2.1. Social capital

In defining social capital, Pierre Bourdieu [17] was the first to define it as the sum of actual or potential resources obtained through institutionalized relationship networks. Coleman [18] emphasized that social capital fosters close ties, obligations, and identity among individuals. Robert D. Putnam [19] provided the most widely accepted definition: social capital is the sum of social networks, social trust, and cooperative and reciprocal relationships formed within communities, which fosters collaboration, development, and democratic participation. Social capital is widely applied in research fields such as economic development, health, crime, education, and governance [20].

Communities are regarded as dispersed networks of interpersonal relationships, and social capital can also be defined as localized social capital. It reflects the strength of bonds, trust, and reciprocity among residents [21]. In terms of social capital quantification, tools such as SCAT (Social Capital Assessment Tools) [22] and A-CAT scales (Harpham, Kawachi) have gradually been adopted. The main dimensions include participation in local groups or organizations, localized social networks, informal social interactions, trust, reciprocity, volunteerism, social support, community cohesion, and community sentiment [23].

Overall, while social capital has a profound impact on areas such as community renewal [20] it still lacks a clear definition and systematic quantification. Evaluation scales lack standardized criteria and comprehensive dimensions [24], which constrains validity analysis to some extent [25]. Member relationships within social capital are influenced by historical and cultural contexts [10]. Therefore, the systematic construction of social capital scales needs to account for the critical factor of regional differences.

2.2. Relationship between social capital and the construction of community public service facilities

The essence of social organizations’ actions is to achieve trzhust and cooperation within the organization [26]. Social capital, an essential element for enhancing community quality and sustainable community development [27], is inseparable from community construction.

Regarding the dimensions of social capital, the disaster resilience of community public service facilities can significantly enhance community cohesion [28], and the suitability of the neighborhood environment is closely linked to residential satisfaction, a sense of belonging [29], and residents’ place identity [30]. Social capital, urban resource equity, neighborhood sense of place, and community sense are key themes in social design. Existing studies indicate that the construction of community public service facilities is related to these themes [11,31].

In terms of facility function categories, community parks or sports activity centers are conducive to creating communities with positive social capital [32]. Building older adult-friendly communities is closely related to community cohesion [33], community green spaces and landscapes are linked to social support and residents’ health [34], and community entertainment facilities are associated with community interactions [35]. However, an increase in the number of certain commercial facilities can affect neighborhood safety and lead to a decrease in social capital [36]. In the context of facility configuration and layout, macroscale factors, such as land-use intensity, facility construction density, and walkability, are all associated with social capital. The higher the accessibility of facilities, such as clinics, hospitals, community centers, and schools, the more beneficial it is to increase social capital [35]. However, high-density residential environments clearly have detrimental effects on residents’ community interactions [9]. Few scholars have explored how multiple associated amenities working together affect social capital at the meso level, and there is a relative paucity of research on how agglomeration patterns formed by multiple types of amenities within the same community’s living sphere act on social capital.

Existing research methods primarily use structural equation models (SEM) [37], partial least squares structural equation models (PLS-SEM) [38], or ANN neural networks [39] to quantify social capital and related concepts, discussing correlations on a global scale. Urban planning and development inherently feature regional variations (citation), with distinct focal points and functional divisions, a factor insufficiently addressed in existing research. Geographically Weighted Regression (GWR) is commonly applied in accessibility research, offering localized models by fitting regression equations for individual variables, thus overcoming the inability of traditional regression models to reflect spatial variations in coefficients [40]. In practical applications, GWR requires testing with Ordinary Least Squares (OLS) regression models to exclude multicollinearity before conducting further analysis. Therefore, exploring the relationship between social capital and community public service facilities through GWR can take into account the development differences of urban areas, addressing the third research question.

2.3. Configuration characteristics and colocation patterns of community public service facilities

The concept of “industry co-agglomeration analysis” was first proposed by Ellison and Glaeser, suggesting that differentiated industries with certain relational ties tend to be spatially proximate [41]. The self-organized spatial layout characteristics of community public service facilities reflect their intrinsic associations and preferences and possess considerable research value in urban planning, geography, and economics.

In quantifying facility configuration characteristics, the proportion of facilities within a unit area reflects the extent to which a region is represented by certain feature types [11], making it more accurate than the area proportion method at smaller spatial scales. The Shannon-Weiner diversity index was proposed in 1948 by Claude Elwood Shannon, the founder of information theory [42]. It is used to measure species richness and the evenness of individual distributions within a system, and is widely applied in fields such as mathematics, communication, and ecology. Compared to balance indices and entropy indices, it offers advantages such as appropriate scalability and no restrictions on sample evaluation, making it a suitable measurement method [43]. In recent years, the research methods of “spatial association” have developed swiftly and refer to patterns of association within a single element or between two or more elements. The concept of colocation patterns was initially proposed by Shekhar and Huang [44], while Leslie and Kronenfeld introduced the Global Co-location Quotients (GCLQ), which enable the detection of spatial associations independent of feature distribution patterns and assess asymmetry in the distribution of spatial elements [45]. Building on this, Cromley introduced the Local Indicator of the Co-location Quotient (LCLQ), which reveals spatially localized variations in the correlation between two sets [46], addressing the GCLQ algorithm’s limitation in overlooking the spatial heterogeneity of settlement patterns. Previous studies have combined two methods to identify regional aging patterns, using GCLQ to determine overall probabilities and LCLQ to reveal specific spatial variations [47]. This approach is applicable for investigating both the overall relationships and the spatial characteristics of community public service facilities.

The layout characteristics of community public service facilities are primarily studied by analyzing industrial spatial distribution patterns via Points of Interest [48], the colocation relationships of industrial clusters [49], and guidelines for medical facility construction [50]. In practical applications, these studies assist in business location decisions [51], identify high-crime regions [52], and pinpoint fire-risk areas [53]. However, research on the overall and regionalized patterns and characteristics of the associative configuration of community public service facilities remains insufficient.

A review of existing research reveals the following:

1. In response to the inconsistent and regionally lacking nature of social capital scales, these scales and indicators need to be refined and supplemented to better meet evolving social needs and lay a solid foundation for future research.
2. Community public service facilities, as a significant part of the neighborhood environment, have unclear characteristics and patterns in their spontaneous construction. The lack of research on the spontaneous construction rules of these facilities within the context of stock development hinders the scientific composite construction of various types of facilities.
3. There is a lack of research on the specific dimensions and the nature of the impact that the associative construction model of facilities has on social capital. Furthermore, there is a shortage of research on this association from the perspective of regional differentiation in urban development.

3.1. Research frameworks

This study calculated the stock of community social capital in residents’ lives through surveys, examining the characteristics of community public service facility construction and its impact mechanisms on social capital across two dimensions: supply the configuration characteristics and colocation patterns of the six types of facilities. The study was divided into three steps. First, residents of the main urban area of Harbin were surveyed using a questionnaire comprising 14 questions related to social capital. The data were quantified and subjected to principal component analysis to summarize the four descriptive dimensions of community social capital. Second, using big data statistics and GIS calculations, the configuration characteristics and colocation patterns of community public service facilities at the sample points were obtained. Configuration characteristics were expressed by the proportion of facility spatial units and the Shannon diversity index. The colocation patterns of facility construction were identified using the global (GCLQ) and local (LCLQ) synergy location entropy values, representing the correlation patterns and degrees. Third, by constructing an OLS multiple regression model, this study explored the impact of community public service facility construction on residents’ social capital. Additionally, a GWR model was used to clarify the spatial heterogeneity of the impact mechanisms within the study area (Fig 1), addressing the limitations of traditional regression models in reflecting local variations in the regression coefficients.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 1. A research roadmap of the impact path of community public service facilities on social capital.

https://doi.org/10.1371/journal.pone.0318144.g001

3.2. Spatial quantitative analysis methods

1. (1) Indicators of facility configuration characteristics

In this study, the Shannon-Wiener Diversity Index and the proportion within unit space can reflect the spatial concentration and type diversity of community public services, effectively characterizing configuration characteristics. The Shannon-Wiener Diversity Index [42] was used to estimate community diversity. The higher the Shannon index, the greater the diversity. The core of facility aggregation is the degree of facility mixing, which is measured in a manner similar to land mixing. The Shannon-Wiener Diversity Index is widely used domestically and internationally to measure the spatial diversity characteristics of facilities.

(1)

P_ij indicates the proportion of the i-th type of facility within the j-th unit relative to the total number of facilities in that unit, and H_j represents the diversity index of the various facilities within the j-th unit [39].

1. (2) Colocation quotient

Global Colocation Quotient (GCLQ) is a spatial statistic used to measure the spatial association between two or more categories of point observations and is widely applied in exploring spatial proximity across various scenarios [46,54]. GCLQ is defined as a probability ratio, where the denominator represents the expected proportion, and the numerator is the observed number of B-type elements neighboring A-type elements. GCLQ_A → B indicates the degree to which A is attracted to B; N represents the total number of points; N_A represents the number of A points; N_B represents the number of B points; N_A → B represents the number of A points that have B points as their nearest neighbors.

(2)

The GCLQ examines the existence of spatial association from the entire study area and the LCLQ further considers the spatial heterogeneity of clustering patterns [55]. LCLQ can be used to explore variations in the dependencies between a given class A-type and the surrounding subset of B-type points in different spaces. LCLQ combines global and spatial regression model geographic weighting parameters to indicate the likelihood of B-type elements appearing within the domain of A-type elements when each element of A-type is determined compared to the overall spatial distribution [47].

N_A and N_B represent the total number of elements A and B, respectively. N_A → B is the number of A nearest neighbor points to B. N is the total number of points in the study area. N_Ai → B is the weighted average of B in the neighborhood of A (Ai). f_ij is a binary variable, where f_ij = 1 if j is a B-type point; otherwise, f_ij =  0, and w_ij is the geographic weight indicating the importance of point j to point i.

(3)

(4)

A GCLQ_A → B and LCLQ_A → B value greater than 1 indicates that A is more likely to be attracted by B in the global [55] or local region, with higher values indicating stronger attraction; a value less than 1 indicates that A is more likely to be isolated from B in the global or local region; and a value of 1 indicates a tendency for random distribution between the two. Through the calculation of GCLQ and LCLQ, the spatial association of the entire region can be explored, local settlement patterns identified, and statistically significant hotspots located.

1. (3) Geographically weighted regression model

GWR is an improved spatial linear regression model based on spatially nonstationary data that reflects the heterogeneity of regression relationships through the variation in regression coefficients at different spatial locations. It provides local models of variables by fitting a regression equation for each feature [56]. This research overcomes the limitation of traditional regression models, which are unable to capture the variation in regression coefficients between facility colocation construction and social capital influenced by urban local environments.

(5)

Where y_i is the observed value; (u_i, v_i) are the coordinates of the i-th sample point; β₀(u_i, v_i) is the regression constant of the i-th sample point; β_k(u_i, v_i) is the regression coefficient of variable k at the i-th sample point; k is the number of independent variables; x_ik is the value of independent variable x_k at point i; θ_i is the random error. The GWR module in ArcGIS Pro was used to construct the model.

3.3. Scope of research and data sources

The area within the Third Ring Road of Harbin was selected as the research area (Fig 2a). As an urban core area, it has well-developed community public service facilities, such as healthcare, cultural education, and social security. It includes most typical communities, making it a suitable research area for this study. Information on community public service facility POIs in the main urban area of Harbin prior to December 2023 was obtained using the DaZhong Dian Ping API (https://www.dianping.com) (Table 1). This platform is one of the most widely used local life information platforms in China, offering a comprehensive POI database and detailed categorization. Referencing the “Standard for Urban Residential Area Planning and Design” (GB50180-2018), this study cleaned and classified the POI data, resulting in six main categories, 17 subcategories, and a total of 8,268 POI entries.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 2. Summary of the scope of the study and research area (a) research area and sampling points (b) summary of gender, age, community type, and residency.

Data source: ArcGIS Online basemap [57].

https://doi.org/10.1371/journal.pone.0318144.g002

Download:

• PNG
  larger image
• TIFF
  original image

Table 1. Type and number of community public service facilities.

https://doi.org/10.1371/journal.pone.0318144.t001

3.4. Characteristics of subjective survey samples

Data collection involved conducting surveys in typical communities from 20 August to 31 August 2024 using door-to-door questionnaires and random online surveys. A total of 198 questionnaires were distributed, and 164 valid questionnaires were returned. The locations of the sampling points are shown in Fig 2a. In the sample characteristics, most respondents were aged between 21 and 60, with a relatively balanced gender distribution. Community types mainly included traditional old neighborhoods, unit-assigned communities, and modern commercial communities, with similar proportions for each residential type (Fig 2b). The information obtained from the questionnaires included the social attributes of the residents and their scores on 14 questions related to social capital.

3.5. Variable description

Community public service facilities serve as interactive platforms, offering primary locations for residents to connect to their social networks. This study combines the existing Sense of Community Index [58] and social capital indicators to screen for potential issues related to the community environment, residents’ activity behaviors, and facility usage from dimensions such as network, local associations, sentiment, trust, solidarity, volunteerism, and cohesion.

With the trend of increased aging, the demand for community aged care [59] has increased, and the relaxation of the “second child” policy has led to a rise in newborns. The spiritual and cultural needs of residents are becoming increasingly diverse [60], and community social support must be more inclusive [61]. Therefore, users were segmented, and the indicators were broken down into three questions: Q6, Q7, and Q8. Based on the grassroots governance model [62] and the integration of diverse community entities, Q10 was summarized. Combining the Sense of Community Index [63], the original Q3 and Q13 of the social capital scale were made more specific and understandable (Table 2). The remaining semantically similar questions were merged to obtain 14 indicators. Respondents rated these items on a five-point Likert scale, where 1–5 represents “completely disagree” to “completely agree.”

Download:

• PNG
  larger image
• TIFF
  original image

Table 2. Research variables and measurement of social capital and community public service facilities.

https://doi.org/10.1371/journal.pone.0318144.t002

In the supply configuration of the facilities, grid cells (300 m ×  300 m) were constructed based on a 5-minute walking range to calculate the Shannon-Wiener Diversity Index of six types of facilities within each grid cell, denoted as H_j (Fig 3a). This was used to explore the degree of aggregation of facility types within the smallest range. Based on the surveyed sampling points, buffers were constructed with an 800-meter radius (approximately 15 minutes walking distance), and the proportion of each of the six types of facilities within this unit range was calculated as P_ij (Fig 3b). GCLQ was calculated using the six types of facilities on a global scale, strong association patterns were filtered out with the GCLQ > 2, their LCLQ was calculated, and the strength of the attraction of the colocation pattern was assessed by the size of the LCLQ, which was then assigned to the sampling points within the unit range.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 3. Facilities POI and diversity (a) diversity of facilities (b) extent of community life circle at sampling sites (c) distribution of POI.

Data source: ArcGIS Online basemap [57].

https://doi.org/10.1371/journal.pone.0318144.g003

4.1. Social capital of the community

We obtained subjective scores for 14 questions regarding community social capital through questionnaires and interviews, extracted indicators for the 14 dimensions, and verified their validity. Using SPSS 26.0, exploratory factor analysis was conducted on the indicators using principal component analysis. The KMO and Bartlett’s test results showed KMO =  0.859 > 0.5, P < 0.01, indicating strong correlations among the original variables; hence, they were suitable for factor analysis. The initial factor loadings were rotated using the orthogonal rotation method (Varimax) to clarify the structure of the factor-loading matrix. Four factors were extracted based on factor loadings > 0.5 and eigenvalues > 1, explaining 65.16% of the variance. By analyzing the factor loadings and combining them with the dimensions of social capital, four aggregate indicators were identified: Cohesion (Q1, Q2, Q3, Q4, Q5), Solidarity (Q6, Q7, Q8), Community Trust (Q9, Q10, Q11), and Community Sentiment (Q12, Q13, Q14) (Table 3). Regarding reliability, Cronbach’s alpha was used to test the internal consistency of the questionnaire data, with all values greater than 0.6 indicating strong internal data correlations for each indicator. Cohesion primarily includes social action networks and interactive activities; Solidarity represents home-based aged care, vulnerable groups, and an inclusive community environment; Community Trust includes trust in community organizations and the neighborhood environment; and Community Sentiment represents community identity, markers, and volunteering. According to the analysis of social capital characteristics, the surveyed residents had the highest sense of Community Sentiment, with more concentrated scores, and 59.4% of residents tended to actively solve community problems. However, cohesion was the lowest, with significant score fluctuations, and only 42% tended to participate in community organizations.

Download:

• PNG
  larger image
• TIFF
  original image

Table 3. Descriptive statistics of the data.

https://doi.org/10.1371/journal.pone.0318144.t003

4.2. Configuration characteristics of community public service facilities

The Shannon-Wiener Diversity Index (H_i) was calculated within the grid cells of the study area and classified using the natural breaks method. As shown in the figure, the passage of trains caused a break in urban development, with the Shannon index values being higher in the south and East and lower in the north and West, using railway tracks as a boundary (Fig 3a). The diversity in facility construction in Harbin’s main urban area is significantly polarized, with a tendency toward single-type facility construction in many units.

Next, the proportion of each of the six types of community public service facilities within the unit space of the sampling points was calculated and denoted as P. Convenience service facilities had the most significant proportion, followed by childcare facilities. Aged care facilities had the lowest proportion, indicating that community aged care still needs to be strengthened (Fig 4). Finally, a hotspot analysis (Getis-Ord Gi * algorithm) [57] was conducted on the six P values to identify hot and cold spots of facility proportions and assess the spatial heterogeneity of these proportions. Finally, the P-values were analyzed using Getis-Ord Gi^* to identify hot and cold spots of each facility’s proportion and evaluate the spatial heterogeneity of facility proportions. P-convenience services showed high-value clustering in the Northeast and low-value clustering in the Southwest of the study area, with the highest number of significant clusters (Fig 4a). P-cultural and sports and P-childcare facilities showed low-value clustering in the northern part of the city and high-value clustering in the southern part (Figs 4b and 4f). P-aged care facilities showed high-value clustering on the city outskirts and low-value clustering in the city center (Fig 4e). P-administrative and P-medical facilities were clustered in the south and dispersed in the north, with a few significant points indicating a uniform distribution (Figs 4c and 4d).

Download:

• PNG
  larger image
• TIFF
  original image

Fig 4. Hot spots and cold spots in terms of percentage of the number of facilities: (a) convenient service; (b) cultural and sports; (c) administrative; (d) healthcare; (e) aged care; (f) childcare.

Data source: ArcGIS Online basemap [57].

https://doi.org/10.1371/journal.pone.0318144.g004

4.3. Colocation patterns of community public service facilities

First, the colocation patterns of facilities across the entire area were calculated using the GCLQ to obtain the overall association patterns, followed by the LCLQ to further determine the distribution characteristics of the significant associations. In accordance with previous research, the 10-order neighbor was used as the adaptive bandwidth, which is most suitable for spatial association at the study area scale [53]. When the GCLQ is close to 1, it represents a significantly dispersed pattern among the facilities. This study selected colocation patterns with a GCLQ >  2 and P <  0.05, representing strong significant associations [54]. A total of 24 association patterns involving 13 facilities across the entire area were identified (Fig 5). The larger the circle, the greater the total number of facilities; dashed lines indicate mutual attraction and solid lines indicate one-way attraction (i.e., A → B means A attracts B); the thicker the association line, the stronger the association. The four strongest colocation patterns were Community Cultural Services →  Childcare Center (4.500), Rehabilitation →  Retirement Facility (4.080), Childcare Center →  Retirement Facility (3.825), and Rehabilitation →  Childcare Center (3.825). The overall attractiveness of aged care, cultural and sports, and childcare facilities is relatively strong. The overall association patterns were as follows:

Download:

• PNG
  larger image
• TIFF
  original image

Fig 5. GCLQ of community public service facilities.

https://doi.org/10.1371/journal.pone.0318144.g005

1. Mutual attraction colocation patterns exist among facilities such as retirement facilities, community public service facilities, retirement facilities and childcare centers, childcare centers, and community cultural service facilities.
2. Facilities within the same main category have associations such as rehabilitation services →  retirement facilities, fitness centers →  financial services, indicating that facilities with similar functions tend to attract each other.
3. Facilities with overlapping user groups are associated, such as retirement facilities →  community health service centers, and community cultural services →  childcare centers. These associations provide multiple services to both older adults and their children.

In the second step, based on the 24 strong colocation patterns identified by GCLQ, the LCLQ values for the six types of facilities and their significantly associated facilities were calculated to detect the colocation patterns and degrees within their local ranges (Fig 6). To explore the correlation patterns of community public service facilities within the smallest community activity range, a bandwidth of 300 meters (five-minute living circle) was set, and statistical significance was tested. Integrating all colocation patterns with GCLQ > 2 within the same subcategories (e.g., Fig 6a shows all association points related to convenience services, such as gymnasiums, community activity centers, and financial services being attracted by fitness centers; fitness centers being attracted by financial service facilities, and community health service centers being attracted by telecommunications business offices. These association points are represented by LCLQ convenience, indicating the LCLQ of convenience service facilities and their associated facilities. (The same principle is applied to the remaining five categories.) As the calculation filters strong association rules, all six types of facilities show significant colocation clustering patterns, with only a few isolated points (9) in convenience service facilities. Surprisingly, the probability of high LCLQ association points appearing in the urban core area was lower than that in the new urban or peripheral areas, indicating that facilities in the core area tended to be more homogeneously matched. In contrast, in peripheral or new urban areas, facilities tended to form a clustered construction model.

Download:

• PNG
  larger image
• TIFF
  original image

Fig 6. LCLQ of community public service facilities.

Data source: ArcGIS Online basemap [57].

https://doi.org/10.1371/journal.pone.0318144.g006

LCLQ-convenience association points show characteristics of large quantity, high degree, and uniform distribution, indicating a strong synergy in the city’s overall facility coordination. LCLQ-cultural and sports and LCLQ-administrative association points were numerous and evenly distributed. The former’s association points are primarily located near new urban areas and university towns, with lower averages, whereas the association points of administrative service facilities have no significant locational characteristics. LCLQ-childcare, LCLQ-healthcare, and LCLQ-aged-care association points were relatively unevenly distributed and fewer in number but had higher average LCLQ values. This indicates that these types of facilities are highly attractive; however, the fairness of resource allocation must be improved across the entire area.

4.4. Association between community public service facilities and social capital

To further statistically analyze the relationship between facility association patterns and community social capital, an 800-meter radius was set as the buffer zone, obtaining the LCLQ values of facilities around the survey sampling points, representing the strength of colocation patterns of facilities within the daily living range of the surveyed subjects. This study aimed to assess the impact of the association patterns of facilities on community social capital. Hence, isolated points were not considered, and if there were multiple values of the same association within the sampling point range, the average value was taken. Statistical analyses were conducted to understand the impact mechanisms of different association strengths on community social capital. The independent variables were normalized using Z-scores in SPSS, followed by OLS model validation, which showed no multicollinearity among the factors. The configuration characteristics and colocation patterns of community public service facilities are associated with the mechanisms of community social capital (Fig 7).

Download:

• PNG
  larger image
• TIFF
  original image

Fig 7. Overview of the OLS model.

https://doi.org/10.1371/journal.pone.0318144.g007

The results indicate that more facility construction is not always better; instead, mutual coordination and joint development are required. The diversity of facility types has a positive impact on community trust but a negative impact on solidarity. Urban areas with more types of facilities may have high vitality and complex travel conditions that are detrimental to the lives of vulnerable groups. Based on facility configuration characteristics and colocation patterns, the following rules were observed:

1. P-convenience was negatively correlated with community cohesion, solidarity, and sentiment in social capital, with no significant impact on community trust. Although LCLQ convenience was not significantly associated with social capital, it had no negative effects. Existing studies have found that high-density or excessive commercial land use adversely affects community capital, and the more facilities there are for daily needs, the lower the residents’ local identity. However, the joint construction of convenience and related facilities helps eliminate these negative feelings and can serve as a reference for composite construction.
2. Although P-aged care was not significantly associated with social capital, P-child care was negatively correlated with community cohesion and sentiment in social capital. However, LCLQ-aged care and LCLQ-childcare had significant positive effects on community cohesion, solidarity, and sentiment. The spontaneous construction of these two types of facilities positively affects social capital and can serve as a reference for subsequent composite construction.
3. P-healthcare was positively correlated with social capital in all four dimensions, and healthcare facilities had a strong impact on its enhancement. However, the colocation patterns of healthcare facilities with aged care and community public service facilities adversely affected social capital. Considering the trend of integrated medical and aged care, this may be due to existing imperfect configurations or conflicts with municipal medical resources, resulting in low social capital.
4. P-cultural and sports and LCLQ-cultural and sports had significant positive impacts on community cohesion and sentiment. The construction of facilities, such as sports venues and community cultural centers, can significantly enhance community social capital. P-administrative and LCLQ-administrative had no significant overall impact on social capital, possibly because of issues such as the small scale and low utilization of this type of facility construction (Table 4).

Download:

• PNG
  larger image
• TIFF
  original image

Table 4. Parameter estimation and test results of the OLS model.

https://doi.org/10.1371/journal.pone.0318144.t004

The traditional linear regression model provides a global estimate of the parameters, and the resulting coefficients of the independent variables are homogenized because of the nature of the global model [40]. To address the inseparable colocation phenomenon associated with geographic factors, a GWR model was used to explore the spatial heterogeneity of the impact of facility aggregation on community social capital, reflecting the variation in regression coefficients across different urban areas. Before constructing the GWR model, it is necessary to exclude the influence of multicollinearity among factors by removing variables with a Variance Inflation Factor (VIF) greater than 7.5 in the OLS model. Calculations revealed that all VIF values in the OLS equation were significantly below 7.5, with the GWR model exhibiting a higher Adjusted R² and lower corrected Akaike information criterion (AICc) than the OLS model, indicating that GWR provides better explanatory results than the OLS model (Table 5). Each spatial unit in the GWR model has specific coefficients, and the average and median values of these coefficients are calculated to provide an overall assessment. The standardized residual values of the GWR were subjected to Global Moran’s I calculation, revealing that none of the four model sets exhibited spatial autocorrelation (−1.65 < Z < 1.65, P > 0.1) and were randomly distributed in space, thus proving that the overall effect of the model is interpretable. Given that this study further investigates the spatial heterogeneity of the impact of facility connectivity on social capital by examining whether it is influenced by the urban environmental context, it aims to guide integrated facility construction. Fig 8 illustrates the spatial variation of the coefficients of the impact of facility colocation patterns on community social capital.

Download:

• PNG
  larger image
• TIFF
  original image

Table 5. Parameter estimation and test results of the GWR model.

https://doi.org/10.1371/journal.pone.0318144.t005

Download:

• PNG
  larger image
• TIFF
  original image

Fig 8. The GWR coefficients of GCLQ factors for community public service facilities.

Data source: ArcGIS Online basemap [57].

https://doi.org/10.1371/journal.pone.0318144.g008

1. The association construction of medical and health facilities with aged care services and community public service facilities generally had a negative impact on community cohesion across the entire area (Fig 8-A4). In terms of social support, community sense of belonging, and community trust, the correlation coefficient of the LCLQ medical decreased and became negative from the Northeast to the Southwest (Figs 8-B4, 8-C4, and 8-D4). In terms of the effects on Solidarity, Sentiment, and community trust, the correlation coefficients of LCLQ-healthcare gradually decreased from Northeast to Southwest and became negative (Figs 8-B4, 8-C4, and 8-D4). According to the urban layout, the linkage construction of healthcare facilities primarily shows significant negative correlations in commercial districts such as Zuo Zhan and convention centers.
2. LCLQ-aged care shows a partial negative correlation with community social capital on the eastern side of the study area, gradually turning positive and increasing in impact on the western side (Figs 8-A5, 8-B5, and 8-D5). The joint construction of aged care facilities with rehabilitation therapy facilities, kindergartens, and community service centers in new urban areas and school cluster zones can enhance community cohesion, support, and sentiment. However, this did not enhance the community’s perception of trust (Fig 8-C5).
3. According to the regression coefficient statistics, the LCLQ-childcare has a largely positive impact on community social capital, with the proportion of positive coefficients affecting community cohesion reaching 84.15%. In contrast to LCLQ-healthcare, joint construction of kindergartens, daycare centers with aged care facilities, and community cultural service facilities in central and northern urban areas—core residential and commercial zones—effectively promotes social capital. Additionally, negative correlations with community trust and sentiment in the northeastern areas may be indirectly related to urban security in the Daoli district (Figs 8-A6, 8-B6, 8-C6, and 8-D6).
4. Regarding the association between LCLQ-cultural and sports, and community sentiment, 72.06% of the regression coefficients were positive. The regression coefficients of LCLQ culture showed a gradual decrease from south to north in the study area (Figs 8-A2, 8-B2, 8-C2, and 8-D2). The southern region, with its numerous universities and primary schools, has a concentrated layout of facilities related to culture and entertainment. Overall, this layout positively affected community social capital. In contrast, mismatched functional focus in the northern urban area showed a negative correlation.
5. The LCLQ-convenience index was not significant in OLS. However, in the GWR model, approximately 50% of the sampled points in the newly developed northwest urban areas showed a significant positive correlation with sentiment (Fig 8-D1). Therefore, joint construction of supermarkets, logistics facilities, and fitness facilities should be considered in similar regions. In the GWR model of solidarity, LCLQ-administrative services showed significant positive correlations in the southeast urban areas, accounting for approximately half of the total samples (Fig 8-C3). This indicates that the joint construction of community public service facilities in old city areas positively supports community life.

In exploring the mechanisms affecting social capital, the regression coefficients of LCLQ-aged care were generally higher in the West than in the East. Simultaneously, LCLQ-healthcare and LCLQ-administrative services were higher in the Northeast than in the Southwest. The regression coefficients of LCLQ-childcare and LCLQ-culture and sports were higher in the south than in the north. Moreover, LCLQ-childcare was positively correlated with popular business districts, whereas LCLQ-healthcare showed a negative correlation. LCLQ culture and sports, as well as LCLQ-aged care, were positively correlated with universities and research institutes.

5.1. Colocation patterns of community public service facilities and their influencing factors

The study established a facility association network aligned with common sense and previous research [64], showing that while similar facilities tend to cluster, elderly care facilities are the most appealing, followed by community cultural centers and nurseries. These findings emphasize the daily entertainment and healthcare needs of older adults and young children, thus addressing the second research question. The study’s emphasis on the importance of an intergenerational integrated facility construction model aligns with related research perspectives [65]. Facilities integrating medical care with elderly care and combining elderly and childcare services conform to residents’ natural living patterns and should be considered a top priority in urban renewal efforts.

Unexpectedly, in the colocation quotient calculations in the “configuration characteristics of community public service facilities” section of this paper, the probability of high LCLQ-childcare values is lower in urban core areas than in newly developed or border areas. Existing research on the colocation patterns of medical facilities has found that basic (local services) and specialized (city-level services) medical facilities, while somewhat related, are spatially mutually exclusive [51]. This study provides a partial explanation for this result. A potential explanation for this phenomenon is the limited total number of facilities in non-core or peripheral areas, where the population of newly settled young and middle-aged residents at the urban expansion boundary exhibits a high demand for childcare and medical services. Another possibility is that facilities within urban areas have high stock and density, and other facilities may have mutually exclusive or incompatible effects on them, resulting in LCLQ values not significantly increasing in high-density mature areas.

5.2. Impact of facility-related construction on social capital

This study found that not all facilities or associations had positive effects on community capital. Unlike previous research [7], the diversity of facility construction can enhance community trust, although it has a negative impact on community solidarity. The data on P-convenience and LCLQ-convenience show that excessive construction of convenience service facilities is not conducive to promoting community social capital and does not inspire residents’ place identity. This is consistent with research results on the association between community facilities and sense of place [11]. In addition, a joint layout of convenience, childcare, and aged care facilities with related facilities is more conducive to increasing social capital than simply increasing the number of such facilities. Therefore, such self-organized colocation patterns enhance residents’ user experience and have promotional value, thus addressing the third research question.

This study primarily explores the relationship between facility construction and social capital using regression models, which are constrained by certain simplifications. Future improvements could involve more complex functional forms or other machine learning methods. Meanwhile, the research findings may also be influenced by other factors, such as regional culture, population density, and site density, necessitating further exploration of these differences across various environments in future studies.

5.3. Insights for urban supply characteristics and integrated facility planning

The study can serve as a foundational information collection method for planning community public service composite facilities, identifying social needs from the bottom up, and providing a reference for urban facility construction proposals. Policymakers should avoid viewing facility construction solely from a functional perspective and instead adopt an integrated and holistic approach to enhancing social capital [11]. Based on the spatial heterogeneity of the development of urban areas, i.e., the development objectives and positioning of different regions and the shortcomings of social capital, it is possible to specify a more compatible pattern of synergistic construction of facilities in different regions, which can lead to a distribution of features that are harmonized with the urban pattern [56].

Regarding the differentiated impacts on social capital across Harbin’s urban development zones, the city can be categorized into traditional old districts (eastern and northern parts), core commercial zones (northern parts), core educational and cultural zones (central and southern parts), and new urban zones (southwest parts). The old districts have relatively complete but aging infrastructure, and enhancing the construction of community medical centers and integrated service centers can improve community trust. The core commercial zones are densely populated and highly vibrant, making them suitable for building children’s interest classes and activity care centers to support intergenerational activities. Core educational and cultural zones, which are dominated by higher education institutions, can significantly enhance various dimensions of social capital through the joint construction of elderly universities and cultural activity centers. Urban new zones, located on the periphery and relatively underdeveloped, should prioritize basic needs by constructing comprehensive supermarkets and convenience service stations.

However, this study primarily examines the attraction of one type of facility to other facility types, lacking broader consideration of other environmental factors within the region. In future studies, a more comprehensive and holistic depiction of the interconnections and impacts within community life circles is desired. In this study, Euclidean distance was used to determine the neighborhood range; however, incorporating factors such as travel distance and time costs would provide a more accurate evaluation of facility construction associations. The next step could involve constructing urban networks to enable more refined and in-depth research.