Accessibility of Elderly Care Facilities Based on Social Stratification: A Case Study in Tianjin, China

Abstract

With the increasingly prominent phenomenon of social stratification in urban development, it is of practical significance to study the accessibility of elderly care facilities for different social groups. The study improves the mathematical model of the two-step floating catchment area method (2SFCA) as regards three aspects: the accurate demand of elderly residents, the comprehensive supply capacity of elderly care facilities, and the precision of travel costs. Taking Tianjin as an example, the study measures the accessibility of elderly care facilities from the perspective of social stratification. The results show that: (1) The improved model is more practical in evaluating the accessibility of elderly care facilities. (2) The spatial distribution of social groups in Tianjin presents a concentric structure and the social stratification in the periphery area is more obvious. (3) The accessibility scores of elderly care facilities are higher in the city center, lower in the periphery area, higher in the south, and lower in the north. (4) High- and middle-income groups have better accessibility, while the elite and low-income groups have worse accessibility.

1. Introduction

China has the largest elderly population in the world. The latest statistics show that 240 million people are over the age of 60, accounting for 17.3% of the total population. The 14th Five-Year Plan of China (2021–2025) pointed out that “China will actively respond to the ageing population, promote the combination of medical care and elderly care, and accelerate the development of the ageing cause and industry”. As an important aspect of the social security system and environment for elderly individuals, elderly care facilities are directly related to the welfare level of elderly individuals. Therefore, the rationality and fairness of the spatial allocation of elderly care facilities have received a great amount of attention [1,2].

Accessibility is a quantitative expression meant to measure the chance of interaction of various nodes in space [3]. The gravity model [4,5] and the two-step floating catchment area (2SFCA) method [6] are the most commonly used methods for evaluating the spatial accessibility of public facilities. Compared with the gravity model method, the 2SFCA method adds the concept of the ‘space threshold’ to constrain the range of interaction between facilities and people [7]. In addition, scholars have made certain contributions to the accessibility of aged care facilities. Di et al. [8] and Tseng. et al. [9] examined the impact of facility costs and travel distance on the accessibility of elderly care facilities. To improve the authenticity of accessibility calculations, Li [10] and Han [11] used internet data to correct the supply and demand relationship between people and facility resources.

Social stratification is the unequal distribution of social resources among different groups. The phenomenon of social stratification has gradually become obvious with the development of society [12], and the inequity of urban public resources in geographic space is also becoming increasingly significant [13]. Li et al. [14] and Tahmasbi et al. [15] found that low-income residents have lower access to public facilities and resources in their areas. Zhang et al. demonstrated that there are significant differences in the accessibility and fairness of public service facilities among the elite, the middle-income, the low-income, and the poverty-stricken groups. Yin et al. [16] indicated that people from different economic backgrounds have different selection probabilities for disparate types of elderly care facilities.

Existing studies have combined the usage and travel characteristics of elderly people in the measurement of accessibility of elderly care facilities; however, there are deficiencies. First, the accessibility research from the perspective of social stratification is insufficient. Factors used in the accessibility model of elderly care facilities, such as the distribution of the elderly population, economic conditions, and transportation convenience, are all related to social stratification. However, the current accessibility measurement treats all elderly individuals as the same, ignoring individual demands from different social groups and their selection probability of different types of elderly care facilities [17]. Second, existing studies often use the number of beds to measure the supply capacity of elderly care facilities [18]; however, elderly care facilities with different types and environments have distinct attractiveness to people from different social groups [19]. The use of a single indicator cannot accurately reflect the actual service supply capacity. Huang et al. [20] and Martin [21] considered that factors such as facility level and medical service can also affect facility service supply capacity in a study of healthcare accessibility. Third, in the traditional accessibility method, a road network model is generally established to represent the geographic space. However, the time spent on traffic congestion, transfer, and walking can only be obtained through estimation, which causes deviations in the calculation results.

Based on social stratification, this paper improves the 2SFCA method in regard to three aspects: the accurate calculation of the elderly’s demands based on differences in social groups, the comprehensive supply capacity of elderly care facilities, and the precise travel cost as calculated by the API (application program interface) of AutoNavi Map. This improved approach is illustrated and validated through a case study in Tianjin and compared with traditional accessibility methods. The results show that this improved method agrees more with the actual situation compared with the traditional method. The improved method can not only show the areas with insufficient accessibility but also indicate the types of facilities needed in the area. This method is helpful for both the equitable construction of elderly service facilities and improvements to the design of urban elderly care facilities.

2. Research Area and Data Acquisition

2.1. Research Area

The research area is an urban area within the outer ring line of Tianjin (Figure 1); it has a population of 4.2 million and an area of 371 square kilometers. It includes six central districts (the Heping, Hexi, Nankai, Hedong, Hebei, and Hongqiao districts) and part of the urban fringe area (the Dongli, Jinnan, Xiqing, and Beichen districts). Since Tianjin has become a deeply ageing society, it provides a good foundation for research on the elderly population. According to the seventh national census of China, the proportion of the population aged over 65 is 14.75% in Tianjin, which is a leading percentage in China.

2.2. Research Data

① The data on residential communities come from three second-hand housing websites, namely Anjuke (https://tianjin.anjuke.com/), Lianjia (https://tj.lianjia.com/), and Fangtianxia (https://tj.fang.com/). After verification, the data contain a total of 1823 communities within the research scope, including community names, average housing price, building structure, construction year, number of households, greening rate, floor area rate, property fee and the number of schools, hospitals, supermarkets and parks within 3 kilometers. ② The data on elderly care facilities are obtained through the official website of the Tianjin Civil Affairs Bureau (https://mz.tj.gov.cn/). The data have a total of 364 elderly care facilities (as of May 2021), including location, nature of facilities, number of beds, and information on medical facilities. The monthly average nursing expenses data, gross floor area, total land-use area, and the number of service types are obtained through the elderly care website (https://www.yanglao.com.cn/). ③ The elderly population of every community is equal to the product of the number of households, the average population per household and the proportion of the elderly in each community. The numbers of households are from the websites mentioned before. The average population per household and the proportion of the elderly in each community are based on the results of the Seventh National Population Census of China conducted in 2020 [22]. ④ The shortest travel time is obtained through the route-planning tool in the API of AutoNavi Map.

3. Method

3.1. Traditional 2SFCA Methods

The traditional 2SFCA method is widely used to study the accessibility of urban public facilities, such as park green space [23], educational facilities [24], and medical facilities [25]. It uses a limited distance or time as a search radius to set a threshold and conducts two mobile searches according to supply location and demand location. Then, it analyses the supply capacity and actual demand of service facilities [26]. The larger the score of the calculation result is, the better the accessibility to the public resource or facility, which is shown in Formula (1).

$$A_i={\displaystyle \sum }_{j\in \left(d_{ij}\le d_0\right)}{R}_j={\displaystyle \sum }_{j\in \left(d_{ij}\le d_0\right)}\left\{\frac{S_j}{{{\displaystyle \sum }}_{k\in \left\{d_{kj},\le d_0\right\}}{D}_k}\right\}$$

(1)

where i represents the residential point, j represents the facility point, A_i represents the facility accessibility of demand point I, S_j represents the capacity of the facility, using the normalized number of beds at facility point j, d_ij is the distance between residential point i and facilities point j, d₀ is the search radius, D_k is the elderly population of settlement k within the search radius, and R_j is the ratio of the beds of facility location j and the population it serves within search radius d₀.

3.2. Social Groups Division

Urban residents usually consider both internal and external factors of a residential area when choosing housing [27]. The present study divides social groups using economic and social data from the community [28]. First, we calculate the average housing price, plot ratio, greening rate, property fee, and age of completion within the community, and the number of schools, hospitals, supermarkets, and parks within 3 km of the community. Then, hierarchical clustering is performed to divide the social groups of the residential quarters in the central urban area into elite, high-income, middle-income, and low-income groups using the Q-type clustering method via the SPSS Statistics software.

3.3. Improved 2SFCA Methods

The study uses the 2SFCA method as a basis to improve the accessibility measurement method and more realistically simulate the accessibility of elderly care. The 2SFCA method is improved for our purposes in regard to three aspects:

(1)

An identification of the demands of the elderly from different social groups for different types of elderly care facilities is performed. First, the elderly care facilities are divided into three categories according to the nature of the facility and monthly nursing expenses incurred: public elderly care facilities (government-run, less than 2000 RMB/month), including a total of 196 public elderly care facilities that offer fewer medical staff and less basic equipment; commercial elderly care facilities (private, 2000–5000 RMB/month), including a total of 136 commercial elderly care facilities in which the equipment and services are considered comfortable; and advanced commercial elderly care facilities (private, more than 5000 RMB/month), including a total of 32 advanced commercial elderly care facilities with advanced and optimal equipment that provide a better living quality. Then, 50 questionnaires were distributed to each of the four types of social groups to investigate trends in the choice of elderly care facilities. The questionnaire showed the probability of elderly residents from different social groups choosing various types of elderly care facilities, as shown in

Table 1. Probability table for elderly residents of different social groups choosing different types of elderly care facilities.

Social Groups	Advanced (%)	Commercial (%)	Public (%)
The elite	50	30	20
high-income group	30	40	30
middle-income group	20	40	40
low-income group	10	30	60

.

(2)

Multiple indicators are used to comprehensively calculate the supply capacity of elderly care facilities. The study incorporates the number of beds, gross floor area, total land-use area, nursing expenses, medical treatment support, and hospital support into the calculation of the supply capacity of elderly care facilities, referring not only to related research [10,11,29] but also to the standard ‘Classification and Accreditation for senior care organization’ of Tianjin city and the ‘14th Five-Year Plan of Tianjin Civil Affairs Development.’ After all the indicators are standardized, the weights of the indicators are calculated via the analytic hierarchy process; the results suggest that the indicators pass the consistency test, as listed in

Table 2. Index weight table for the comprehensive service capability evaluation of elderly care facilities.

Indices		Weighting Coefficient	Calculation
Facility capacity	The number of beds	0.5574	The standardized number of beds in the facility
	Gross floor area	0.10837	The standardized value
Facility conditions	Total land-use area	0.08362	The standardized value
	Nursing expenses	0.15902	The standardized monthly nursing expenses
medical service	Medical treatment support	0.05866	The standardized number of service types
	Hospital support	0.03292	The standardized number of hospitals within 1 km

.

(3)

The API of AutoNavi Map is used to obtain travel costs. The APIs offered by the navigation service providers have been used in accessibility calculations in recent years due to their advantages in the simulation of complex urban road conditions [30,31]. This research uses the AutoNavi API path-planning interface to obtain the shortest travel time from each residential community to each elderly care facility as the travel cost.

Based on the three improvement aspects, the study uses the Gaussian function for distance decay and establishes an accessibility model. The Gaussian function decays slowly when approaching the search threshold, which conforms to the actual travel situation of the elderly [30].

In the first step, for each elderly care facility point j, we search for all the residential points k within the threshold range (using j as the center and d₀ as the threshold). A Gaussian function is used to calculate the decay of the elderly population in these districts and then summed. Then, we divide the supply capacity of the elderly care facility by the sum of the elderly population to obtain the supply–demand ratio R_j of elderly care facility j. The result R_j is the service capacity value of elderly care facility j, as shown in Formula (2).

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

(2)

where M_j represents the supply capacity of elderly care facility j, referring to Table 2. d_kj represents the travel time cost from residential point k to elderly care facility point j. P_k is the facility demand scale of residential point k within the search range, as measured by the number of elderly residents. P_t is the probability of different social groups choosing elderly care facilities by type (Table 1). According to a travel survey in Tianjin, most elderly families tend to choose elderly care facilities within 1 h of their homes; thus, d₀ is taken as 1 h. G (d_kj, d₀) is a Gaussian function that considers the effect of distance decay, and the calculation formula is shown in Formula (3).

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

(3)

In the second step, for each residential point i, we search for all elderly care facility points j (using i as the center and d₀ as the threshold range). Similarly, we sum the supply–demand ratio R_j through Gaussian function decay and obtain the accessibility index A_i of each cell point i, as shown in Formula (4).

$$A_i={\displaystyle \sum }_{i\left\{\in d_{ij}\le d_0\right\}}G\left(d_{ij},d_0\right)\times R_j\times P_t$$

(4)

where R_j is the ratio of supply to the demand for elderly care facility j within the threshold range. d_ij is the shortest travel time between residential point i and elderly care facility j. A_i represents the elderly care facility accessibility index of residential point i. The larger the value of A_i is, the better the accessibility of residential point i is.

4. Results and Discussion

4.1. Spatial Characteristics of Social Groups

After the hierarchical clustering of residential areas, the results for the four social groups are listed in

Table 3. Classification of social groups and their housing property.

Social Groups	Amount (Proportion)	Average Price per Square Metre/RMB	Property Fee/RMB/Year	Building Age/Year	Greening Rate/%	Plot Ratio	Schools within 3 km	Hospitals within 3 km	Shops within 3 km	Parks within 3 km
The elite	58 (3.18%)	61,494	2.16	23.8	28.48	2.08	174.8	53.7	1189.8	38.5
high-income group	153 (8.39%)	49,133	1.76	24.9	24.26	2.12	193.0	60.6	1278.8	41.5
middle-income group	835 (45.8%)	28,903	0.97	24.4	25.3	1.86	158.4	43.8	1011.1	25.6
low-income group	777 (42.62%)	21,856	0.99	25.0	26.44	1.75	100.0	21.5	587.39	13.8

, and the spatial distribution is shown in Figure 2.

The elite residential communities account for 2.59% of all communities in the research area. They are mostly concentrated in the center of the city and the areas near high-quality landscapes, such as hills and rivers. Residents of these communities possess great wealth and status and have higher requirements for their living environment and quality. The high-income residential communities account for 5.20%. They are mainly concentrated in the city center, such as Heping District, northern Hexi District and northern Nankai District. The residents of this group have successful careers and high requirements for regional positioning, medical resources, and educational resources. The middle-income residential communities account for 46.78%, and they are mainly distributed in the northern Nankai District, northern Hexi District, southwestern Hebei District, and southern Hongqiao District. The income of the residents within this group is at the social average wage level, and these individuals tend to strike a balance between location, environment and housing price. The low-income residential communities account for 45.43%. They are distributed in various areas of the city, including old residential areas, public housing units and urban villages in the city center, and affordable housing in peripheral areas. The residents in this group have not reached the average wage level and cannot purchase commercial housing by themselves.

In general, the distribution of social groups shows a concentric structure. From the center area to the periphery of the city, they are the elite, high-income group, middle-income group, and low-income group in sequence. The social stratification phenomenon is not obvious in the center of Tianjin. However, the phenomenon gradually increases in the peripheral areas. Higher-income residents are attracted by high-quality landscapes and gather around ecological landscapes; lower-income residents gather in industrial areas, affordable housing areas and others.

4.2. Accessibility of Elderly Care Facilities in Tianjin

First, the accessibility distribution of elderly care facilities is obtained using the traditional method. The accessibility results are normalized and divided into five grades based on the Jenks natural breaks classification method: low, relatively low, normal, relatively high, and high, as shown in Figure 3a. A total of 66.91% of the communities have scores that are normal or above, and they are mainly located in areas close to the city center, such as Heping District, Nankai District, Hedong District and Hebei District. Urban construction in these areas occurred earlier and the elderly care facilities are sufficient; therefore, residents in these areas can access these resources more beneficially. A total of 23.3% of the areas with relatively low scores are mainly located in the transition zone between the city center and the city fringe. A total of 9.86% of the areas with low accessibility scores are located on the fringes of cities. Urban construction lags behind in the peripheral areas of the city; thus, the number of elderly care facilities is relatively small, and the construction is relatively concentrated. Therefore, the accessibility scores of these areas are relatively low.

Second, the improved accessibility model is used to calculate the accessibility scores of different strata of communities to elderly care facilities in the central urban area of Tianjin. The accessibility calculation results are normalized and divided into five grades based on the same Jenks natural breaks: low, relatively low, normal, relatively high, and high, as shown in Figure 3b. From an overall perspective, the accessibility scores of elderly care facilities are higher in the city center, lower in the periphery area, higher in the south and lower in the north. Only 48.5% of the residential communities in Tianjin reached the normal accessibility score and above. They are mostly distributed in the northern part of Hexi District, north of Nankai District and west of Hedong District. The areas with relatively low and low scores are distributed in the old city and the periphery area.

To compare the accessibility of elderly care facilities from different social groups, the accessibility distribution maps of the four social groups are shown in Figure 4. From the elite to the low-income group, the communities whose accessibility to elderly care facilities reached normal or above accounted for 49.7%, 72.8%, 59.3% and 26.4% respectively. Among them, the high-income group has the highest accessibility to elderly care facilities with relatively small internal differences, and the demands of most elderly residents are met; the middle-income group has higher accessibility to elderly care facilities, but the internal differences are large; and the elite and low-income groups have lower accessibility. The service supply for advanced commercial elderly care facilities required by the elite and public elderly care facilities required by the low-income group is still insufficient.

4.3. Comparison of Models

By comparing the results of each method (Figure 3a,b), the improved accessibility method is found to be different from the traditional method. The improved method shows that the distribution of accessibility scores presents a multivariate distribution, with the northern part of Nankai District and the northern part of Hexi District serving as the two main cores. There are also some areas with higher scores located in the periphery areas of the city. In addition, the traditional results of some communities in the southern Hexi District, southwestern Beichen District, and central Jinnan District are lower, while their scores based on the improved method are higher. Although there are few facilities located in these areas, they can meet the demands of residents. While some communities in the eastern Hebei District and northern Hedong District have higher accessibility scores using the traditional method, their scores based on the improved method are lower. Although there are abundant facilities in these areas, they are not well-adapted to the demands of the social groups.

To further compare the difference between the traditional and the improved method, Figure 5 shows the accessibility plot of each community. The traditional method generally tends to overestimate accessibility scores compared to the improved method, especially in the city center, such as Heping District and Hedong District. However, in peripheral areas, the traditional method generally tends to underestimate accessibility. This is because the traditional accessibility method treats the demands of elderly citizens as homogenous. The accessibility results are closely related to the number of facilities and beds; thus, the accessibility scores of the community in the city center are generally higher and decrease as one moves from the city center to the edge.

4.4. Discussion

The improved method has been demonstrated to better reflect the real accessibility distribution of elderly care facilities. Although there are plenty of elderly care facilities located in the city center and fewer located in the suburbs, this does not mean that the residents in the city center have better accessibility than the residents in the periphery area. As shown, many residents have a low accessibility level, regardless of whether they reside in the center area or the periphery area. While accessibility research focuses on space, the evaluation of accessibility is also limited by nonspatial factors. Different types of elderly care facilities have significant gaps in attractiveness to different elderly individuals, which is closely related to the economic status of residents. Therefore, by combining various factors based on social stratification, one can more accurately calculate the supply capacity of elderly care facilities to improve the accuracy of accessibility results. In addition, the traditional method can only show the areas that lack services, while the improved method can point out the types of facilities that need to be added in areas where supply and demand do not match.

The study also finds that there is obvious inequity of accessibility to elderly care facilities among the social groups in Tianjin. High- and middle-income groups have better accessibility, while the elite and low-income groups have worse accessibility. This issue is due to not only an insufficient number of facilities but also the mismatch between the construction of elderly care facilities and the demands of residents of different groups; this mismatch results in lower accessibility scores of elderly care facilities. In places where higher-income people are located, a large number of public elderly care facilities reduce the accessibility of residents because higher-income residents are more concerned with the quality of service rather than a favorable price. In contrast, in some places where lower-income people are located, advanced commercial elderly care facilities cannot meet their demands. This outcome also shows that the accessibility scores in periphery areas where low-income groups are distributed are generally lower than those found in the city center. Hence, more affordable public elderly care facilities should be developed in the periphery areas.

Social stratification implies unequal access to public resources. To bring more elderly care resources to disadvantaged groups and reduce the disparity in accessibility between social groups, the following suggestions are presented for the planning and construction of elderly care facilities. First, an increase in the number of elderly care facilities and beds does not improve accessibility. Adjusting the distribution of public services according to the demands of different social groups can allow more people to enjoy pension services and reduce the gap between social groups. More affordable public elderly care facilities should be planned in the areas where lower-income residents live, and advanced commercial elderly care facilities should be planned in the areas where higher-income residents live to better match the residents’ demands. Second, the government should consider the spatial rationality of the location of elderly care facilities. Factors such as the environment, medical service facilities, and traffic should also be taken into consideration for the construction of new elderly care facilities. In the city center, new elderly care facilities can be built next to public service facilities, such as hospitals, so that the elderly can make better use of the surrounding service resources. In the suburbs, new facilities next to scenic areas can improve accessibility. Medical facilities and public transportation, such as shuttle buses running from communities to facilities, also need to be added. Finally, for existing elderly care facilities that have a mismatch between supply and demand, their services should be adjusted according to the demands of residents in the respective areas. They can provide more types of elderly care services through government–enterprise cooperation and other methods.

Due to the many aspects involved in the accurate measurement of accessibility for elderly care facilities, some shortcomings remain in the current study. In addition to economic factors, special physical conditions, such as disease and disability, also affect the choice of elderly care facilities. Future studies should further optimize the measurement methods by considering more factors that influence the selection of elderly care facilities.

5. Conclusions

With the development of the social economy, the ageing problem has become more obvious in China; the growth of the ageing population has led to the elderly care facilities in cities no longer being able to meet the actual demands of the residents. A method is needed to assess the current situation of elderly care facilities and suggest improvements for the future. By identifying the demands of elderly individuals, we can allocate pension resources better and more equitably. Therefore, based on social stratification, the current study improves the 2SFCA method in regard to three aspects: the accurate calculation of the elderly’s demands from different social groups, the comprehensive supply capacity of elderly care facilities, and the precise travel cost as calculated by API.

The current study takes Tianjin, China, as a case study and the following conclusions are drawn: (1) Compared with the traditional method, the improved method can reflect reality more closely and indicate the types of elderly care facilities needed in underserved areas. (2) The spatial distribution of social groups in Tianjin presents a concentric structure, i.e., extending from the center to the edge of the urban area are the elite, the high-income group, the middle-income group, and the low-income group, in order. The social stratification in the periphery area is more obvious than that in the city center. (3) From the perspective of the city, the accessibility scores of elderly care facilities are higher in the city center, lower in the periphery area, higher in the south and lower in the north. (4) There are significant differences in accessibility between the social groups in Tianjin, i.e., the high- and middle-income groups have better accessibility, while the elite and low-income groups have worse accessibility.