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Detecting heterogeneity of spatial accessibility to sports facilities for adolescents at fine scale: A case study in Changsha, China

  • Shuang Cheng , Wuxin Liu , Wangyang Jiang and Chen Li EMAIL logo
Published/Copyright: April 13, 2024
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Abstract

It is crucial for social sustainability that adolescents have access to social sports services fairly. However, there are few research studies on requirements for sports facilities and spatial accessibility of adolescents at a fine scale. Further, identifying the heterogeneity of the relationship between spatial accessibility and other factors and their scales simultaneously would be conducive to reveal the variations of spatial accessibility effectively under the potential scale effect. This research aims to explore the heterogeneity of spatial accessibility to sports facilities at a fine scale in Changsha, China. The Gaussian-based two-step floating catchment area model is first employed to evaluate spatial accessibility. Then, multiscale geographically weighted regression (MGWR) is applied to examine the relationship between spatial accessibility and its associated factors. The mean accessibility in Yuelu District (0.158) is the highest as well, and the standard deviation (0.236) is also the highest one. Both the accessibility (0.019) and its standard derivation (0.029) in Furong District are the lowest. The results show that there is a lack of balance of spatial accessibility for the clusters with different accessibility levels distributed in the study area. Some socio-economic factors, such as housing price and nighttime light intensity, have significant impacts on spatial accessibility for adolescents with spatial and scale heterogeneity by using MGWR. Based on heterogeneous distribution and association, suggestions for promoting spatial accessibility to sports facilities for adolescents are proposed.

1 Introduction

Regular physical exercise is an effective way to reduce the risk of chronic disease, e.g., diabetes, obesity, and some cancers [1,2]. The government and researchers have paid more attention to public participation in physical exercise A large number of research studies have presented a positive relationship between spatial accessibility to sports facilities and physical exercise [3,4,5]. Due to spatial differences in socio-economic status, maldistribution of sports facilities may lead to unbalanced supply and demand, and further cause varied spatial accessibility to sports facilities [6]. Therefore, it is beneficial to improve greater equity of sports facilities by understanding spatial accessibility.

Spatial accessibility describes the convenience that the residents to reach their destination or infrastructure [7]. Spatial accessibility to sports facilities, which represents the convenience of physical activity, can be defined as the ability to reach the sports facilities based on the above general definition. A series of studies have analyzed spatial accessibility to facilities [8,9]. According to the different contents, existing studies mainly focus on two aspects: one is the assessment or measurement of spatial accessibility for more accurate results. The other is detecting the association pattern between spatial accessibility and other factors, which aims at exploring the reason or impact of the variations of spatial accessibility.

Different age groups result in different demands for sports facilities [10]. Nevertheless, existing research on spatial accessibility mainly focuses on the whole age group rather than a certain age group at fine scale, which cannot reveal the unbalanced supply demand. In addition, because of the general existence of spatially varying relationships among spatial variables [11], it is important to detect the association pattern between spatial accessibility and other factors by spatial regression. Therefore, this research aims to detect the distribution of spatial accessibility to sports facilities for adolescents at a fine scale and then model the relationship between spatial accessibility and the associated factors that explores the heterogeneity of spatial accessibility to sports facilities.

The structure of this article is organized as follows: In Section 2, a literature review of about the related research is given, and the specific issues are highlighted. In Section 3, the study area and data sets are introduced. Subsequently, the methods including the measurement of spatial accessibility and the association analysis between spatial accessibility and related factors are provided in Section 4. In Section 5, the experiment results in the study area are described. The discussion and conclusion are provided in Sections 6 and 7, respectively.

2 Literature review

As mentioned earlier, existing research on spatial accessibility to sports facilities mainly is divided into two categories: spatial accessibility measurement and modeling the relationships between spatial accessibility and the related factors.

The assessment or measurement of spatial accessibility is usually related to spatial scales (spatial scope or spatial analysis units) and methods. Spatial scales, especially spatial analysis units, seriously depend on the granularity of initial observations or statistics [12]. For example, official census data are widely applied to the analysis of spatial accessibility. Because of public privacy protection, census data are aggregated and released at the sub-district or street scale [13], and spatial analysis units generally correspond to the sub-district or street scale based on the census. Hence, it is difficult to accurately determine the geographical location of demand points.

The analysis method is another critical issue in spatial accessibility. Common methods for measurement can be roughly divided into two categories, namely simple indicators and spatial interaction models [14]. Simple indicators are mainly based on the distance measurement method and opportunity accumulation method [15,16,17], that is, the distance (space, time, cost, etc.) between the supply point and demand point of sports facilities or the opportunity of getting close to the sports facilities from a certain location would be defined as the indicator. These indicators are simple and intuitive, but the influence of distance effect, spatial interaction, and scale cannot be handled well.

Spatial interaction models tend to integrate the action intensity of the supply point and demand point to measure spatial accessibility, which are mainly represented by the two-step floating catchment area (2SFCA) method [18]. The 2SFCA method essentially belongs to gravity models that investigate flows or movements between two locations with consideration of distance effect [19,20]. The fundamental process to assess spatial accessibility to sports facilities involves the allocation of supply and the satisfaction of demand. A series of improved 2SFCA methods have been presented by extending the underly assumption in the classical 2SFCA method, such as the Gaussian-based 2SFCA method [21] and the multiple catchment sizes 2SFCA method [22], the gravity-based variable 2SFCA method [23]. Although lots of 2SFCA variants can be used to measure spatial accessibility, it is reasonable to select appropriate models instead of complex methods.

Compared with the assessment or measurement of spatial accessibility, there are only a few literature studies on the association pattern between spatial accessibility and other factors, especially the impact of spatial accessibility of sports facilities on associated factors. For example, by exploring the association between spatial accessibility and frequency of physical activity, Macdonald finds that the frequency of physical exercise is related to spatial accessibility of sports facilities with specific types near the workplace or home [24]. To investigate whether a change in the number or distance of the sports field is associated with a change in metabolic equivalent task hours/weeks, it is demonstrated by Halonen et al. that the level of physical exercise might be affected by changes in the availability of facilities [4]. Han et al. attempt to examine whether the improvement of spatial accessibility could contribute to the reduction of the obesity of adults, and the result shows that the number of local public sports facilities is not significantly associated with local body mass index [25].

As reviewed earlier, fruitful progress has been made in the related research on spatial accessibility to sports facilities. Nevertheless, there are still several issues to discuss. The first one is the assessment of spatial accessibility at a fine scale. The data, which are from a statistical yearbook or questionnaire and have high reliability, can recognize the distribution characteristics of the supply demand of sports facilities at the county or street level, however, does not provide detailed distribution within the region [26]. Consequently, it is difficult to reveal the supply and demand of sports facilities at the fine scale, which may result in the mismatch in the layout of sports facilities is still not clearly discovered. Additionally, there are varied requirements for physical exercises among different age groups. In children and adolescents, vigorous-intensity aerobic activities, as well as those that strengthen muscle and bone, are recommended at least 3 days a week, but functional balance and strength training at moderate or greater intensity are suggested for adults aged 65 years and above [10]. So, it is reasonable to carry out research for different age groups at a fine scale.

The second one is about modeling heterogeneous relationships between spatial accessibility and other factors. Spatial heterogeneity means the non-stationarity of the spatial processes generating the observed data, which reflects the changes of spatial distribution or spatial relationships among spatial variables [11]. That is, the association pattern between spatial accessibility and other factors may vary over the space. Geographically weighted regression (GWR), which has been also employed to quantify the reason for the variation of spatial accessibility, is an effective approach to deal with spatial heterogeneity [27,28]. The GWR model assumes the effects of different associated factors on spatial accessibility at the same spatial scales; namely the variation of the relationships from different factors is similar [29]. Actually, the situation may be inconsistent. For example, the variation of the effect of housing price may exhibit different spatial ranges or scales. Thus, modeling the relationships between spatial accessibility and other factors needs to consider the heterogeneity of relationships and their scales simultaneously [30].

This research aims to detect heterogeneity of spatial accessibility to sports facilities for adolescents at a fine scale. Adolescence (10–19 years of age) is a period of rapid transition in life from “childhood” to “adulthood,” and this is an extremely critical growth phase, during which the adolescent goes through physical and mental changes [31]. Physical activity plays a crucial role in promoting physical and mental health, and spatial accessibility to sports facilities for adolescents is of great significance. We want to obtain the spatial distribution of spatial accessibility, identify the unbalanced characteristic of the supply and demand of sports facilities, and reveal the heterogeneity of the association pattern between spatial accessibility and related factors in the study area, the city of Changsha, China.

3 Study area and datasets

3.1 Study area

Changsha is selected as the sample that is located in the northeast of Hunan Province, China. Technical Guide for Spatial Planning of Special Land for Sports Facilities in Cities and Counties of Hunan Province was published in 2023, which aims to increase the effective supply of public sports service facilities and public welfare. As the capital city of Hunan Province, the study area with the largest population has been paid more attention.

There are six urban districts (Furong, Tianxin, Yuelu, Kaifu, Yuhua, and Wangcheng), one county (Changsha County), and two county-level cities (Liuyang City and Ningxiang City) in China. Its land area is 11819.50 km2 with a built-up area of 567.32 km2. According to the seventh National Census, as of November 2020, the permanent population of Changsha was about 10.0479 million, accounting for 15.12% of the province's total population, and the urbanization rate was about 82.60%. Considering that the city is the place with the most intense human activities and the fitness sites are mainly distributed in the built-up area, the built-up area of Changsha is selected as the research area and divided into 1-km resolution grids as the basic spatial analysis unit. The spatial distribution of the study area and grid units is shown in Figure 1.

Figure 1 
                  Map of the study area.
Figure 1

Map of the study area.

3.2 Datasets and data preprocessing

The data include that (1) Point of interest (POI): POI data with sports category obtained from Gaode map include the name and geographical coordinate information of facilities. (2) Population data: From the open worldpop population data product (https://www.worldpop.org/), the 1 × 1  km grid population density data in 2020 are employed as the quantitative basis for the demand for sports facilities. (3) Basic geographic information data: they include road network and administration boundary of county-level and street. The road network data also come from OpenStreetMap (https://www.openstreetmap.org), which can be used for network analysis through spatial topology processing. (4) Remote-sensing nighttime light image: The NPP/VIIRS nighttime satellite data sets in 2020 (https://eogdata.mines.edu/products/vnl/) were collected to extract the nighttime light intensity. (5) Housing price data: These data in 2020 were obtained based on the housing sale intermediary platform (https://Fang.com).

In data preprocessing, sports facilities related to adolescents are selected, except for senior citizen activity centers, etc. There are 744 sports facilities the spatial distribution of sports facilities is shown in Figure 1. According to the age group by the WHO, the age range of adolescents is 10–19 years, and adolescent population density (Figure 2) is estimated based on the population age structure from the population data product. The housing price and nighttime light intensity in each street unit were obtained by calculating the average values of all records within each street unit. The spatial distribution of these two variables is shown in Figures 3 and 4, respectively. The housing price and nighttime light intensity were defined as the associated variables.

Figure 2 
                  Spatial distribution of adolescent population density.
Figure 2

Spatial distribution of adolescent population density.

Figure 3 
                  Spatial distribution of housing price.
Figure 3

Spatial distribution of housing price.

Figure 4 
                  Spatial distribution of nighttime light intensity.
Figure 4

Spatial distribution of nighttime light intensity.

4 Methods

The methodological framework for detecting heterogeneity of spatial accessibility at a fine scale is shown in Figure 5. Based on multi-source data sets, the spatial distribution of sports facilities and adolescents can be extracted and the supply and demand capacity can be further obtained at each grid unit. Especially, the spatial distribution of sports facilities is extracted from POI data that only sports facilities which are suitable for adolescents are selected in this research. Based on the types or levels of sports facilities, the supply capacity of each sports facility is estimated. The spatial distribution of adolescents is from population data. The quantity demanded is directly defined as the total number of adolescents at each grid. Although a part of adolescents may not participate in sports exercises, it is difficult to estimate the participation rate, and therefore, this research assumes that all adolescents require physical exercise.

Figure 5 
               Methodological framework.
Figure 5

Methodological framework.

Next, there are two methods that are applied to detect heterogeneity of spatial accessibility at the fine scale, namely the Gaussian-based 2SFCA method and multi-scale geographically weighted regression (MGWR) [21,32]. The supply capacity information, the demand capacity information, and the distance information of supply–demand locations are inputted into the Gaussian-based 2SFCA to generate the results of spatial accessibility. The MGWR is then applied to model the relationships between spatial accessibility defined as dependent and independent variables. Spatial heterogeneous supply–demand relationships are mainly reflected in two aspects: one is a spatial discrepancy of spatial accessibility, and the other is a spatial variation of the effects of independent variables on spatial accessibility. The principles of the Gaussian-based 2SFCA and MGWR will be introduced in subsections 4.1 and 4.2.

Especially, the spatial distribution of sports facilities for adolescents is extracted from POI data that only sports facilities for adolescents are selected in this research. Based on the types or levels of sports facilities, the supply capacity of each sport facility is estimated. The spatial distribution of adolescents is from population data. The quantity demanded is directly defined as the total number of adolescents at each grid. Although a part of adolescents may not participate in sports exercises, it is difficult to estimate the participation rate, and therefore, this research assumes that all adolescents require physical exercise. The supply capacity information, the demand capacity information, and the distance information of supply–demand locations are inputted into the Gaussian-based 2SFCA to generate the results of spatial accessibility.

4.1 The Gaussian-based 2SFCA method

Gravity models are a classical method to measure spatial accessibility by considering the supply–demand capacity and distance. However, this model cannot describe the competitions among different demand sites. To overcome this limitation, the 2SFCA method is developed by incorporating demand competition effects into gravity models. Subsequently, the 2SFCA are widely used to assess spatial accessibility to different facilities and meanwhile, a series of improved 2SFCA methods are proposed to enrich the theory and methods of spatial accessibility. As a member of the family of 2SFCA, the Gaussian-based 2SFCA method was developed by integrating the distance decay mechanism on the supply–demand interactions in 2SFCA [21], and the Gaussian-based 2SFCA method has been proven to measure spatial accessibility to sports facilities effectively [14]. Sports facilities usually have limited capacities that some people use it while others don't, and the competition of sports facilities should be considered [33]. Therefore, the Gaussian-based 2SFCA method is first selected to assess the spatial accessibility of sports facilities.

The Gaussian-based 2SFCA method mainly includes two steps: the first step is to search for all demand points within the catchment area defined as a circle centering each supply point j with a radius d 0. The ratio of supply–demand R j corresponding to each supply point j can be computed as:

(1) R j = S j k { d kj d 0 } G ( d kj ) D k ,

where S j is the supply capacity at the supply point j; d 0 represents the service scope of the supply point; D k is the demand capacity at the demand point k; d kj is the distance between the supply point j and the demand point k; the demand point k is obtained based on the inequation condition d kj d 0 ; G ( d kj ) is the Gaussian weight representing the distance decay of the supply–demand relationship, which is defined as follows:

(2) G ( d kj ) = e 1 2 × ( d kj d 0 ) e 1 2 1 e 1 2 , if d kj d 0 0 , othewise .

The second step is to search for all supply points within the catchment area defined as a circle centering each demand point i with a radius d 0. The spatial accessibility of demand point i can be calculated by the Gaussian weighted average of the corresponding ratio of supply demand of all searched supply points. The expression can be written as follows:

(3) A i = j { d i j d 0 } G ( d i j ) R j .

Based on equations (1)–(3), each demand point can be obtained. Notably, a critical issue among the Gaussian-based 2SFCA or 2SFCA method is to define the distance measurement functions between the supply and demand points. Considering that human travel model mainly involves in network space rather than Euclid space, the network distance was then selected in the Gaussian-based 2SFCA method in this research.

4.2 Multiscale GWR

Traditional regression or ordinary least squares (OLS) regression aims to establish a global model to describe the relationship between dependent variables and independent variables that assumes the relationship are constant over space. Assuming that n samples are observed at spatial location i (i = 1, …, N), the regression equation of OLS can be written as

(4) y i = a 0 + k = 1 m a k x i k + ε i ,

where y i is the dependent variable; x ik is the kth independent variable; a 0 is the constant term; a k is the kth coefficient, and ε i represents the error term.

However, the potential assumption violates spatial non-stationarity that spatial data are not all generated by a certain distribution [27]. To capture spatial non-stationarity, GWR was developed by adopting a locally varying model, whose parameters change across spatial locations. The model expression is

(5) y i = a i 0 + k = 1 m a ik x ik + ε i ,

where a i 0 is the constant term at location i; a ik is the coefficient of the kth variable at location i. A geographically weighted least squares approach is used to calibrate local regression models.

MGWR is a new variant of GWR by allowing the conditional relationships between the independent and dependent variables to vary at different spatial scales [32]. The regression equation is described as follows:

(6) y i = a i 0 + k = 1 m a bw ik x ik + ε i ,

where bw ik in a bw ik represents the bandwidth used for calibration of the kth conditional relationship at spatial location i. A back-fitting algorithm is used to conduct model calibration and bandwidth parameters selection.

5 Results

5.1 Results of spatial accessibility analysis in the study area

The capacities of supply and demand are the main variables in the Gaussian-based 2SFCA method. The demand capacity is derived from the total number of adolescents. There is only name and location information in the datasets, so it is difficult to measure the supply capacity of each sports facility. In this research, according to the Technical Guide for Spatial Planning of Special Land for Sports Facilities in Cities and Counties of Hunan Province, there are four levels for sports facilities including regional level, municipal level, district (county) level, and street level. It is assumed that a higher level of sports facilities means a stronger supply capacity and larger service radius. Further, the supply capacity and service radius under different levels were set according to sport management experts (Table 1). For example, the supply capacity and service radius of regional level, such as Helong Stadium, are 100 and 15 km, respectively. The street level, such as the Baishang Sports Football Stadium, is 3 and 1 km. Although the specific values of supply capacity (100 or 3) cannot be interpreted (the “relative” unitless supply capacity values are set to each sports facility), they are mainly used to reflect the relative size of the supply capacity.

Table 1

The supply capacity and service radius of different levels of sport facilities

Category Sample Supply capacity Service radius (km)
Regional level Hunan provincial stadium 100 15
Municipal level Helong stadium 50 10
District (County) level Sports ground of Hunan University 15 5
Street level Baishang Sports Football Stadium 3 1
Community level Resident Activity Center of Shangpo Community 1 0.3

The normalized results of spatial accessibility at grid units are shown in Figure 6(a). The spatial distribution of accessibility exhibits spatial autocorrelation obviously means the existence of aggregative patterns. Clusters with low accessibility are mainly located in marginal areas while clusters with high accessibility are located in the transition area between the edge and the center of the area. Considering that the grid units lack semantic information, the results of spatial accessibility at the grid units are aggregated into street units, and the spatial accessibility of a street unit is obtained by the average of all grids within the street unit. The spatial distribution of spatial accessibility at the street scale is shown in Figure 6(b). Because the results at the street scale are based on those at the grid scale, spatial distribution at the street scale is similar to that at the grid scale.

Figure 6 
                  Spatial accessibility of sports facilities at gird (left) and street (right) scales.
Figure 6

Spatial accessibility of sports facilities at gird (left) and street (right) scales.

Statistics of spatial accessibility for sports facilities at the district/county scale are listed in Table 2, which includes the numbers of street areas and grid units (excluding the grid without adolescent population or demand of physical exercise), mean and standard variation of spatial accessibility within each district/country. According to the descending order of spatial accessibility, the regions are Yuelu, Wancheng, Kaifu, Tianxi, Changsha County, Yuhua, and Furong, respectively. The mean accessibility in Yuelu District (0.158) is the highest, followed by Wangcheng District (0.088), Kaifu District (0.073), Tianxi (0.070), and Changsha County (0.063). The regions with the lowest mean accessibility are Yuhua and Furong, respectively. In contrast, the whole spatial accessibility at the Furong is the lowest.

Table 2

Statistics of spatial accessibility of sport facilities at district/county scale

Region Number of street areas Number of grids Mean Standard variation
Changshaxian 5 186 0.064 0.098
Furong District 14 204 0.019 0.029
Kaifu District 16 199 0.073 0.130
Tianxin District 12 183 0.070 0.136
Wangcheng District 7 176 0.088 0.107
Yuelu District 20 378 0.158 0.236
Yuhua District 12 317 0.032 0.045

Although the total accessibility at Yueluis better than that in other areas, its standard deviation of spatial accessibility is 0.236, which is also the highest one. The high variability indicates that the spatial imbalance between supply and demand is serious. The standard deviation of spatial accessibility in Furong, Yuelu, Kaif, Yuhua, Tianxin, and Wangchen is very similar. The standard deviation of spatial accessibility in Yuhua and Furong are 0.045 and 0.029, respectively, both of which are the smallest in all regions.

5.2 Results of spatial regression analysis in the study area

According to the MGWR model, housing price and remote sensing nighttime light intensity are selected as independent variables. The Pearson correlation coefficient of these two factors is 0.273, which indicates a weak linear correlation or no linear correlation. To compare the coefficients of different variables, both of the variables were normalized to the range from 0 to 1. The OLSs regression and GWR are selected for comparative analysis. GWR and MGWR are based on the software MGWR V2.2.2 (https://github.com/pysal/mgwr). The AICc is first selected as an optimization criterion. In the GWR model and MGWR model, the parameters corresponding to the minimum AICc are finally identified as the optimal selection by adjusting different parameters (kernel function types, bandwidth parameters, or bandwidth searching methods). The adaptive bandwidth and Gaussian kernel are finally identified in both GWR and MGWR models.

The diagnostic information for different models is shown in Table 3. The AICs for OLS, GWR, and MGWR are –394.038, –429.328, and –453.505, respectively. The AICs in MGWR are lower than those in the OLS model and GWR model. The adjusted coefficient of determination in these models are 0.03, 0.537, and 0.682, respectively, and the value in MGWR is the highest. Therefore, the MGWR model can effectively identify the variation of associated factors of spatial accessibility by considering both relationship heterogeneity and scale heterogeneity.

Table 3

The diagnostic information for different models

Index OLS GWR MGWR
AICc –394.038 –429.328 –453.505
R 2 0.06 0.701 0.812
R 2 adj 0.03 0.537 0.682

Compared with GWR, MGWR can effectively describe different effect scales of independents, rather than the average effect scale of all independents. The bandwidths for different models are listed in Table 4. For GWR, the bandwidths of all variables are the same, and the value is 25. However, for MGWR, the optimal bandwidths of housing price and nighttime light intensity are 18 and 13, respectively. Both of them are smaller than that in the GWR model, and the bandwidth of housing price is slightly larger than that of nighttime light intensity. It means that there is a higher variation between spatial accessibility and housing price than that between spatial accessibility and nighttime light intensity.

Table 4

Accuracy evaluation results for different models

Independent Bandwidth of GWR Bandwidth of MGWR
Housing price 25 13
Nighttime light intensity 25 18

The regression coefficient of housing price under spatial distribution is shown in Figure 7. The coefficient of housing price ranges from −0.037 to 0.345. The street units with negative coefficients are mainly located in the central part and southern part, where higher housing prices contribute to the decrease in spatial accessibility. The remaining street units exhibit a positive correlation that increasing housing prices results in an increase in spatial accessibility. The number of street units with negative coefficients is almost equal to that with positive correlation.

Figure 7 
                  Spatial distribution of the regression coefficient of housing price at street scale.
Figure 7

Spatial distribution of the regression coefficient of housing price at street scale.

Regression coefficient of nighttime light intensity under spatial distribution is shown in Figure 8. The coefficient is from −0.347 to 0.042. Nighttime light intensity also has both positive and negative effects on spatial accessibility. The street units with positive effects are mainly distributed in the marginal areas of the study area, especially most parts of Tianxin and Changsha County. The positive effect means that the increase in nighttime light intensity will lead to higher spatial accessibility. In contrast, the number of street units with negative effects is far greater than that with positive effects, which indicates that the increase in nighttime light intensity will result in less spatial accessibility in the most parts of the study area.

Figure 8 
                  Spatial distribution of the regression coefficient of nighttime light intensity at street scale.
Figure 8

Spatial distribution of the regression coefficient of nighttime light intensity at street scale.

6 Discussion

Spatial accessibility to sports facilities has an important influence on the frequency of residents’ participation in physical exercise [4,5]. This research examines the heterogeneity of spatial accessibility to sports facilities for adolescents from two aspects: the first is spatial accessibility measurement by the Gaussian-based 2SFCA method, and the second is exploring the heterogenous relationships between spatial accessibility and the associated factors according to the MGWR model. At the grid scale, spatial accessibility exhibits obvious aggregative patterns that are reflected on different clusters of spatial accessibility distributed in spatial regions. Through spatial aggregation statistics, at the street scale and district/county scale, spatial accessibility in Yuelu is the highest, but the highest variation means serious inequality in this district. Actually, Yuelu, where universities are most densely distributed, mainly focuses on education. Sufficient sport facilities can significantly improve the spatial accessibility of adjacent areas. The areas far from these universities have low spatial accessibility, which results in severe imbalance. Furong and Yuhua have low means and variations of spatial accessibility. Despite the variability of accessibility in this area being the lowest, the overall low accessibility makes balanced spatial relationships unmeaning. In other districts, the means and variances of spatial accessibility are similar at the middle level.

Existing researches on the accessibility of sports facilities rarely quantitatively analyze the heterogeneity and multi-scale influencing mechanism of accessibility [6,14], this research employs the MGWR model to reveal the impacts of different factors on spatial accessibility. It is assumed that the results of the regression model with the highest R 2 or the low AICs are more reasonable or accurate in explaining the relationships. GWR and OLS are generally selected to compare with MGWR [30]. Table 3 shows that MGWR is superior to GWR and OLS in modeling the relationships between spatial accessibility and the independent variables. It further confirms that MGWR can better reveal the association pattern after considering spatial heterogeneity and multi-scale effects [28,30]. Socio-economic factors are generally applied to explore their impacts on spatial accessibility to other facilities [34]. Because of the limitation of socio-economic data collection, only housing prices and nighttime light intensity are selected in this research. The results based on MGWR indicate that housing price has both positive and negative impacts on spatial accessibility.

Spatial accessibility essentially depends on the supply–demand relationships of sports facilities matched by the road network. The street units with negative coefficients of housing price are mainly located in the central and southern parts of the study area, where the density of the adolescent population has a high value. These streets with higher housing prices have better transportation infrastructure and education that attract lots of families. It leads to an increase in demand for sports facilities. However, higher housing prices limit the supply of sports facilities for higher construction costs of sports facilities. Consequently, housing prices have a negative influence on spatial accessibility.

The street units with positive coefficients are located in the areas with low density of adolescent population. In contrast, rising housing price corresponds to better transportation that may improve the spatial accessibility to sports facilities. In most parts of the study area, nighttime light intensity has a negative influence on spatial accessibility. Nighttime light intensity is an effective indicator to measure human activity [35]. Generally, higher intensity of nighttime light means stronger population activity. In these units, the demand for sports facilities may increase significantly. The incremental supply for sports facilities cannot effectively match the demand for sports facilities, which may result in negative influence.

The above findings can provide helpful information for promoting fairness in spatial accessibility to sport facilities for adolescents. On the one hand, the results at different scales clearly show the approaches to improve spatial accessibility for adolescents. Meanwhile, the results also indicate that different regions have different priorities in promoting equity in sports facilities. On the other hand, the regression results also can provide valuable guidance. For example, sports facilities can be divided into public sports facilities and commercial sports facilities [36,37]. From the scale heterogeneity by MGWR, housing prices are significantly associated with spatial accessibility to sports facilities. Especially, commercial sports facilities may be seriously influenced by housing prices. In order to promote fairness in spatial accessibility, the government can provide subsidies for controlling the cost of public facilities and increase sports facilities in those areas with lower accessibility, especially in those areas with stronger human activity.

It is a critical and challenging topic in sports resource management that explores the difference in spatial accessibility [29]. This content involves many complicated contents that have been further discussed in this research. The first one is the spatial analysis of basic units. The modifiable areal unit problem (MAUP) is regarded as one of the critical elements in spatial data analysis; that is, the results depend on the size of analysis units or grids [38]. Grid units at 1 × 1 km spatial resolution are selected as the demand unit that we do not explore the results at other resolutions or scales. Therefore, it is one of the future research contents that integrates the MAUP into spatial accessibility.

The second is the supply–demand relationship for sports facilities. Obviously, adolescents have personalized sports demand that adolescent’s preference for physical activity is different and leads to different types of sports facilities. This research does not consider different physical activities, which may lead to inaccuracy in calculating spatial accessibility. Meanwhile, it is assumed that there is a positive relationship between the level of sports facilities and supply capacity. A larger service radius presents a higher supply capacity for sports facilities. Although the assumption is reasonable, it is difficult to define a specific value of each sport field. The supply capacity and service radius are defined based on expert experience in this research. More effective supply capacity may be quantified by factors, such as the size and type of sports facilities, which can further support the use of an interpretable mode, such as spatial availability [33], in further work.

In addition, the diversity of travel modes is also simplified in the measurement of spatial accessibility. The travel modes including walking, cycling, and public transportation for adolescents may result in the results of evaluating spatial accessibility to sports facilities [14]. The travel model plays a significant role in the choice of human activities including physical exercise, and meanwhile, the service radius of sports facilities is also associated with the travel model. Because the travel model selection is also associated with the individuals or groups, the related data is not collected. Therefore, this research only employs the road network distance to match the supply and demand of sports facilities and does not discuss the complicated travel modes. It is another problem to be solved that how to integrate the travel modes into spatial accessibility.

7 Conclusion

This research explores the supply–demand relationship of sport facilities for adolescents under spatial heterogeneity at a fine scale. The process involves two main steps: the Gaussian-based 2SFCA method is first used to evaluate the spatial accessibility of sports facilities, and the MGWR model is then applied to reveal the relationships between spatial accessibility and the associated factors. The results in Changsha show that spatial accessibility exhibits heterogeneous distributions, which indicates that there exists an obvious unbalance in the supply and demand of sports facilities. By the MGWR model, the scale effect of two variables, namely housing price and nighttime light intensity, is discovered. The bandwidth or scale of housing price is slightly larger than that of nighttime light intensity. Both negative and positive effects of these variables have been detected with inconsistent spatial characteristics, and the effect mechanism is essentially dependent on the changes in the supply–demand relationships of sports facilities.

Acknowledgments

This study was supported by the Basic Ability Enhancement Program for Young and Middle-aged Teachers of Guangxi (No. 2023KY0242), the Science and Technology Innovation Program of Xiangtan Institute of Technology (No. 2023YB26), and the Scientific Research Starting Foundation of Guilin University of Technology (No. GUTQDJJ2020032).

  1. Conflict of interest: Authors state no conflict of interest.

  2. Data availability statement: Data will be made available on request.

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Received: 2023-08-02
Revised: 2024-01-13
Accepted: 2024-02-03
Published Online: 2024-04-13

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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