Research on Spatial Distribution Characteristics and Influencing Factors of Pension Resources in Shanghai Community-Life Circle

Abstract

With population ageing being a notable demographic phenomenon, aging in place is an efficient model to accommodate the mounting aging needs. Based on the community scale, this study takes the 15-min community-life circle as the basic research unit to investigate the imbalanced distribution of pension resources and its influencing factors in downtown Shanghai. We obtained six types of elderly care facilities data from the Shanghai elderly care service platform and utilized the Gaussian 2-step Floating Catchment Area method to calculate the accessibility of 6-type elderly care facilities. Then, we used the Entropy Weight Method to calculate the comprehensive accessibility of elderly care facilities. The Getis–Ord Gi* method was adopted to analyze the overall distribution, identifying the well-developed and the under-developed areas. To explore the influencing factors of the distribution, this paper obtained multi-source data to construct a total of 17 indicators and established a Random Forest model to identify the feature importance. With the selected eight factors, the Geographically Weighted Regression (GWR) model was applied to study the spatial heterogeneity of influencing factors, and the model showed a good performance with the AdjR² being 0.8364. The findings of this research reveal the following: (1) The distribution of six types of elderly care facilities is extremely uneven, with obvious spatial aggregation characteristics. Amongst the seven administrative regions, Huangpu District has the best accessibility to pension resources, while the resources in the other six regions are highly inadequate. (2) Essential influencing factors of the comprehensive accessibility of community-based elderly care facilities are accessibility of nursing institutions (positive), hotel density (positive), catering density (negative), education density (positive) and medical density (negative), while “rents”, “plot ratio” and “building density” have little impact on comprehensive accessibility. (3) The results of GWR revealed that the eight indicators are heterogeneous in space, all of which have bidirectional effects on comprehensive accessibility. By investigating the spatial distribution patterns and influencing factors of pension resources in Shanghai, this research could further contribute to establishing a sound community-based elderly care service system that improves older adults’ quality of life and promotes social fairness and justice.

1. Introduction

1.1. Background

Population ageing has been a notable demographic phenomenon in both developed and developing countries worldwide [1]. According to the World Health Organization, the proportion of the world’s population over the age of 60 will increase to 34% from 2020 to 2030. By 2050, the number of older adults will increase to 1.4 billion, of which about 65% will come from low-income and middle-income countries [2]. As a typical representative of developing countries, China is about to experience a serious aging problem. Data from the National Bureau of Statistics shows that, by the end of 2021, China’s population over the age of 65 accounted for 14.20% [3], which means that China has entered an “aged society”. At the same time, because of the group commonly referred to as “post-1960s baby boomers [4,5]” aging in the next 5–10 years, China is expected to enter a super-aged society by around 2033 [6]. A serious aging trend has brought about a series of problems for the government and society, such as a large aging population, a mounting elderly dependency rate (defined as the ratio between the aging population and the working-age population [7], and ‘growing old before getting rich’ [8].

With the increasing number of aging populations worldwide, providing social security and service for older adults has become a major concern [9]. At present, there are mainly three pension service modes, family-based pension, community-based pension, and institution-based pension, whilst family-based pension and community-based pension are collectively referred to as the “Aging-in-place” model [10]. This approach referred to a person staying in the inhabitation of their choice for as long as they can with the comforts that are important to them, making it possible to retain connections with friends and family in their communities [11], which has become a worldwide consensus strategy. Nowadays, in developed countries, many elderly care services are encouraged to move from institutions into homes or communities [12], such as the “Active Adult Retirement Community” and ”Continue Care Retirement Community” model proposed by the United States [13,14], the “Multigenerational community” model proposed by Germany [15], the “Community-based Integrated Care System” proposed by Japan [16] and the “Communities of Care” model proposed by Singapore [17]. In contrast, China’s pension industry started rather late. The Chinese local governments have initiated proactive policies such as the goal of “9073” and “9064”, which have eventually merged a basic pension system for older adults of “home-based, community-depended and institution-supported” [9,18]. Among them, the “Ageing-in-place” model, including home-based and community-based modes, needs to accommodate 96% (“9064“) or 97% (“9073”) pension needs with balanced resource allocation, which is an important but arduous task. In terms of the needs of the older adults, there are many practical requirements for the availability of community-based pension resources [19]. In the meantime, more options in elder care services have meant more choices for families regarding senior patients’ rehabilitation and nursing [20].

The conditions of the older adults change along with the growth of age, their physical function will decline, their activities will be limited, and they are more likely to get injured [21,22]. However, after retirement, they have more free time compared with the population of other ages, so they are more sensitive to the quality of the community-based living environment [23]. On the other hand, due to the family structure with fewer children (“4-2-1” family structure), the burden of children taking care of their families is becoming heavier than ever before [24]. However, children normally lack adequate nursing knowledge to take care of older adults on their own. Therefore, the accessibility and availability of local pension services are becoming more significant. For older adults aging in place, accessing more effective care and basic medical services can receive timely nursing and may even improve their intrinsic capacity, leading to a healthier aging life [25]. From the emotional needs, affected by the Chinese filial piety culture, older adults are more willing to accept their children’s company and are more likely to enjoy their old age in a familiar environment [26,27].

Since 2012, China’s old-age care industry has ushered in a period of rapid development [28]. Under this background, the layout of elderly care institutions is improving rapidly, but there are still multiple challenges in allocating community-based pension resources properly. In 2016, the Shanghai government proposed the concept of the 15-min community-life circle (which states that, within the range of 15-min walking cost, essential services should be provided to form a safe, friendly, and comfortable social living environment), clearly putting forward the construction goal of elderly care services in the life circle [29]. However, the concept per se has not been fully promoted in practice, and the current community-based elderly care facilities have not met the actual needs in terms of quantity, scale, content and quality [30].

Equitable access to pension services is a critical goal for overcoming social disparities. The research on the spatial distribution of pension resources is usually evaluated from the perspective of the matching of population and resources. Through quantitative analysis of the layout of existing facilities, we can effectively identify where there are unevenly distributed amenities that provide layout suggestions for further improvement [31].

Accessibility assessment is one of the main methods of research on the equilibrium distribution [32], which is widely used in the evaluation of opportunities to access services, such as education, medical treatment, elderly care facilities, parks, and green space [33,34]. The 2-step floating catchment area (2SFCA) method was widely applied to evaluate the spatial accessibility, and there are various enhanced efforts to this method. For example, Tao and Cheng developed a multi-mode and variable-demand 2-step floating catchment area model for measuring spatial accessibility of older adults and healthcare services [25]. Lopes et al. used the enhanced 2SFCA method to measure the spatial accessibility of health-care services [35]. Fuyuan and Kaiyong develop an improved two-step floating catchment area method to assess the spatial accessibility of ecological recreation spaces in the Pearl River Delta Region [36]. Huang et al. used the 2SFCA method to measure spatial access to health care for older adults [37]. Han and Luo applied the improved 2SFCA method to evaluate the accessibility of home-based elderly care facilities [38]. Zhang et al. evaluated various accessibilities to community-based service centers for older adults [8].

In general, we have identified that the previous studies are limited in the following aspects: The research pays less attention to community-based pension resources and the actual life needs of older adults. The research scale does not conform to the daily travelling ranges of older adults, which is difficult to reflect the actual pension needs; And they failed to pay attention to a variety of pension resources, which are complementary at the community level; Besides, for the reason of the unbalanced distribution status, there lacks exploration about the influence factors. In our last paper [39], we have studied two categories, including eight types of pension services from the actual life of older adults, but we could not evaluate the comprehensive accessibility and furtherly explore the influencing factors on it. Based on the above, focusing on the aging-in-place mode, this project aims to fill those gaps by two aspects: firstly, we conduct a large-scale and refined overall comprehensive evaluation of the distribution status of community-based elderly care facilities in Shanghai; then, we further explore the influencing factors that cause this distribution of pension resources. Using GIS (Geographic Information Systems)-based digital evaluation and analysis approaches, this study can further contribute to the development of a more age-friendly, sustainable, and inclusive city.

1.2. Research Framework

From the perspective of the actual life of older adults, based on the community scale, this study takes the 15-min community-life circle as the basic research unit to study the balanced distribution of pension resources in downtown Shanghai and explore the influencing factors on the distribution status. We obtained six types of elderly care facilities data from Shanghai elderly care service platform, used the Gaussian 2-step Floating Catchment Area method to calculate the accessibility of 6-type elderly care facility, and then used the Entropy Weight Method to calculate the comprehensive accessibility of elderly care facilities. The Getis–Ord Gi* method was adopted to analyze the overall distribution, identifying the well-developed and under-developed areas for the future optimization of community-based service allocation. In order to explore the influencing factors of the distribution, this paper obtained multi-source data, including remote sensing data, POI (point of interest) data, road network data, building morphology data and population data to construct a total of 17 indicators. Finally, we established a Random Forest model and a Geographically Weighted Regression model. Through the analysis results of the model, we could explain the influencing factors of the distribution of community-based pension resources and provide guidance for urban planning designers and other decision-makers. The research framework is shown in Figure 1.

2. Materials and Data

2.1. Study Area

Shanghai is considered the first city in China to enter the aging era, and it is also one of the provinces with the most serious aging problems at present. According 2021 Shanghai Statistical Yearbook, the population of registered older adults (60 or above years old) accounts for 36.08% of the total demographic. The aging problem in downtown Shanghai, the economic engine of the city and an intellectual powerhouse with many young immigrants, is also very serious, where the proportion of people over 60 years old in the seven districts exceeds 35% [40]. Therefore, this paper focuses on the distribution balance of elderly care resources in downtown Shanghai. The restudy area is shown in Figure 2.

2.2. Multi-Source Data Acquisition

2.2.1. Demographic Data of the Aging Population

We use python to extract 14,577 communities’ information (containing location coordinate, household count, average property price, and other information) in downtown Shanghai from the real estate business website (fang.com, accessed on 15 January 2021). According to the Shanghai Statistical Yearbook 2021, the average number of persons per household is 2.63 [40], which allows us to calculate the number of people in each district. Then, combined with the proportion of the aging population, we can obtain the number of older adults in each community.

2.2.2. Data of the Elderly Care Facilities

Shanghai elderly care service platform (shweilao.cn, accessed on 20 April 2022) has registered the data of all elderly care service resources in Shanghai, with various types, complete data, and information authority. Therefore, this study obtains various types of elderly care facility service resources from this platform. The effective data obtained this time are: Type-A (170), nursing home, providing medium and short-term care services; Type-B (725), elderly day care institution, providing day care services; Type-C (1741) meal aid service point; Type-D (259), community elderly care service organization, providing door-to-door services community; Type-E (360) comprehensive services center; and Type-F (168), nursing station.

2.2.3. Acquisition of Community Life Circle Data and Service Catchment Data

Mapbox’s Isochrone API was used to obtain geographic data of the life circle and service catchment data of all communities within a specified amount of time from a location. The time for community life circle was set at 15-min walking time cost in accordance with the Shanghai Master Plan’s current urban development criteria [29]. The time for service catchment data was set at 30-min walking time cost.

2.2.4. Multi-Source Data Acquisition of Influencing Factors

The multi-source data used to calculate the index value in Section 3.2.1. includes: elderly care institution data from Shanghai elderly care service platform; land use type data and green space data from remote sensing data; POI data, building data and road network data from Baidu map; Population data from worldpop.org; house price data and income data are from MetroDataTech company (Shanghai, China).

3. Methods

3.1. Comprehensive Evaluation on the Spatial Distribution Characteristics of Community-Based Pension Services

3.1.1. Calculating the Spatial Accessibility of Elderly Care Facilities

The 2-Step Floating Catchment Area (2SFCA) approach, modified by Luo and Wang [41], is an effective method for assessing the rationality of public service distribution [42], which calculates accessibility through two steps: calculating the supply–demand ratio and then calculating the spatial accessibility of facilities, which can account for the influence of supply scale, demand scale, and spatial impedance factors between supply and demand sites. This method takes into account the spatial matching ability of the elderly population and elderly care facilities resources. Different from Euclidean distance, this method considers the real travel distance of residents.

With the following calculation processes, the 2SFCA method estimates the accessibility of elderly care service facilities in two phases, depending on the place of supply and demand, respectively.

Step 1: Calculate the supply–demand ratio. Considering that the elderly’s choice of pension resources is not limited to the boundaries of administrative regions, the supply–demand ratio is calculated in total Shanghai, to meet the actual supply–demand ratio $R_j$. $S_j$ is the number of facilities, k is community, and $P_k$ is the population of older adults. $d_0$ is chosen as the threshold.

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

(1)

Step 2: Calculate the spatial accessibility of each community $A_i$. The life circle polygon obtained in Section 2.2.3. was chose as the catchment area. Then, total these weighted supply–demand ratios to obtain the elderly facility accessibility for each community.

$$A_i={{\displaystyle \sum }}_{l\in \left\{d_{il}\le d_0\right\}}G\left(d_{il},d_0\right)R_{j },$$

(2)

However, this method of calculating accessibility has two sensitive factors to consider—catchment size and distance decay [43]—which result in a certain deviation between the calculation results and the reality.

In this study, the setting of catchment size is different in two steps. In the first step, when calculating the supply–demand ratio, the service range of elderly care facilities is set as a 30-min walking distance. The second step is to use a 15-min walking distance when calculating the accessibility of pension resources. For the distance decay factor setting, the Gauss equation’s attenuation curve is more in line with subjective experience. In the catchment area, the Gaussian equation is employed for distance decay to determine the weight of supply and demand capacity of different facilities. Gaussian equation is as follows:

$$G\left(d_{kj},d_0\right)=\left\{\begin{array}{c}{e}^{-\left(1/2\right)\times {\left(d_{kj}/d_0\right)}^2}-e^{-\left(1/2\right)}, if{d}_{kj}\le d_0\\ 0, , if{d}_{kj}>d_0\end{array}\right.,$$

(3)

where $d_{kj}$ is the distance between the supply point k and the demand point j, and $d_0$ is the threshold.

This study uses Gauss 2-Step Floating Catchment Area method to calculate the accessibility of six-type elderly care facilities. The spatial interpolation method can convert the measured data of discrete points into continuous data surfaces for comparison with the distribution patterns of other spatial phenomena. So, the Kriging interpolation method is used to draw map from the community scale in ArcGIS.

3.1.2. Calculating the Comprehensive Accessibility of Elderly Care Facilities

Different elderly care facilities have different degrees of impact on the lives of older adults. To comprehensively evaluate the accessibility of different kinds of elderly care facilities in each community, this study uses the Entropy Weight Method to calculate the weight of various elderly care facilities, and finally obtains the comprehensive accessibility in each community.

Entropy Weight Method determines the objective weight of the indexes according to the variability of the index. Generally speaking, the smaller the information entropy of an index, the greater its role in the comprehensive evaluation and the greater the weight it attains [44,45]. The calculation process is as follows:

Firstly, calculate the proportion of index values using

$$P_{ij}=\frac{Z_{ij}}{{{\displaystyle \sum }}_{j=1}^n{Z}_{ij}},$$

(4)

The measured value of the index i in the sample j is recorded as $Z_{ij}$. The standardized value of the index i in the sample j is denoted as $P_{ij}$.

Then, calculate the information entropy of each index using

$$H_i=-\frac{1}{lnn}{{\displaystyle \sum }}_{j=1}^n{P}_{ij}ln{P}_{ij},$$

(5)

where $H_i$ is the entropy of the index i, and n is the number of samples.

Thirdly, calculate the weight of each index I using

$$W_i=\frac{1-H_i}{{{\displaystyle \sum }}_{i=1}^m\left(1-H_i\right)} ,$$

(6)

where $W_i$ is the entropy weight of the index i, and m is the number of indexes, $W_i\in \left[0, 1\right]$. The larger the $W_i$ is, the greater the differentiation degree of index i is, and more information can be derived.

Finally, calculate the comprehensive accessibility of elderly care facilities. For each sample j, the comprehensive accessibility $S_j$ of elderly care facilities is calculating as follows:

$$S_j={{\displaystyle \sum }}_{i=1}^m{Z}_{ij}{W}_i ,$$

(7)

The calculation results are mapped in ArcGIS using the Kriging interpolation method.

3.1.3. Analysis on Spatial Distribution Equilibrium

To analyze the spatial distribution characteristics of elderly care facilities, this paper uses spatial autocorrelation tools to study the resource distribution. Compared to statistic Gi method proposed in Getis and Ord (1992), the Getis–Ord Gi* method (1995) takes into account the central feature, which was employed to analyze the distribution area of cold and hot spots of the accessibility. Using this method, regions with statistical significance clustering can be identified [46]. This method is given as:

$$G_i^{*}=\frac{{{\displaystyle \sum }}_{j=1}^n{W}_{i,j}{x}_j-\overline{X}{{\displaystyle \sum }}_{j=1}^n{w}_{i,j}}{S\sqrt[2]{\frac{\left[n{{\displaystyle \sum }}_{j=1}^n{w}_{i,j}^2-{\left({{\displaystyle \sum }}_{j=1}^n{W}_{i,j}\right)}^2\right]}{n-1}}},$$

(8)

where $x_i$ and $x_j$ are attribute values for features $i$ and $j$; $w_{i,j}$ is the spatial weight between feature $i$ and feature $j$; and n is the number of features in the dataset. $\overline{X}=\frac{{{\displaystyle \sum }}_{j=1}^n{x}_j}{n}$, $S=\sqrt{\frac{{{\displaystyle \sum }}_{j=1}^n{x}_j{}^2}{n}-{\left(\overline{X}\right)}^2}$.

When the Gi* statistic is higher than the mathematical expectation and passes the hypothesis test, it is a hot spot; otherwise, it is a cold spot.

3.2. Analysis on Influencing Factors of Spatial Distribution Imbalance

3.2.1. Index Construction

This study also aims to further explore the influencing factors of the current distribution of elderly care facilities in the central urban area of Shanghai. According to previous work, the layout planning of elderly care facilities is affected by a series of factors, including land cost, transportation convenience, medical resource allocation, economic development level, population density and so on [47,48,49]. For example, researchers such as Chen et al. found that the density of residential areas and road network are important factors affecting the accessibility of elderly care facilities, while the resident attribute index has no direct correlation with the spatial distribution of existing elderly care facilities [50].

In February 2022, Shanghai Civil Affairs Bureau issued the draft of planning for the Layout of Shanghai Elderly Care Facilities (2021–2035), which put forward requirements for the layout of facilities. For example, being close to medical and health facilities; considering the convenience; easily accessible by public transportation; avoiding sections close to intersections with high traffic volume; trying to choose sections with good environment; keeping away from pollution sources, and so on.

Based on the background above, this study uses multi-source data to build seven index categories (17 variables), including caring, morphology, land use, transportation economy, population, and business forms. The description of each indicator is shown in

Table 1. Influencing factors of spatial distribution imbalance.

Category	Variable	Description
Caring	Accessibility of nursing institutions	Within a 15-min walking, accessibility of elderly care institutions, such as nursing institutions, welfare homes, etc.
	Medical density	Within a 15-min walking, density of medical facilities, such as hospitals, clinics, etc
Morphology	Plot Ratio	Within a 15-min walking, ratio of total building area to life circle area
	Building Density	Within a 15-min walking, ratio of floor area to life circle area
	Building height	Within a 15-min walking, average height of buildings
Land Use	Land use mix	Within a 15-min walking, mixed degree of land use
Transportation	Intersection density	Within a 15-min walking, density of road intersections
	Bus Station density	Within a 15-min walking, density of bus stops,
Economy	Housing_price	Within a 15-min walking, average value of house prices
	Rents	Within a 15-min walking, average value of rental prices
Population	Residential density	Within a 15-min walking, average value of population density
	Income	Within a 15-min walking, average value of per capita income
Business Forms	Catering density	Within a 15-min walking, the density of catering places, such as Chinese food, Western food, teahouses, etc
	Attractions density	Within a 15-min walking, the density of scenic spots, such as parks, green spaces, scenic spots, etc
	Factory density	Within a 15-min walking, density of sports and leisure factories.
	Education density	Within a 15-min walking, educational and cultural density, schools, museums, etc
	Hotel density	Within a 15-min walking, density of hotels.

.

3.2.2. Machine Learning Regression Model and Feature Screening

All indicators are dimensionless through Z-score standardization, to meet the normal distribution with mean value of 0 and variance of 1. Python’s SciPy package is employed for Pearson correlation test. Pearson correlation coefficient is used to measure the linear correlation between two variables, and the range is between −1 and 1. The correlation degree between variables can be seen visually by drawing the heatmap of the correlation matrix.

In this study, we use Random Forest algorithm to construct a regression model to reveal the global impact of different influencing factors on the accessibility of elderly care facilities. A total of 17 indexes built in Section 3.2.1. were selected as independent variables; comprehensive accessibility and the six single types of accessibility were dependent variables. Random Forest is one of the ensemble machine learning algorithms, which combines several randomized decision trees and aggregates their predictions by averaging [51], and it better represents the genuine relationship between the predicted and predictor variables [52]. The random forest is among the most popular and powerful supervised machine learning algorithms [53,54].

The Gini coefficient method of Random Forest is used for feature selection, and the relevant formula is as follows:

$$Gini\left(D\right)={\displaystyle \sum }_{k=1}^k{P}_k\left(1-P_k\right)=1-{\displaystyle \sum }_{k=1}^k{P}_k{}^2,$$

(9)

where D is the dataset, k is the Random Forest decision tree species, and $P_k$ is the probability that the sample belongs to k.

Each tree in the Random Forest will split according to a certain node, and the reduction in Gini coefficient before and after splitting is used as the standard to judge the importance of feature. Import the scikit learn machine learning package into python, use the Random Forest algorithm, and sort the importance of variables from high to low. Then, draw the layout chart of feature importance to assist in feature screening.

In this section, we selected the top eight variables from the above feature selection results, which are used in the next section to improve the model fitting effect.

3.2.3. Geographically Weighted Regression Model

In order to reveal the local impact of different influencing factors on the accessibility of elderly care facilities, this study adopts Geographical Weighted Regression (GWR) model with the help of ArcGIS platform. Variables selected in Section 3.2.2. are set as independent variables, with comprehensive accessibility as dependent variables. Geographically Weighted Regression, proposed by Brunsdon et al. [55] detects the nonstationarity of spatial relationships by embedding spatial structures into linear regression models. With a clear analytical expression of the estimation results and the obtained parameter estimation statistically tested, this method has been more and more applied [56].

$$Y_i={\beta }_j\left({\mu }_i,{\vartheta }_i\right)+{\displaystyle \sum }_{j=1}^p{\beta }_j\left({\mu }_i,{\vartheta }_i\right)X_{ij}+{\epsilon }_i,$$

(10)

where $Y_i$ is the comprehensive accessibility at point i, ${\beta }_j\left({\mu }_i,{\upsilon }_i\right)$ represents spatial geographic location data, ${\beta }_j$ represents the regression coefficient of local variables, $\left({\mu }_i,{\mathsf{\upsilon }}_i\right)$ represents the geographical coordinates of point i, $X_{ij}$ represents the observed value of variable j at point i, and ${\epsilon }_i$ represents the random error.

4. Results and Discussion

4.1. Results of Accessibility

The calculation results of the comprehensive accessibility of community-based elderly care facilities and the accessibility of six single types are shown in the Figure 3. The comprehensive accessibility score decays outward from the center. Communities with higher scores are mainly distributed in the area between Beijing Middle Road and Huaihai Middle Road in Huangpu District. In this area, there are government departments, business centers, central green spaces, etc., where the regional advantage is obvious. As a city card, the communities here began to perfect and carry out the construction of elderly care facilities earlier; However, the comprehensive accessibility score of the community located at the edge of the downtown is poor. Because the construction of community pension resources is often related to the economic level and policies, communities located in the surrounding areas are obviously not paid enough attention.

From the accessibility calculation results of six types of facilities, the calculation results of Type-A are similar to the comprehensive accessibility results, where the communities with high accessibility are mainly located in Huangpu District, while the communities located in the edge area have low accessibility to Type-A. The score of Type-B in Huangpu District is high, and there are also districts with high scores at the junction of Putuo, Jing’an and Changning. Type-C has a higher score in the central area of Huangpu District. For Type-D, the distribution of higher scores is similar to the comprehensive accessibility, but the overall spatial distribution is extremely uneven, and the accessibility is poor in other areas of the whole region. Type-E is relatively better in Huangpu region, Northwestern Putuo and Northern Yangpu. The high-value area of Type-F presents a scattered distribution. In general, the distribution of accessibility scores is uneven, and there is a central aggregation characteristic. The area between Beijing Middle Road and Huaihai middle road in Huangpu District is relatively better in terms of comprehensive accessibility and single accessibility of six types of facilities.

4.2. Analysis on Imbalancd Spatial Distribution

The calculation results of Getis–Ord Gi* can identify the cold and hot spots of accessibility numerical distribution, to reveal the spatial clustering location of accessibility. The following conclusions can be seen from the Figure 4 and Figure 5.

4.2.1. Distribution of Comprehensive Accessibility

For comprehensive accessibility, there are two identified hot spots, respectively (Figure 4). The two hot spots are connected, indicating that the comprehensive accessibility of elderly care facilities in the communities in these two regions is better, while there are more cold spots in other regions. The strategy guidance for each administrative district formulated in the Layout of Shanghai Elderly Care Facilities (2021–2035) lists Huangpu, Putuo, Hongkou and Jing’an as the consolidation and optimization areas, which means these four districts are better than others. However, from the perspective of this study, only Huangpu has the best matching of elderly care facilities with the needs of the elderly population, while the other three regions, especially the northern regions of Jing’an and Hongkou, show relatively dense cold spots. Cold spots are also widely distributed in Yangpu, Changning and Xuhui. In this regard, the matching ability of pension demands and supply in the central urban area of Shanghai is relatively weak in six districts except Huangpu. In the future, these six districts still need to strengthen the construction of community-based elderly care facilities.

4.2.2. Distribution of Single Accessibility

• For accessibility of Type-A, there are two independent hot spots, one large and one small. The large hot spot is in Huangpu District, and the small hot spot is in the junction area of Jing’an and Changning. As a community-based elderly care facility providing medium and short-term elderly care, it mainly provides institutional residential care, rehabilitation care after serious illness discharge, breathing service and door-to-door service for the older adults. The quality of Type-A is closely related to the aging care in the community.
• For accessibility of Type-B, it has similar spatial distribution of cold and hot spots with Type-A. Such facilities provide day care services such as care and nursing, rehabilitation assistance, spiritual comfort, cultural entertainment, and travel assistance who are in need.
• For accessibility of Type-C, it has a hot spot area and several small hot spots, while Putuo and Jing’an both show many cold spots. Such facilities provide meal assistance services for older adults, meeting the needs of older adults to enjoy convenient and affordable meal assistance services.
• For accessibility of Type-D, the identified hot spots are mainly in the north of Huangpu District, and the cold spots are relatively scattered. Such facilities are community elderly care service organizations that provide door-to-door or community services for older adults.
• For accessibility of Type-E, hot spots are in Huangpu District, the junction of Putuo, Jing’an and Changning, and some areas of Yangpu District. Type-E, including nursing homes, daycare centers, meals, nursing stations, are “hub” elderly service complexes. Older adults can basically enjoy various elderly care services such as daycare, full care, meals, baths, rehabilitation, and nursing.
• For accessibility of Type-F, the biggest hot spot appears along the junctions of the six districts: Huangpu, Xuhui, Changning, Putuo, Jing’an and Hongkou. South of Huangpu District is also a hot spot. The cold spot area is mainly around the hot spot area. Similarly located at the north of Huangpu District, it is worth noting that there are hot spots of Type-F but cold spots of five other types. Such facilities are nursing stations, which provide medical care and nursing services for the elderly.

In summary, in terms of the accessibility of the six single types of facilities, Type-A and Type-B focus on strengthening the improvement of facilities in the north of Xuhui District, the south of Jing’an District, the south of Yangpu District and Hongkou District; Type-C focuses on strengthening the construction of Jing’an District, the east of Changning District and the southeast of Putuo; Type-D focuses on strengthening Hongkou District, the east of Changning District and the north of Xuhui District; Type-E focuses on strengthening the north of Xuhui District and the south of Jing’an District; Type-F focuses on strengthening the parts between the two hot spots, namely, the eastern part of Changning, the northern part of Xuhui District, the northern part of Huangpu District and the southern part of Yangpu District.

4.3. Interpretation of Random Forest Model Results

4.3.1. Interpretation of Overall Model Fitness

From the model results in

Table 2. Model diagnostics.

Model	R2	RMSE	MAE
Comprehensive	0.66	0.57	0.30
Type-A	0.57	0.66	0.32
Type-B	0.61	0.63	0.45
Type-C	0.66	0.59	0.41
Type-D	0.67	0.61	0.25
Type-E	0.46	0.72	0.54
Type-F	0.47	0.73	0.55

Where R² refers to the Goodness of Fit, the larger value of which indicates the better fitting degree. RMSE and MAE are abbreviations of the Root Mean Square Error and Mean Absolute Error, respectively; the lower value of both indexes indicates better performance of model.

, the fitting degree of the comprehensive accessibility, Type-C and Type-D, is better, and the goodness of fit is more than 65%, indicating that these 17 indicators (Table 1) have a strong ability to explain the dependent variables in these three models. The ${\mathrm{R}}^2$ of Type-E and Type-F is low, but also more than 45%, relatively speaking, which is within the acceptable range.

4.3.2. Interpretation of Feature Importance

Figure 6 (left) is the feature importance results of Random Forest, from which we can see the factors that greatly impact the comprehensive accessibility of community elderly care facilities: accessibility of nursing institutions, hotel density, catering density, education density and medical density. Combined with correlation analysis (Figure 6 (right)), we can see that “accessibility of nursing institutions”, “hotel density” and “education density” are positively correlated with comprehensive accessibility; “medical density” and “catering density” are negatively correlated with accessibility. However, “rents”, “plot ratio” and “building density” have little impact on comprehensive accessibility.

According to the feature importance results of Random Forest, eight indexes were selected for Geographical Weighted Regression analysis, which were accessibility of nursing institutions, hotel density, catering density, education density, medical density, attractions density, land use mix and building height.

4.4. Interpretation of Geographical Weighted Regression Results

4.4.1. Interpretation Global Performance

As shown in

Table 3. Model diagnostics.

Model Diagnostics
R2	0.8409
AdjR2	0.8364
AICc	15,210.4544
Sigma-Squared	0.1636
Sigma-Squared MLE	0.1591
Effective Degrees of Freedom	14,176.7299

Where AIC is the abbreviation of “Akaike Information Criterion” and AICc is a bias correction to AIC for small sample sizes, where the model with the lower AICc value provides a better fit to the observed data.

, the results of geographically weighted regression show that the adjustment R-square is 0.8364. Compared with the Random Forest regression model established with 17 indicators in 4.3, the selected 8 indicators are good at explaining the dependent variables.

4.4.2. Local Spatial Heterogeneity

The results of the GWR model allow us to examine the spatial variation of the relationships between the dependent and independent variables with the coefficient from each model. As can be seen in Figure 7, overall, there are great differences in the fitting degree. The high fitting degree of the model in the whole region is located in some areas of Huangpu, Changning and Yangpu, where the ${\mathrm{R}}^2$ of these areas is above 0.5. The ${\mathrm{R}}^2$ of some areas is below 0.3, for example, the north of Yangpu District and Putuo District. There is a very poor fitting ring around Huangpu District, indicating that in this region, the explanatory ability of the eight variables to the dependent variables is highly differentiated in space.

Each of the factors that represented the spatial distribution of their coefficients is shown in Figure 8:

• For attraction density, overall, the influence of this factor on comprehensive accessibility varies greatly, reflecting obvious heterogeneity in space. The positive relationship between it and comprehensive accessibility appeared mainly in the junction of Xuhui District and Changning District, the northwest of Xuhui District and the junctions of Huangpu District, Jing’an District and Hongkou District. However, in north Huangpu, the local coefficients are negative, which means this index in Huangpu District has a bidirectional influence on comprehensive accessibility.
• For catering density, communities near the people’s Square in Huangpu District show a strong positive impact, but the surrounding area shows a negative impact, indicating that the influence of catering density on comprehensive accessibility in Huangpu District is quite different. In addition, there are also positive impacts in the west of Jing’an, the junction of Hongkou and Yangpu.
• For education density, the degree of influence is relatively significant in Huangpu District, and the degree of influence presents two directions. There is a positive impact at the junction of Huangpu District, Jing’an District, and the eastern part of Huangpu District. At the junction of Hongkou District and Yangpu District, there is a strong negative impact in the middle of Changning District.
• For building height, this factor has obvious spatial heterogeneity, which shows a strong positive impact in the southeast of Huangpu District and a strong negative impact in the north of Huangpu District. There is also a negative effect at the edge of downtown Shanghai.
• Overall, the impact is weak for hotel density in many regions, such as the north of Yangpu District and the east of Hongkou District. Strong negative and positive impacts appear in the west of Changning District.
• For accessibility of the nursing institution, as a whole, there is a circular feature, and the positive influence and negative influence are alternately distributed. With the people’s Square in Huangpu District as the center and near the people’s Square, there is a strong positive impact, and then there is a strong negative characteristic in the outward area. It is also reflected as a positive impact in Yangpu District and Hongkou District.
• For land use mix, in the overall range, the positive influence of this factor on comprehensive accessibility is distributed in a large range. It is worth noting that there is a great difference in Huangpu, and the influence degree of the north and south parts is opposite.
• For medical density, there is a strong positive impact in the east of Huangpu District, the junction of Jing’an District and Huangpu District, the west of Changning District and other places. At the same time, there is a strong negative impact in the west of Huangpu District and the east of Changning District. Besides, the impact is weak in Yangpu District and Jing’an District.

Figure 8. The spatial distribution of the GWR local coefficients.

Figure 8. The spatial distribution of the GWR local coefficients.

The results of GWR revealed significant spatial heterogeneity in the impacts of different factors. From the above eight influencing factors on comprehensive accessibility, the eight indicators are heterogeneous in space, and the influence degree and direction are different based on geographical locations, where there are bidirectional effects. From the perspective of seven districts, eight influencing factors have noticeable spatial heterogeneity in Huangpu District. According to the impact results of the indicators, when the government later improves the resources of community-based elderly care facilities, it can accurately locate the priority factors of the community and improve them according to the spatial heterogeneity of different elements.

5. Conclusions

Based on the community scale, this study takes the 15-min community-life circle as the basic research unit to study the imbalanced distribution of various community-based pension resources in downtown Shanghai and to further explore the influencing factors that cause this distribution status. We obtained six types of elderly care facilities data from the Shanghai elderly care service platform, using the Gaussian 2-step Floating Catchment Area method to calculate the accessibility of 6-type elderly care facility. Then, we used the Entropy Weight Method to calculate the comprehensive accessibility of elderly care facilities. The Getis–Ord Gi* method was adopted to analyze the overall distribution, identifying the well-developed and under-developed areas. To explore the influencing factors of the distribution, this paper obtained multi-source data to construct a total of 17 indicators and established a Random Forest model to identify the feature importance. Finally, with the selected eight factors, the Geographically Weighted Regression model was adopted to study the spatial heterogeneity of influencing factors:

Overall, the essential findings are concluded corresponding to the two aims:

(1) As for the distribution features of pension resources in downtown Shanghai,

• the distribution of pension resources in the downtown of Shanghai is extremely uneven. The six single types of facilities show high scores in some areas centered on Huangpu District, and generally show the characteristics of single point center radioactivity.
• Community-based elderly care facilities in Huangpu District are mainly presented as a hot spot area, while the other six districts mainly show as cold spot agglomeration. Therefore, it is considered that the construction of pension services in these six districts needs to be strengthened.

(2) As for the influencing factors that cause this distribution of pension resources,

• factors that have a great impact on the comprehensive accessibility of community elderly care facilities are as follows: accessibility of nursing institutions, hotel density, catering density, education density and medical density. Moreover, “accessibility of nursing institutions”, “hotel density” and “education density” are positively correlated with comprehensive accessibility; “medical density”; and “catering density” are negatively correlated with accessibility. However, “rents”, “plot ratio” and “building density” have little impact on comprehensive accessibility.
• The results of GWR revealed that the influence effects of eight indicators are heterogeneous in space, and the influence degree and direction of accessibility are different in different geographical locations, where there are bidirectional effects. From the perspective of seven districts, eight influencing factors have spatial heterogeneity in Huangpu District particularly.

Providing systematic elderly care services for the older adults aging in place is an important implementation path to solve the emerging aging problems and reflects the capability of urban management organizations to allocate resources reasonably. Family members can fulfill their maintenance obligations conveniently, which is in line with the meaning of filial piety in Chinese traditional culture. The better elderly care environment in the community life circle is conducive to the realization of elderly care mutual assistance, so that the elderly lives in a familiar environment. Abundant elderly care facilities and professional elderly care services can effectively solve the problems encountered by the aged communities. At the same time, it eased the shortage of resources in nursing institutions and saved social resources. The significance of this study is to describe the distribution of pension facilities and study the relevant factors. The findings of this research are immediately significant to the urban planning and urban design community, as well as health planners and the age-care community. With these findings, we acknowledge that establishing a sound community elderly care service system could improve the quality of life of older adults and promote social fairness and justice.