs that are closely related to residents’ daily lives, referring to the Spatial Planning Guidance to Community Life Unit [48].

Table 1. Data description and sources.

Type	Description	Year	Source
POI	Point of Interest; POI data were acquired for 14 types of LSAs	2023	Map Lab (https://lbs.amap.com, accessed on 22 October 2023)
AOI	Area of Interest; AOI data were acquired for each residential complex
Pedestrian road network	The road network data were transformed using the ArcGIS Editor for OSM plug-in, obtaining the pedestrian road network	2023	Open Street Map (https://openstreetmap.org, accessed on 29 October 2023)
Demographic data	This includes statistical data such as the population, gender, and age composition of each sub-district of Xi’an	2020	Seventh Census
Property data	This includes information such as spatial location, the number of households, and housing prices for each complex. The number of households can be used to convert the population of each residential area, and the housing price can represent residents’ income levels [49]	2023	Anjuke Property (https://anjuke.com, accessed on 22 October 2023)

presents detailed descriptions of the data.

2.2. Methods

This study proposes to apply the modified 3SFCA model to quantify the accessibility of 14 types of LSAs at the residential complex level while taking into account the differentiated demands of various age groups. In the horizontal spatial equity, a supply–demand index was used to explore the imbalance between the absolute supply and demand of LSAs. In the vertical spatial equity, many socioeconomic factors, including age and income level, were chosen in the analysis. For the age divisions, residents are divided into three groups: children (0–14 years old), the young and middle aged (15–59 years old), and the elderly (60 years old and above). The bivariate local Moran’s I and Mann–Whitney U tests were used to analyze the spatial correlation between the accessibility of LSAs and socioeconomic characteristics. The data flow is shown in Figure 2.

2.2.1. Quantification of the Differentiated Demands of Residents

Age is the main factor influencing the daily behavioral demands of residents, so the demands of the three age groups are quantified separately. Firstly, the walking distance thresholds of LSAs for different age groups were determined. The 5 min, 10 min, and 15 min walking distances were set at 500 m, 1000 m, and 1500 m for children and the young and middle aged, and 300 m, 600 m, and 900 m for the elderly [46]. Secondly, the service radius of the 14 types of LSAs was determined based on the national standard Spatial Planning Guidance to Community Life Unit [48,50], as shown in

Table 2. Service radius for the 14 types of LSAs.

Service Dimension	Type of LSAs	Service Radius
Ecological Landscape	Square	10 min
	Park	15 min
Traffic and Transportation	Bus Stop	5 min
	Metro Station	15 min
Education and Culture	Kindergarten	5 min
	Primary School	10 min
	Middle School	15 min
Healthcare	Pharmacy	10 min
	Hospital	15 min
Shopping Service	Supermarket	5 min
	Shopping Mall	15 min
	Vegetable Market	10 min
Sports and Leisure	Stadium	15 min
	Gym	10 min

.

The relative importance of LSAs for different age groups was determined by the Delphi method and the Analytic Hierarchy Process (AHP) [51]. Firstly, the Delphi method was utilized to organize 12 experts in conducting multiple rounds of anonymous questionnaires, reaching a consensus on the importance of the 14 LSAs across different age groups. Subsequently, the AHP was employed to construct a model, where experts performed pairwise comparisons of elements across different levels. After consistency checks, average values were taken to determine the comprehensive weights (w) for each LSA within each age group, as shown in

Table 3. Importance of the 14 types of LSAs.

Age Group	Tier 1 Dimension		Tier 2 Type		Comprehensive Weight (w)
	Dimension	Weight (%)	Type	Weight (%)
Children (0–14 years)	Ecological Landscape	9.63	square	35.56	0.0342
			park	64.44	0.0620
	Traffic and Transportation	12.59	bus stop	40.63	0.0511
			metro station	59.38	0.0747
	Education and Culture	24.58	kindergarten	24.30	0.0597
			primary school	32.10	0.0789
			middle school	43.60	0.1072
	Healthcare	23.33	pharmacy	38.53	0.0899
			hospital	61.47	0.1434
	Shopping Service	10.22	supermarket	41.58	0.0425
			shopping mall	28.38	0.0290
			vegetable market	30.04	0.0307
	Sports and Leisure	19.66	stadium	64.93	0.1277
			gym	35.07	0.0690
The young and middle aged (15–59 years)	Ecological Landscape	7.95	square	32.57	0.0259
			park	67.43	0.0536
	Traffic and Transportation	18.55	bus stop	32.18	0.0597
			metro station	67.82	0.1258
	Education and Culture	14.58	kindergarten	19.52	0.0285
			primary school	28.06	0.0409
			middle school	52.42	0.0764
	Healthcare	25.94	pharmacy	36.81	0.0955
			hospital	63.19	0.1639
	Shopping Service	14.76	supermarket	19.90	0.0294
			shopping mall	33.14	0.0489
			wet market	46.96	0.0693
	Sports and Leisure	18.21	stadium	44.03	0.0802
			gym	55.97	0.1019
The elderly (60 years and above)	Ecological Landscape	14.33	square	41.47	0.0594
			park	58.53	0.0839
	Traffic and Transportation	15.20	bus stop	59.23	0.0900
			metro station	40.77	0.0620
	Education and Culture	6.08	kindergarten	34.59	0.0210
			primary school	33.95	0.0206
			middle school	31.45	0.0191
	Healthcare	39.29	pharmacy	27.92	0.1097
			hospital	72.08	0.2832
	Shopping Service	10.11	supermarket	22.88	0.0231
			shopping mall	16.59	0.0168
			wet market	60.52	0.0612
	Sports and Leisure	15.00	stadium	60.35	0.0905
			gym	39.65	0.0595

.

2.2.2. Accessibility Assessment for LSAs

We developed walking road networks in ArcGIS 10.8 (Redland CA) and used the network analysis tool to establish an OD cost matrix for each age group so that the road network distance between each residential complex and LSA was calculated. The accessibilities of the fourteen types of LSAs across three age groups {$M_1$, $M_2$, $M_3$} are quantified using the M3SFCA method. The method consists of the following three steps.

• Step 1: Calculate the selection probability of each type of LSA for each age group.

Considering the competition between LSAs, the Huff model is introduced into the calculation of the selection probability. The total population $P_k$ at demand point k was divided into n age groups, which could be expressed as $P_k$= {$P_{k,M_1}{, P}_{k,M_2}$,…, $P_{k,M_n}$}. For the group $M_n$ at demand point i, the probability of selection for amenity j, Huff, can be calculated as follows:

$$Huff={\displaystyle \frac{S_j{G}_{ij}}{\sum _{k\in \left\{d_{ik}\le d_0\right\}}{S}_k{G}_{ik}}}$$

(1)

where $S_j$ is the capacity of amenity j. There is no specific measurement unit, and any indicator that reflects the amenity’s capacity can be used (area, staff count, etc.). When there is little individual variation in amenities, S_j can be artificially defined as a fixed value. Due to the lack data, we assumed that each amenity’s $S_j$ was equal to 1; $d_{ij}$ is the road network distance between subgroup $M_n$ at demand point i and amenity j, and $d_0$ is the distance threshold for subgroup $M_n$.

$G_{ij}$ is the Gaussian function, which can be calculated as follows:

$$G_{ij,M_n}=\left\{\begin{array}{c}{\displaystyle \frac{e^{-\left(\frac{1}{2}\right)\times {\left(\frac{d_{ij}}{d_0}\right)}^2}-e^{-\left(\frac{1}{2}\right)}}{1-e^{-\left(\frac{1}{2}\right)}}},if{d}_{ij}\le d_0 \\ 0, if d_{ij}>d_0\end{array}\right.$$

(2)

• Step 2: Calculate the supply–demand ratio of each type of LSA for each age group.

Calculate the supply–demand ratio $R$ of each type of LSA. In addition, considering the differentiated demands of different age groups, the importance $w$ of each type of LSA is quantified.

$$R={\displaystyle \frac{1000S_j}{\sum _{M_1}^{M_n}\sum _{i\in \left\{d_{ik}\left(M_n\right)\le d_0\left(M_n\right)\right\}}{Huff}_{ik,M_n}w{P}_{M_n}}}$$

(3)

where $P_{M_n}$ is the size of the population group $M_n$ at demand point i, and $w$ is a coefficient reflecting the degree of importance, as shown in Table 3. Due to the low value of ”per person“, we use ”per thousand“ by multiplying the numerator by 1000.

• Step 3: Calculate the single accessibility and the comprehensive accessibility.

Based on the supply–demand ratio $R$ for the population group $M_n$ at demand point i, accessibility $A_{M_n}$ can be calculated as follows:

$$A_{M_n}=Huff{G}_{ij,M_n}R$$

(4)

Then, the accessibility $A$ of all populations at demand point i is calculated, which is used to subsequently analyze the spatial correlation between the accessibility of LSAs and socioeconomic characteristics.

$$A=\sum _{M_1}^{M_n}{A}_{M_n}$$

(5)

2.2.3. Standardization of the Accessibility Index

The supply–demand index represents a standardized and absolute measure of equity. It is used to determine the balance degree between supply and demand based on minimum service standards [52]. The supply–demand index $\mathrm{e}$ for each type of LSA is calculated as follows:

$$e={\displaystyle \frac{Max\left(R\right)}{Max\left(A\right)}}\times A$$

(6)

where R and A are in Equations (3) and (5). The supply–demand index e is divided into five levels to reflect the spatial equity of LSA supply, as shown in

Table 4. Supply and demand balance and spatial equity.

Level	Value Range	Supply–Demand Situation	Spatial Equity
I	0 ≤ e < 0.25	Weak supply	Seriously inequal
II	0.25 ≤ e <0.5	Insufficient supply	Slightly inequal
III	0.5 ≤ e <0.75	Balanced supply	Equal
IV	0.75 ≤ e ≤1	Sufficient supply	Slightly inequal
V	e > 1	Oversupply	Seriously inequal

.

2.2.4. Spatial Autocorrelation between the Accessibility of LSAs and Socioeconomic Characteristics

In order to explore whether there are differences in access to the various types of LSAs for different social groups, we analyzed the relationship between accessibility to LSAs and socioeconomic indicators (

Table 5. Socioeconomic indicators.

Variables	Description
PD	Population density (population/km2)
HP	Housing prices
CP	Children proportion (age < 15 years)
YP	Young and middle-age proportion
EP	Elderly proportion (age ≥ 60 years)
MP	Male population
FP	Female population

).

First, the Spearman correlation analysis was conducted, and for each type of LSA, the indicators with a significant correlation (p < 0.05) with their accessibility were selected. On this basis, a random forest regression model was constructed using the Random Forest Package in R language 4.4.0 (R Development Core Team) to filter and obtain the key socioeconomic factors that play an important role in influencing the accessibility of LSAs. According to the model, the importance of each factor was calculated using the percentage increase in the mean square error (%IncMSE), and variables that were notably significantly generalizable in the accessibility of each type of LSA were selected as key factors.

Then, the spatial relationship between LSA accessibility and key socioeconomic indicators was analyzed using the bivariate local Moran’s I. The local indicators of the spatial association (LISA) were calculated using GeoDa 1.22 software (Arizona State University, Tempe, AZ, USA). Their equations are as follows:

$$I_{kl}^i=Z_k^i{\sum }_{j=1}^n{w}_{ij}{Z}_I^j$$

(7)

$$z_k^i={\displaystyle \frac{X_k^i-\overline{X_k}}{{\mathsf{\sigma }}_k}}$$

(8)

$$z_I^i={\displaystyle \frac{X_I^i-\overline{X_I}}{{\mathsf{\sigma }}_I}}$$

(9)

where $w$ is the spatial weighting matrix at demand point i and amenity j, $X_k^i$ is the socioeconomic indicator, and $X_I^i$ is the accessibility of LSAs; $\overline{X_k}$ and $\overline{X_I}$ are the average values, and ${\mathsf{\sigma }}_k$ and ${\mathsf{\sigma }}_I$ are the variances.

Moreover, the socioeconomic indicators were examined using the Mann–Whitney U test to determine whether a significant difference existed between high and low accessibility of LSAs. It will help to explore whether they were beneficial to specific socioeconomic groups, and the equations are as follows:

$$U=n_1{n}_2+{\displaystyle \frac{n_2\left(n_2+1\right)}{2}}-\sum _{i-n_1+1}^{n_2}{R}_i$$

(10)

$$Z={\displaystyle \frac{U-m_U}{{\sigma }_U}}$$

(11)

where $n_1$ and $n_2$ are the number of samples; $R_i$ is the rank, which ranks all values from smallest to largest and assigns a ranking to each sample. U indicates the difference between the rank sums; $m_U$ is the average value; ${\sigma }_U$ is the standard deviation of U; and Z is the score that distinguishes the two groups of values.

3. Results

3.1. Horizontal Spatial Equity of LSAs

Figure 3 shows the supply–demand index (e) results of the 14 types of LSAs in the main urban area of Xi’an. The spatial distribution of the supply levels of the LSAs in different areas of Xi’an varies greatly, with an overall center–periphery pattern. Meanwhile, due to the different service radii of the LSAs, the rate of decline in accessibility varies with the increase in travel time and population age; thus, the supply–demand index of each type of LSA has its own unique spatial pattern. However, the supply and demand of LSAs in most of the areas are unbalanced or have spatial distribution inequity in Xi’an, especially in a large proportion of areas with an oversupply.

The supply–demand index of squares and parks showed a decreasing pattern from the urban center to the periphery. The overall supply level of stadiums was insufficient, with only some residential complexes meeting demand in the northern, south–central, and southwestern parts of the main urban area. There was significant spatial heterogeneity in gyms, with low-value zones in the center of the city and high-value zones in the south, north, and eastern edges of the peripheral areas. In order to promote the national fitness program and the construction of Park City, Xi’an has built a large number of fitness places and parks in recent years, but the mismatch between the new amenities and the population distribution has failed to effectively alleviate the increasingly prominent contradiction between residents and land.

The bus stop amenities’ supply–demand index showed a pattern of high values in the urban center and low values in the periphery of Xi’an. The metro station amenities’ supply–demand index was higher along the east–west axis and north–south axis and decreased overall from the urban center and southeast to the periphery. The metro station amenities’ supply–demand index was more evenly distributed, which can form a supplement with the low-value zones of bus stops in some areas.

The healthcare amenities’ supply–demand index was polarized, indicating that scarce resources may be concentrated in some areas. Pharmacies showed significant spatial heterogeneity, with anomalously low-value zones in the inner city, including Qingnian Rd, Xiyi Rd, and Jiefangme, Zhongshanmen, Beiyuanmen, Nanyuanmen, and Baishulin sub-districts, and two low-value belts were adjacent to the western and eastern areas of the urban center, including Lianhu, Xincheng, and Beilin sub-districts. Hospitals were well supplied in most areas, with some low-value zones in the suburbs. Healthcare amenities play important roles in building a healthy community life circle, providing basic health services for residents and being the fundamental guarantee for responding to public health emergencies [53]. Notably, 25.6% of the selected residential complexes did not have pharmacy accessibility, and 16.4% of the residential complexes did not have hospital accessibility.

The kindergarten amenities’ supply–demand index showed a “low-high-low” spatial pattern from the urban center to the periphery, while primary schools were well supplied in most of the areas, with low-value areas mainly scattered in the suburbs. Since the service radius of kindergarten and primary school is shorter, distance has a greater impact on accessibility, so the spatial heterogeneity of the supply–demand index was significant. The distribution of middle schools was more aggregated, decreasing from the center to the periphery, which reflected a high supply level in the urban center and a low level in the newly developed areas.

The overall supply level of supermarkets was good, with only scattered low-value zones in the suburbs. The shopping mall amenities’ supply–demand index showed a fan-shaped pattern, decreasing from the central and southern urban areas to the periphery, with anomalously high-value zones occurring in Zhangjiabao sub-districts. The high-value zones of the wet market were mainly concentrated in the northwest, east, and southern edges of the main urban area.

3.2. Vertical Spatial Equity of LSAs

3.2.1. Identification of Socioeconomic Indicators Influencing Accessibility to LSAs

The correlation analysis between the accessibility of LSAs and socioeconomic indicators is shown in Figure 4, and the random forest regression model is constructed after screening out the relevant indicators, and the results of $R^2$ are shown in

Table A1. The $R^2$ of random forest regression model for the accessibility of the 14 LSAs.

LSAs	Square	Park	Bus Stop	Metro Station	Kindergarten	Primary School	Middle School
R2	0.2918	0.3603	0.5502	0.3499	0.0931	0.2775	0.5424
LSAs	Pharmacy	Hospital	Supermarket	Shopping Mall	Vegetable Market	Stadium	Gym
R2	0.1134	0.4922	0.3164	0.4102	0.2300	0.1124	0.2070

. The results of the importance of the indicators influencing the accessibility of the fourteen types of LSAs are shown in Figure 5, and the top four indicators that mainly affect the accessibility of the fourteen types of LSAs are the proportion of children, the proportion of young and middle-aged people, the proportion of elderly people, and the income level.

3.2.2. Spatial Cluster Identification of Age Group Proportion and Accessibility of LSAs

LISA was used to represent the spatial association between socioeconomic characteristics (different age group proportions and income levels) and accessibility, which could be classified into five categories: HH (high-value socioeconomic index and high-value accessibility), LL (low-value socioeconomic index and low-value accessibility), LH (low-value socioeconomic index and high-value accessibility), HL (high-value socioeconomic index and low-value accessibility), and NS (a nonsignificant relationship at the 0.05 level).

For age, we will pay more attention to the HL and LH areas in the analysis to indicate spatial mismatch status, which is related to oversupply and the insufficient supply of LSAs. The LISA values of the three age group proportions and the accessibility of the fourteen types of LSAs are shown in Figure 6 and Figure A1, Figure A2, Figure A3, Figure A4 and Figure A5. The results of the Mann–Whitney U test are shown in

Table 6. Mann–Whitney U test for age characteristics.

Type	Variable	High Access	Low Access	Mann–Whitney U test
		Median	Median	Z	p-Value
Square	0–14	0.1365	0.1479	13.837	0.000 ***
	15–59	0.6875	0.6875	4.750	0.000 ***
	>60	0.179	0.1452	−12.109	0.000 ***
Park	0–14	0.1387	0.1479	12.752	0.000 ***
	15–59	0.6885	0.6836	−1.854	0.064
	>60	0.1768	0.1485	−5.630	0.000 ***
Bus Stop	0–14	0.1365	0.1464	9.131	0.000 ***
	15–59	0.6836	0.6875	4.555	0.000 ***
	>60	0.179	0.1485	−9.305	0.000 ***
Metro Station	0–14	0.1351	0.1464	12.995	0.000 ***
	15–59	0.681	0.7028	10.670	0.000 ***
	>60	0.1971	0.1485	−16.235	0.000 ***
Pharmacy	0–14	0.1428	0.1428	3.059	0.002 **
	15–59	0.6875	0.6838	−0.748	0.454
	>60	0.1689	0.1689	−2.436	0.015 *
Hospital	0–14	0.1387	0.1501	14.193	0.000 ***
	15–59	0.6836	0.7036	6.639	0.000 ***
	>60	0.1768	0.13	−13.426	0.000 ***
Stadium	0–14	0.1462	0.1428	0.455	0.649
	15–59	0.7036	0.6836	−1.070	0.285
	>60	0.1689	0.1689	−0.645	0.519
Gym	0–14	0.1365	0.1464	10.972	0.000 ***
	15–59	0.6836	0.7027	2.264	0.024 *
	>60	0.179	0.1485	−8.778	0.00 ***
Kindergarten	0–14	0.1387	0.1428	0.867	0.386
	15–59	0.6875	0.6875	−2.344	0.019 *
	>60	0.1689	0.1702	2.852	0.004 **
Primary School	0–14	0.1365	0.1479	12.351	0.000 ***
	15–59	0.6836	0.7027	2.245	0.025 *
	>60	0.1768	0.1485	−8.653	0.000 ***
Middle School	0–14	0.13	0.1479	19.820	0.000 ***
	15–59	0.6671	0.7028	13.735	0.000 ***
	>60	0.2055	0.1485	−22.132	0.000 ***
Supermarket	0–14	0.1428	0.1387	−0.339	0.735
	15–59	0.6838	0.7063	5.181	0.000 ***
	>60	0.1702	0.146	−5.422	0.000 ***
Shopping Mall	0–14	0.132	0.1479	18.752	0.000 ***
	15–59	0.6946	0.6836	−5.227	0.000 ***
	>60	0.1768	0.1689	−5.813	0.000 ***
Vegetable Market	0–14	0.1428	0.1387	−4.340	0.000 ***
	15–59	0.6875	0.6875	−1.841	0.066
	>60	0.146	0.1702	6.414	0.000 ***

* p < 0.05; ** p < 0.01; *** p < 0.001.

. Education and culture amenities are the most frequently visited by children. For children, the number of residential complexes categorized as HL significantly exceeds those categorized as LH, with a significant spatial imbalance. LH clusters (kindergarten, 367, 14.69%; primary school, 211, 8.44%; and middle school, 468, 18.73%) were mainly located in the inner city and the Shilipu sub-district on the periphery of the main urban area, which had a low proportion of children but had highly accessibility to education and culture amenities. The HL clusters (kindergarten, 417, 16.69%; primary school, 700, 28.01%; middle school, 844, 33.77%) were mainly located in the peripheral areas of Zhangjiabao, Zhangba, Xiwang Street, and Textile City sub-districts, which had a high proportion of children but a relatively insufficient provision of education and culture amenities, especially in primary schools and middle schools. The Mann–Whitney U test results further revealed a strong negative correlation (p < 0.001) between the proportion of children and the accessibility of primary and middle schools, while the proportion of the elderly showed a strong positive correlation. This suggests that communities with predominantly children face lower accessibility, reflecting the inequity in the provision of education and culture amenities for children.

Traffic and transportation amenities are more important for young and middle-aged people. For them, the LH clusters (bus stops, 361, 14.45%; metro stations, 509, 20.37%) were concentrated in the inner city, as well as the northern part of Changlefang, Taiyi Road, Wenyi Road sub-districts, and the north of Dayanta sub-districts. The HL clusters (bus stops, 243, 9.72%; metro stations, 567, 22.69%) were concentrated in Hancheng, Hongmiaopo, Zhangba, Changyanbao, and Xiwang sub-districts on the periphery of the main urban area. In addition, there were significantly fewer HH clusters and LL clusters in the young and middle-aged groups compared to the elderly groups. Combined with the Mann–Whitney U test results, there was a strong positive correlation between the proportion of elderly people and the accessibility of convenient transportation facilities, while the proportion of young and middle-aged people had a strong negative correlation. This suggests that residential complexes dominated by young and middle-aged people are more likely to have lower accessibility, revealing a potential inequity in the supply of traffic and transportation amenities for young and middle-aged people. Healthcare amenities play a vital role in the daily lives of the elderly. For the elderly group, the LH clusters (pharmacies, 61, 2.44%; hospitals, 28, 1.12%) were much less than that of other age populations, and the number of HH clusters and LL clusters was relatively larger, suggesting that the elderly have reached a more balanced supply and demand for healthcare amenities. The Mann–Whitney U test results showed that the proportion of the elderly was weakly (p < 0.05) and strongly positively correlated with the accessibility of pharmacies and hospitals, respectively. The results show that there is no obvious inequitable supply of healthcare amenities for the elderly, and the elderly are in a more favorable position to access healthcare resources compared with other age groups.

Ecological landscape amenities, shopping service amenities, and sports and leisure amenities are almost equally distributed for all age groups. For ecological landscape amenities, the HH clusters and LH clusters of all age groups were mainly located in the inner city, indicating that there was high accessibility in general. While nearly one-half of the HL clusters for children were located in the western edge and northeastern part of the main urban area, nearly one-third of the HL clusters for young and middle-aged people were located in the western edge of the main urban area and Qujiang sub-district in the southeast. In contrast, the HL clusters of the elderly were much less than those of other age groups and were concentrated in Xinjiamiao, Daminggong, and Taihua Road sub-districts in the northeast. In addition, there were significantly more HH and LL clusters among the elderly, suggesting a more balanced supply and demand of ecological landscape amenities for the elderly. The Mann–Whitney U test further revealed a strong positive correlation between the accessibility of squares and parks and the proportion of the elderly and a strong negative correlation with the proportion of children and young and middle-aged people. Nonetheless, ecological landscape amenities are predominantly located in older urban areas with a larger elderly population, resulting in a better fulfillment of the needs of the elderly, while children and young and middle-aged people are more located in peripheral areas.

For shopping services, in the inner city, supermarkets showed HH clusters or LH clusters for all age groups, indicating that supermarket accessibility was generally higher, while shopping malls showed LL clusters or HL clusters in the east and west, indicating that accessibility to shopping malls was only higher in the central and lower in the west and east. In the periphery, the HL clusters of supermarkets and shopping malls for children and young and middle-aged people were mainly located in the western and southern edges of the study area, and for the elderly, the HL clusters of supermarkets were mainly located in Xinjiamiao and Textile City sub-districts. For vegetable markets, there were many more HL clusters for the elderly compared to the other age groups, and they were mainly located in the southeastern half of the inner city and the peripheral areas adjacent to its northeast and south. The Mann–Whitney U test showed a strong negative correlation between the accessibility of supermarkets and shopping malls and the proportion of young and middle-aged people, indicating that supermarkets and shopping malls had a serious inequitable supply problem for young and middle-aged people. Similarly, there was a strong negative correlation between the accessibility of vegetable markets and the proportion of elderly people, implying that vegetable markets had an inequitable supply for them.

For sports and leisure amenities, the number of HL clusters significantly exceeded LH clusters across all age groups, revealing a generalized issue of short supply. The imbalance between supply and demand in the child group was particularly significant. The HL clusters (stadiums, 786, 31.45%; gyms, 718, 28.73%) and LH clusters (stadiums, 322, 12.89%; gyms, 411, 16.45%) were much greater than other age groups, and they were mainly distributed in the western and eastern edges of the study area, as well as in the northern part of the study area in the streets of Zhangjiabu, Weiyanggong, Taihua Road, and Xinjiamiao sub-districts. The Mann–Whitney U test results further indicated a strong negative correlation between the accessibility of gyms and the proportion of children, and there was a strong positive correlation with the elderly, indicating that sports and leisure amenities were inequitably supplied to children while being more friendly to the elderly.

3.2.3. Spatial Cluster Identification of Income Levels and Accessibility of LSAs

For income level, we will pay more attention to the LL and HH areas in the analysis to reveal the inequities in LSAs caused by income level differences. The LISA values of income level and accessibility to each type of LSA are shown in Figure 7, and the Mann–Whitney U test results are shown in

Table 7. Mann–Whitney U test for income level characteristics.

Type	High Access	Low Access	Mann–Whitney U Test
	Median	Median	Z	p-Value
square	11,791	11,862	−1.522	0.128
park	11,970	11,500	−4.838	0.000 ***
bus stop	11,111	12,436.5	6.838	0.000 ***
metro station	11,785	11,891	−0.862	0.389
pharmacy	11,875	11,704.5	−2.016	0.044 *
hospital	11,764	12,859.5	1.492	0.136
stadium	11,764	12,859.5	1.492	0.136
gym	12,360	11,396.5	−7.463	0.000 ***
kindergarten	11,875	11,818	0.737	0.461
primary school	11,578	12,288	2.216	0.027 *
middle school	11,302.5	12,156	3.028	0.002 **
supermarket	11,807	12,100	0.358	0.919
shopping mall	12,141.5	11,597	−6.202	0.000 ***
wet market	11,411	12,105	5.764	0.000 ***

* p < 0.05; ** p < 0.01; *** p < 0.001.

. Overall, HH clusters were mainly concentrated in the southern part of the study area, which reflected the trend of Xi’an’s economic development from the inner city to the southern new area and the spatially guiding role of urban planning and development strategies. In addition, the large number of LL clusters of various types of LSAs indicated that lower-income groups tend to face greater challenges in accessing LSAs, revealing the inequitable distribution of social resources. In addition, the spatial distribution of the LH clusters of some LSAs, such as stadiums and gyms, was dependent on HH clusters, indicating that lower-income residents were equally able to enjoy the corresponding service resources in economically prosperous areas. Based on the Mann–Whitney U test results, the correlations between the accessibility of LSAs and income level can be categorized into three types. The results showed a strong negative correlation for bus stops and vegetable markets, indicating that these amenities are more favorable to lower-income groups. The results showed strong positive correlations for parks, stadiums, gyms, and shopping malls, indicating that lower-income groups are in the most vulnerable position when it comes to accessing these LSAs. The healthcare and education amenities were relatively equally accessible to groups of different income levels.

Medical and health amenities, as well as education and culture amenities, meet the most fundamental demands of residents, regardless of income level. The results showed that there was no significant correlation between the accessibility of both types of amenities and the income level in most areas. The proportion of HH clusters was less than 5%, further indicating that there was no significant positive correlation between high-income levels and high accessibility. The number of LL clusters was higher than that of HL clusters, suggesting that lower-income groups remained the majority of those with limited access to healthcare and educational resources. In addition, the number of LH clusters was higher than that of HH clusters, and these LH clusters gradually converged to the center as the level of amenities increased. This may be related to the fact that high-level healthcare and education amenities are more likely to be located in the inner city, which is a low-income area for the city’s further development. The current school district delineation empowers the lower-income groups sometimes enjoy higher accessibility to healthcare and education resources.

Traffic and transportation amenities play a vital role in the provision of social services for lower-income groups. For bus stops, LH clusters were significantly greater than HH clusters, indicating that lower-income groups account for a larger proportion in areas with high accessibility of bus stops. The same was not true for metro stations, where LL clusters significantly exceed that of HL clusters, indicating that lower-income groups also account for a larger proportion in areas with low accessibility to metro stations. Despite these differences, the complementary role of bus stops and metro stations alleviated the problem of uneven accessibility to some extent. After that, some areas still had insufficient accessibility for lower-income groups and were mainly located in Taihua Road sub-district in the northeast, Hongmiaopo sub-district in the northwest, and a small number of residential complexes in the western edge of the city.

The results for ecological landscape amenities showed that LL clusters were mainly located in the northeast and west of the peripheral areas and the northwestern edge of the city, and HH clusters were mainly located in the east of Changyanbao sub-district. This suggested that the square and park resources in these areas tend to be concentrated towards higher-income groups rather than lower-income groups. HL clusters had a similar distribution pattern to LL clusters, but the number was significantly smaller, indicating that lower-income groups still account for a large proportion in areas with low accessibility to ecological landscape amenities. LH clusters were mainly in the central part of the inner city and the Textile City sub-district, suggesting that the lower-income groups residing in these areas can enjoy more convenient ecological landscape amenities. The results for sports and leisure amenities showed that LL clusters were mainly distributed in the peripheral areas, similar to the distribution pattern of HL clusters, but the number of LL clusters was significantly higher, indicating that lower-income groups still account for a large proportion of the areas with low accessibility to sports and leisure amenities. In addition, this study also found that the LH clusters of sports and leisure amenities were dependent on the HH clusters in terms of spatial distribution, forming a southwest–northeast trending LH belt in the south–central part of the main urban area. LH clusters in Zhangjiaobao sub-district in the north of the peripheral areas suggested that lower-income groups were able to access sports and leisure resources similar to those of the higher-income groups.

Supermarkets showed no significant correlation in most areas, indicating that residents of different income levels had relatively equal access to supermarket services. However, the distribution of shopping malls showed a significant correlation with income levels, manifesting as LL clusters or HH clusters in nearly half of the residential complexes, with LL clusters mainly located in the northern half of the peripheral areas and HH clusters mainly in the south of the peripheral areas. This indicated that in these areas, LL clusters might be disadvantaged, while higher-income groups enjoy more convenient shopping mall services. For vegetable markets, the number of LH clusters was significantly higher than that of HL clusters, and only 2.96% of residential complexes belonged to HH clusters, suggesting that lower-income groups were more likely to have access to vegetable market service than higher-income groups. However, there still were 34.37% of residential complexes belonging to LL clusters, mainly located in the southeastern half of the inner city and the northern and southern parts of the periphery, with a similar distribution pattern of HL clusters, indicating that both high-income and low-income residents of these areas were facing the low vegetable market accessibility.

3.3. Comprehensive Equity of LSAs

We selected some representative vertical and horizontal results for spatial overlay analysis. Specifically, the vertical layer with the proportion of young and middle-aged people was selected for traffic and transportation amenities, the vertical layer with the proportion of elderly people was selected for medical and health amenities, and the vertical layer with the income level was selected for all other types of amenities. The distribution of the spatial horizontal equity and spatial vertical equity patterns of the LSAs is shown in Figure 8.

Residential complexes with results of lower $e_{ij}$-HL in terms of age and lower $e_{ij}$-LL in terms of income level fail to achieve equity in both horizontal and vertical dimensions, making them the worst condition for LSA allocation, and they should be prioritized for attention. The residential complexes with the worst comprehensive equity for traffic and transportation amenities, as well as ecological landscape amenities, were mainly located in the western and northeastern parts of the peripheral areas, with metro stations and squares accounting for more than one-fifth of the residential complexes. Shopping malls and vegetable markets had prominent issues in terms of comprehensive equity, accounting for almost one-third of all residential complexes. Shopping malls were found in the western, northern, and eastern peripheries, while vegetable markets could be found in the southeastern half of the inner city and the northern periphery. For educational and cultural amenities, the eastern and northern periphery had a high number of worst-condition residential complexes, with middle schools having the most equity issues, with nearly one-third of them in the worst condition. Sports and leisure amenities exhibited significant comprehensive equity issues, with half of the stadiums and one-third of the gyms in the worst-condition residential complexes, primarily in the periphery.

The results of the overlay analysis also revealed a correlation between horizontal and vertical equity in the accessibility of LSAs. For most LSAs, residential complexes that achieve horizontal equity in resource allocation also exhibit higher vertical equity, a finding that supports the notion that inclusive and diverse community planning and policymaking are essential to achieving equal treatment among residents of different ages and income levels. However, for some LSAs, such as parks, squares, and supermarkets, vertical equity issues persisted, even when horizontal equity was achieved. This suggests that the resource allocation strategy may place too much emphasis on universality and parity and neglect to take care of specific groups, such as low-income households or children, thus exposing potential problems in the resource allocation strategy and priority setting. Further analysis found that vertical inequity is more prevalent in residential complexes with lower horizontal equity, revealing the cumulative effect of inequity, i.e., once horizontal inequity occurs, it may manifest itself in multiple dimensions. Moreover, even in some residential complexes where vertical equity has been achieved, horizontal inequity is still prevalent. This suggests that vertical equity may be independent of horizontal equity in some cases; for example, in the case of limited resources, policymakers may need to meet the needs of specific groups while having to sacrifice a certain degree of horizontal equity, reflecting trade-offs in resource allocation.

The comprehensive analysis shows that there is a complex interaction between horizontal and vertical equity in the accessibility of LSAs. The vertical equity analysis in this study focuses on equity among groups based on age and income level, but it is worth noting that even if equity is achieved in these dimensions, inequities based on other socioeconomic characteristics (e.g., gender, race, disability, etc.) may still exist. Therefore, even if vertical equity as defined in this study is met, community planners and policymakers still need to work on enhancing equity in the horizontal dimensions to ensure more comprehensive equity coverage. Further, in order to achieve comprehensive equity, a more integrated approach that considers both horizontal and vertical equity and seeks the right balance in resource allocation is necessary. This is to ensure that all residents, irrespective of their socioeconomic background, have equal access to LSAs.

4. Discussion

4.1. Difference in Supply and Demand for LSAs

This study used the supply–demand index to assess the horizontal equity of LSA supply. First, the accessibility of LSAs in Xi’an’s main urban area is generally the center-periphery pattern, with some LSAs showing significant spatial heterogeneity. The low-value zones of the supply–demand index that appeared in the inner city lacking LSAs, such as kindergartens, stadiums, wet markets, and so on, are due to the limit land spaces and road conditions concerning the historical conservation, while the supply of amenities in the newly built residential complexes surrounding the inner city is more sufficient. The high-value zones of the supply–demand index in the periphery are mainly in the southern area because of the intensive and rapid construction of the new areas with a larger number of LSAs and an adequate level of supply. Second, the proportion of LSAs with a balanced status of supply and demand is quite low, most of them falling into oversupply and weak supply, indicating that the current spatial layouts and the supply–demand relationship of LSAs are irrational. We discovered that high accessibility did not mean balanced supply and demand, while many LSAs had high accessibility values ceased by an oversupply situation. According to Xi’an’s Territorial Spatial Master Plan (2021–2035), the eastern part of the main urban area with insufficient LSA supply is designated as a housing density enhancement zone, which may lead to further spatial inequality if infrastructure development is not accelerated. Thirdly, low-level LSAs perform poorly in terms of accessibility. Specifically, amenities that provide basic services, such as pharmacies, kindergartens, and vegetable markets, have failed to achieve a balance between supply and demand, which is precisely the key to meeting residents’ daily needs. Part of the reason may be that Xi’an focuses more on meeting per capita quantity targets and the construction of high-level LSAs while ignoring the diversity of LSAs and the balance between supply and demand. In addition, Xi’an attaches more importance to economic development in urban planning practice, resulting in land use that can bring economic benefits, which is often prioritized in land use decisions.

4.2. Socioeconomic Characteristics and Spatial Inequities in LSAs

This study discovered a significant inequality between LSAs and social groups in Xi’an. This inequality is especially prominent among children, young and middle-aged people, and lower-income groups living in peripheral areas. Although high accessibility is seen as an important indicator of urban development, we find that is not equally distributed among social conditions or groups. This reflects the neglect of vertical equity of LSAs in the planning empowered rapid urban expansion and spatial pattern change, which not only reduces the efficiency of spatial resource utilization but also may lead to a series of social problems [54].

The results of this study on the spatial association between age groups and accessibility reveal significant intergenerational inequity in the main urban area of Xi’an. As a typical city with an aging population, Xi’an’s performance in meeting the demands of LSAs for the elderly is positive, which may be related to the growing emphasis on aging-friendly society construction in recent years [55]. However, the proportion of children and young and middle-aged people is generally negatively correlated with the accessibility of LSAs, highlighting the “high demand-low accessibility” contradiction. Although many scholars have embarked on research on children’s needs and resources, providing various theoretical supports and strategic recommendations for building child-friendly cities [56,57], the effects in practice are not yet effective. Young and middle-aged people, as the largest demographic, have the lowest overall accessibility in the analysis. This could have resulted from two main reasons. The first is that the demands of young and middle-aged people are largely overlooked in current urban infrastructure planning, which overemphasizes friendliness to vulnerable populations, such as children and the elderly [58]. The second is that young and middle-aged people, as the family’s pillars, tend to make their housing choices in order to take care of the requirements or needs of the elderly and kids in the family, such as convenient living conditions or school district housing, which results in their competing and disadvantaged accessibility to LSAs. Governments and policymakers should fully consider the differences in the age structure of the community population in future planning. In particular, HL areas, i.e., those with a high proportion of age groups but limited accessibility, should be the focus of future housing and LSA increases. These areas may face shortages of specific LSAs for different age groups, and planners need to conduct in-depth analysis of these areas and develop targeted planning strategies to ensure that the needs of all age groups are met equally.

The results of this study on the spatial association between income level and accessibility indicated that lower-income groups in the central city enjoyed higher accessibility to LSAs, while higher-income groups were advantaged with regard to accessibility in the peripheral areas. This is related to the past Xi’an City Master Plan, which emphasized the preservation of historical and cultural heritage, especially the Ming City Wall and its surrounding areas. This policy has largely limited the renewal of the inner city, resulting in the aging and mismanagement of the residential complexes. Due to the historical path dependence of urban development, Danwei communities and traditional dilapidated communities are mainly located in or near urban centers [59]. Although the living environment of these two types of residential complexes is gradually deteriorating, benefiting from historical path dependence and geographic location advantages, they are surrounded by abundant opportunities. However, the results showed that lower-income groups, while having better access to basic demand amenities, were at a disadvantage in accessing high-level LSAs, such as ecological landscape amenities and sports and leisure amenities, which tend to be more concentrated in the areas where the higher-income groups are located, emphasizing the importance of high-level LSAs in social stratification. We argue that groups with higher socioeconomic status are generally more capable of choosing high-quality living environments [9]. In Xi’an, higher-income groups tend to reside in the newly developed suburbs, where large-scale developments offer an abundance of high-level LSAs and an improved quality of life. Whereas, guided by housing policies, economically disadvantaged migrants are usually concentrated in affordable housing on the urban peripheries, which typically suffer from a relative lack of LSAs [60]. China’s affordable housing strategy is still in the growing stage, focusing mainly on quantitative supplements while ignoring housing quality improvement and support. In newly developed suburbs, resources are more skewed toward higher-income groups. This residential segregation may lead to lower-income groups being at risk of social exclusion and isolation.

4.3. Factors Affecting the Imbalance between the Supply and Demand of LSAs

The spatial disparities in the equity of LSAs reflect the imbalance between the process of urbanization and the provision of public services, which is not only a direct result of urban planning but also intricately linked to the city’s historical legacy, historic preservation policies, economic activity, fiscal policy, and residential mobility in Xi’an.

During the planned economy, many urban residents worked in state agencies or government-affiliated institutions, enjoying welfare housing and basic services, such as healthcare and education [61]. The urban planning paradigm, characterized by the “unit complex” model, left a legacy of centralized public services in the urban core [62]. In contrast, the underdeveloped peripheral areas rely on the collective economy for welfare provision, such as collectively funded education, resulting in a dearth of tangible LSAs [63]. This urban–rural dual public service system explains the prevailing center–periphery pattern.

Since the reform and opening up, Xi’an has attracted a large number of migrant workers who mainly live in old urban areas and substandard rental communities, putting pressure on the construction and maintenance of urban infrastructure. As the ancient capital of the 13th Dynasty, Xi’an’s strict historic preservation policies have further constrained the ability of urban conservation areas to meet new demands, thus exacerbating the spatial heterogeneity of LSA accessibility.

With the transition from a planned to a market economy, market-oriented reforms have facilitated the entry of a variety of enterprises and non-profit organizations into the LSA supply market, promoting the marketization of public services [64]. LSAs such as public transportation, shopping malls, and parks have been commoditized into house prices, further widening the gap in access to public services among different income groups.

Since the reform of land marketing in China’s cities, land finance has not only become the main source of local public finance but also the main driving force of economic growth and urban development in modern China [65]. As independent urban landowners, local governments pursue both self-interest and public welfare, which affects the quality of public services to some extent [66]. Local governments earned extra-budgetary revenue by converting rural land to urban land and leasing land for development. But, in their pursuit of economic development and urban competitiveness, they tended to prioritize land use that brings economic benefits while under-investing in low-income areas, under-representative populations, and new districts, which may weaken equity and inclusion.

Residential choice behavior, as an informal “voting” mechanism of residents on public services, also affects the accessibility of LSAs. Social distance leads to unequal access to resources and services, and residents choose where to live based on their social characteristics and perceived preferences [67], thus affecting the balance between supply and demand. In Chinese society, which values family ties, consensus within families often determines residential choices, with some families prioritizing accessibility to public transportation and some focusing on proximity to quality schools [68,69]. However, for some groups, economic constraints or other reasons limit their agency in choosing better residential locations, resulting in passive choices that may not align with their needs.

4.4. Urban Planning and Policy Recommendations

In order to alleviate the spatial equity problems caused by the irrational allocation of LSAs in Xi’an, this study, based on the results of a comprehensive analysis of horizontal and vertical equity, suggests that the government should prioritize paying attention to the areas with particularly prominent comprehensive equity problems, including the southeastern part of the old urban area, as well as the western and northeastern parts of the peripheral area’s residential complexes. These areas not only have horizontal equity deficits in the distribution of living services but also have significant intergenerational equity issues between different age groups in the southeastern part of the Old City, while low-income groups face a greater risk of social exclusion in the western and northeastern parts of the peripheral areas. In view of this, this study proposes the following recommendations for urban planning to promote the equitable distribution of LSAs and improve the community living environment and the quality of life of residents.

(1)

Strengthening public participation and addressing the wide interests of different social groups

Wide public participation is regarded as essential to the success of public programs [70]. Many scholars generally agree that strengthening public participation is the key to solving urban issues [71,72]. But, even with the positive intentions of bottom-up planning approaches, equity in the urban renewal process is often not adequately represented, resulting in the voices and demands of some groups being ignored [73,74,75]. Under the requirement of high-quality urban development, it is far from enough to emphasize the interests of specific groups. The government should emphasize public participation and empowerment to ensure that residents of all age groups and economic statuses have equal access to urban resources. The government should adopt a multi-dimensional needs assessment mechanism to carry out the equitable allocation of LSAs based on the response to the differentiated demands of the population. This requires a detailed analysis of the population structure and encourages local residents to participate in filling out questionnaires to identify the differentiated needs of different groups for various types of LSAs. On the premise of considering total control, the allocation of different types of LSAs should be prioritized and adjusted according to the urgent needs of local residents. There is also a need to ensure that vulnerable groups, such as lower-income groups, children, and the elderly, have a full voice in community planning and updating, and to design appropriate ways or forms to involve them actively.

(2)

Promoting service resource sharing

The planning and layout of LSAs should adopt a systematic perspective for comprehensive decision making. Considering the spatial spillover effect of LSAs in the relationship between supply and demand [76] and the limited spatial resources of cities [77]. For the old or inner urban areas with scarce land resources, neighboring residential complexes can be integrated by supplementing the construction of a community pedestrian road network so as to promote resource sharing and complementarity. For example, for residential complexes in the southeastern part of the inner city, it is necessary to improve the construction of a pedestrian road network with the newly built oversupplied residential complexes in the surrounding areas to realize the sharing of surplus services. For the peripheral areas, urban planners should rationally allocate service resources and formulate housing development policies based on the strength of the spatial agglomeration relationship between LSAs and different groups of people so as to improve urban spatial differentiation. For example, urban planners should prioritize high-quality schools and hospitals in the western and northeastern parts of peripheral areas where children and low-income groups are concentrated. In addition, developers should be required to build a certain percentage affordable housing in new urban areas in the south. This rational allocation of resources and housing can meet the basic needs of lower-income groups, helping to break down residential segregation and enhance community integration.

(3)

Promoting mixed land use

Land resources in Xi’an’s main urban areas are relatively tight, and a mixed land use strategy may be a key to alleviating land pressure. Studies have shown that mixed land use can optimize land allocation and enhance the multifunctionality and livability of the community [78]. In addition, mixed land use allows for more opportunities for interaction between different social groups, contributing to social cohesion [79]. Therefore, the government and developers need to develop and implement mixed land use strategies to ensure they are in line with stated planning goals. Specifically, functional integration zones can be built to improve the matching of supply and demand for LSAs. By integrating the basic service functions of different age groups into the same LSAs, the efficiency and quality of LSAs are improved by adopting the method of shared use and common layout. For example, modes could be explored to integrate medical amenities with residential complexes, including elderly care centers and family doctor clinics in residential developments, which not only facilitate residents’ access to medical services but also promote interaction between different age groups within the community.

4.5. Innovations and Limitations

The innovations of this study mainly include the following. First, this study takes residential complexes as the basic unit for demographic data accuracy refinement. The spatial distribution and number of households in residential complexes were determined through the real estate registration information, which was better than using only census data in previous studies. Second, this study takes into account the differentiated demands of different age groups to quantify the accessibility of LSAs. It allows for a reflection on the heterogeneous and accurate accessibility of different age groups, even if they are living in the same area. Third, this study conducts a comprehensive assessment combining both horizontal and vertical equity perspectives, taking into account the socioeconomic characteristics of the population.

There are some limitations to this study. First, we did not consider the quality attributes of LSAs due to data availability. Second, due to the difficulty in obtaining income data, this study only characterized residents’ income levels using the average housing price of residential complexes. This fails to really reflect the wealth disparities among residents of the same residential complexes, such as loans and debts in house purchasing. Finally, the method of assessing the importance of LSAs using the results of the expert questionnaire in this study has some limitations in representing the actual situation. In future research, for our next step, we will designate and distribute questionnaires in local communities.

5. Conclusions

With the late stage of China’s urbanization process and the demand for improving quality of life in the new era, how to apply people-oriented and equity principles into LSA planning and management has become a new challenge in urban infrastructure and residential complex development. This study evaluates the accessibility of the 14 types of LSAs in Xi’an’s main urban area using the M3SFCA model, revealing the equity statuses in the spatial distributions of LSAs from horizontal and vertical perspectives and discussing the multiple influencing factors behind them.

The supply of LSAs in Xi’an’s main urban area follows a center–periphery pattern, with some LSAs showing significant spatial heterogeneity. The overall supply and demand were unbalanced, and the accessibility of low-level LSAs was poor. Xi’an has made some progress in meeting the demands of the elderly for LSAs, and children and young and middle-aged groups face significant inequality in accessing LSAs. Intergenerational inequities are especially prominent in the inner city due to historical protection limits and demographic characteristics. In addition, lower-income groups living around the city center have some benefits in accessing basic LSAs, but the majority of lower-income groups living in the suburbs remain disadvantaged, especially in accessing high-level amenities. This shows that access to high-level LSAs remains a key factor affecting social equity in social stratification.

The spatial inequity of LSAs is mainly due to the impact of urban planning decisions, historical legacies, historic preservation policies, economic activities, institutional factors, fiscal policies, and residential mobility. This study offers implications and evidence from Xi’an for other cities that want to conduct a comprehensive evaluation and equitable planning of LSAs. We suggest that future planning decisions should pay more attention to the equity of the demands of different socioeconomic groups, ensuring the basic supply of LSAs. The government should strengthen public participation to empower residents of all ages and economic statuses to have equal access to urban public resources. The implementation of differentiated housing strategies can help break down residential segregation and promote service resource sharing. Mixed land use strategies can optimize land resource allocation while also enhancing social cohesion. The results of this study provide recommendations for policies and practices aimed at planning LSAs and assisting in the promotion of spatial equity and social sustainability.