Potential Assessment and Community Environment Support Strategies for Social Interaction, Based on the Spatiotemporal Behavior of Accompanying Elderly Migrants: A Case Study in Hangzhou

Abstract

With the growing trend of population mobility and the aging process in China, a significant number of accompanying elderly migrants have moved to major cities. However, in community public spaces, the behavioral differences between caregiver-oriented elderly migrants (CO-AEMs), family reunion-motivated elderly migrants (FR-AEMs), and local elderly residents hinder social interactions between these groups. This study aims to explore opportunities for cross-group social interaction within the community environment. By utilizing GPS data collection and activity log analysis, along with spatiotemporal behavioral research methods, this study reconstructs the spatiotemporal trajectories of three groups of elderly individuals. The study proposes a social interaction potential (SIP) model based on the “support-constraint” framework. Through qualitative analysis of spatiotemporal behavioral characteristics and quantitative measurement of the degree of spatiotemporal behavioral co-occurrence across four modes, this study reveals the differentiated impact mechanisms of spatial and behavioral factors on social interactions, ultimately assessing SIP in differentiated community spaces and activities. This research highlights differences across spatial, behavioral, and temporal dimensions that hinder social interactions between the groups. Spatial and behavioral differences are primarily attributable to the lifestyle habits and activity preferences of the elderly, while temporal discrepancies reflect varying degrees of family-related constraints across the different groups. Furthermore, informal community public spaces show higher SIP than formal facilities. Additionally, the similarity in behaviors across groups facilitates social interactions. FR-AEMs and local elderly residents show higher SIP in self-care behaviors, while CO-AEMs and local elderly residents demonstrate stronger SIP in behaviors related to their family and grandchildren. Based on the segmented assimilation theory, this study proposes hierarchical community governance and spatial optimization strategies for activities and spaces with different SIP. The aim is to cultivate opportunities for interaction while respecting the characteristics of accompanying elderly migrants and to foster the construction of an inclusive community environment. The findings provide theoretical support and practical pathways for community space planning and social governance in the context of an aging society.

1. Introduction

The 21st century is commonly called “The Age of Mobility,” a period driven by globalization, improved transportation, and rapid information exchange, which have spurred unprecedented population movement worldwide [1]. In recent decades, urbanization and economic reforms have resulted in the largest internal migration in history in China [2]. Unlike migrant populations in foreign countries, the mobile population of China is a concept derived from the household registration system, referring to individuals who have left their registered domicile and are residing in other areas. As of 2022, the total number of people in the mobile population has grown to 376 million, representing 26.6% of the total population. Major urban agglomerations, including the Yangtze River Delta, Beijing–Tianjin–Hebei, and the Pearl River Delta, have previously attracted over 60% of this mobile population [3]. At the same time, many countries in Asia, particularly in East Asia, are rapidly becoming an aging society [4]. Among these countries, China’s aging population issue has become particularly prominent due to the implementation of the “one-child policy” and an ongoing decline in birth rates. By 2022, the elderly population of China had reached 297 million. Under the dual influences of aging and population mobility, the number of elderly migrants in urban areas continues to rise. By 2016, their numbers had reached 18 million [5], comprising 7.2% of the total mobile population and 8.4% of the elderly population (Figure 1). Hence, elderly migrants have become a significant demographic within urban societies.

Elderly mobility is a global phenomenon, with motivations for relocation varying widely among individuals. Some elderly people actively relocate to distinct regions or countries to meet their personal needs, such as retirees seeking more livable environments or lower living costs, or cultural nomads exploring diverse lifestyles and cultures [6]. Conversely, others are compelled to migrate due to external factors like natural disasters, wars, or economic hardships, forming groups of migrants such as disaster victims, refugees, and economic migrants [7,8]. In China, a country influenced by traditional family values, there is a distinctive group of elderly migrants with a unique local characteristic. They typically relocate with their children for two main reasons: to care for their grandchildren (43%) and to rely on their own children (25%) [5]. As a result, elderly migrants in China are often referred to as “accompanying elderly migrants”.

While accompanying elderly migrants appear to migrate voluntarily [9] and receive basic protection, such as the medical care, pensions, and insurance provided by top-down policy systems, many elderly individuals are reluctant to leave their familiar living environment. Meanwhile, their dual vulnerability as migrants and elderly people commonly leaves them struggling to integrate into daily life [10]. As migrants, relocating to a new environment leads to the near-total disruption of their original social networks [11], including ties based on geography, kinship, blood relations, and work [12]. They also face challenges regarding psychological acceptance and identity struggles due to language and cultural differences, as well as differing customs [13]. As elderly individuals, their physical abilities, ideological beliefs, social interaction skills, and adaptability to new environments are significantly lower than those of younger people [14], making it difficult for them to build new social connections.

In recent years, social isolation has emerged as a significant threat to the physical and mental health, as well as the overall quality of life, of accompanying elderly migrants [15]. Among accompanying elderly migrants, depression rates are consistently higher than those of the elderly population, ranging from 6% to 29.4% [16]. They face a heightened risk of conditions such as stroke, insomnia, and dementia [17]. Moreover, extreme incidents like suicide and violence have been reported [18], making them a destabilizing factor in the family and the community. Social isolation among Chinese migrants is not caused by long-standing prejudice or discrimination based on historical, cultural, or religious factors but rather arises from differences in group attributes [19,20]. Regarding the inevitable differences between migrant groups and residents, Simmel highlighted that social interactions enable groups to gradually build deeper mutual understanding and connection by sharing experiences, values, and cultural backgrounds [21]. This process fosters the formation of social relationships, helps alleviate negative emotions such as loneliness, anxiety, and depression, and plays a crucial role in an individual’s physical and mental health.

Due to the limited mobility of elderly people, their social interactions are mainly centered around the community, which is heavily influenced by the community environment. First, daily community activities shape the social environment for the elderly. While formal events can expand social circles, their high costs and complexity often lead to fragmented and unstable participation. Daily activities, which are more integrated with everyday life, promote social interaction in a continuous and subtle way [22]. Second, community spaces and facilities shape the physical environment. Places like community squares, neighborhood centers, and public green areas are essential for these daily activities. According to environmental design theory [23], the physical environment significantly impacts social behavior. Community spaces not only offer venues for social interaction, but effective design can also facilitate and enhance social interactions among groups. Therefore, daily activities and community spaces are crucial for fostering social interaction among accompanying elderly migrants and local elderly residents.

With the rapid development of urbanization, mobile populations are increasingly distributed across urban residential communities in rental housing, creating a spatial pattern where migrants and local residents coexist in mixed communities. The shared community environment provides accompanying elderly migrants with opportunities for social interaction, which is crucial for their physical and mental health as it promotes mental well-being, maintains cognitive function, and establishes a social support system [24]. However, Krivo et al. found that living in the same community does not necessarily eliminate feelings of isolation [25]. The differences between these groups have become more subtle, manifesting in dimensions such as space, time, and behavior [26]. To explore social interaction opportunities in the community environment, the objectives of this study are to: (i) identify the similarities and differences in the spatiotemporal behaviors of different groups at the community scale; (ii) propose methods and approaches for assessing opportunities for social interaction; and (iii) clarify the value orientation of social integration and propose community governance and spatial strategies for the social integration of accompanying elderly migrants. This work seeks to identify ways to help them establish new social networks, alleviate feelings of loneliness, and ultimately contribute to the creation of a more inclusive and harmonious urban environment.

2. Literature Review

2.1. Social Integration Theories and Optimization of the “Social Interaction Potential” Model

The concept of social integration has evolved significantly in response to changes in historical contexts and research subjects, expanding from assimilation theory to multiculturalism and segmented assimilation theory (SAT). Before the 1990s, social integration primarily focused on advancing assimilation processes, positing that disadvantaged groups, such as the impoverished and refugees facing basic survival challenges, should gradually abandon their cultural traits to adapt to the culture and values of mainstream society [27]. With the intensification of globalization and increasing waves of migration, a “people-centered” value orientation approach brought multiculturalism to the forefront as a new theoretical paradigm. This perspective emphasizes mutual respect and coexistence between distinct cultures [28]. Nevertheless, studies have verified that excessive emphasis on independence can undermine social cohesion [29]. Against this backdrop, the SAT was introduced to alleviate the binary opposition between migrants and residents. It respects the desire of migrants to preserve their lifestyles and traditional cultures, while also focusing on providing effective support for integration opportunities to promote mutual understanding and acceptance among diverse groups [30].

Social interaction is the foundation for establishing social relationships between groups and promoting social integration [15]. The emergence of social interaction is a gradual process, involving the transition from potential contact opportunities to actual interactions [21]. Compared to real social interactions, focusing on these potential opportunities can stimulate more interactions. This perspective has garnered widespread attention across multiple disciplines, including sociology, psychology, and geography, leading to the concept of social interaction potential (SIP), which comprehensively describes the latent possibilities for social interaction between groups [31,32]. The traditional SIP model focuses on the intensity of interactions between individuals. However, this method fails to capture the true nature of interactions. Social interaction not only requires environmental support but is also influenced by other factors. As a result, high interaction potential may not always represent the possibility of real social interactions taking place. Some studies have pointed out that the content of activities can influence the occurrence of social interactions. For instance, von Granitz et al. found that activities related to hygiene, diet, and dress significantly supported individual participation in social activities, while leisure activities provided comparatively less support [33].

As the economic and social status of migrant populations improves, particularly that of accompanying elderly migrants, we need to approach immigrant integration from a more egalitarian perspective. The SAT tells us that social integration not only requires us to respect the intentions of the group but also to explore opportunities for social interactions that can promote integration. Traditional research on SIP has focused solely on the supportive role of the community environment. However, as defined in the Oxford English Dictionary, the term “potential” refers to the latent developmental possibilities of individuals, organizations, or events in the future. It not only indicates that something has significant potential for growth due to an existing support structure but also suggests that it may be constrained by certain factors that prevent the immediate realization of growth. A similar pattern can also be observed in social interactions. To truly understand SIP, we should also consider the impact of activity content and spatial types, conducting a comprehensive assessment of the integration opportunities available to migrant groups in society.

2.2. Measuring SIP Through Time-Geographic

Although the concept of SIP originated in sociology and psychology, these fields primarily focus on exploring the triggering mechanisms and influencing factors of social interactions, which makes it challenging to quantify SIP. With the development of spatiotemporal prism theory, an increasing number of studies have shown that there is a clear association between spatiotemporal co-occurrence and social relationships [34,35]. Spatiotemporal co-occurrence refers to the phenomenon where two or more entities (such as individuals and transportation vehicles) appear at the same geographic or virtual location within a specific time frame [36,37]. In the field of computer science, approaches leveraging spatiotemporal co-occurrence are commonly employed to predict the strength of user relationships [22,38]. For instance, Liu et al. used the frequency of spatiotemporal co-occurrence of different individuals visiting a specific webpage to predict the likelihood of social relationships forming between groups, highlighting how repeated encounters in cyberspace increase interaction potential [39].

Planning and geography focus more on SIP in physical spaces. Traditional research primarily focused on the similarity of static residential spaces. However, with the increasing mobility and complexity of daily life [40], spatiotemporal characteristics represent an increasingly important perspective for examining SIP between groups [39]. For instance, Farber et al. assessed the frequency of spatiotemporal overlaps within activity spaces to evaluate the opportunities for social interactions between groups [31]. As individuals have limited capacity to engage in multiple activities, the amount and allocation of their discretionary time reveal their priorities and habits [41]. Consequently, the temporal dimension is considered more fundamental than geographic location or specific behaviors for understanding spatial and behavioral patterns [42]. For instance, Wang et al. demonstrated variations in group behavior preferences by analyzing time allocation across activities [43], while Davis explored the segregation of daily activity rhythms among income groups by analyzing the patterns of travel time [44].

Some studies have pointed out that spatiotemporal co-occurrence is not merely a passive condition but rather a dynamic aspect influenced by behavioral patterns, travel routines, and activity schedules [31]. For instance, Chai found that although two groups shared a common space, there were differences in their usage behaviors, which led to the phenomenon of group isolation [45]. Moreover, Byrne’s similarity-attraction theory suggests that the similarity between groups is a potential factor triggering social interactions, meaning that individuals are more likely to form connections with others who share similar values, lifestyle habits, and attitudes [46]. Bruggencate et al. found that elderly individuals often share similar personal habits and activity needs, and even though they may have never met before, they are more likely to form social connections once they interact [47]. In contrast, differences between groups may limit social interactions, even if they occur in the same spatiotemporal context [48].

As the field of time geography gradually deepens, research points out that the spatiotemporal characteristics can effectively reflect the similarities in individuals’ travel patterns and lifestyle habits [45,49,50]. Therefore, in order to address the limitations of traditional research that neglects individual behavior, this study measures SIP based on the principle of individual daily activity similarity, focusing on the co-occurrence and the extent of time, space, and behavior.

3. Research Method

3.1. Framework

Due to high-dimensional data involving time, space, and behavior, traditional spatiotemporal prism visualization methods are limited in terms of presenting such information. Therefore, this study applies the dimensionality reduction approach to the data (Figure 2). First, a qualitative assessment is conducted to evaluate how spatial and behavioral factors support or constrain activity patterns, based on the similarities and differences in daily activity patterns across different groups. Next, the study introduces four co-occurrence relationships that capture SIP, derived from the interactions between time, space, and behavior, and quantitatively measures their co-occurrence degree. Ultimately, these factors collectively reflect SIP.

3.2. Research Sample and Scope

The current work sought to identify a mixed community within an urban setting with a high concentration of accompanying elderly migrants. In recent years, factors such as the natural environment, employment opportunities, and urban public services, coupled with relaxed residency policies reducing the difficulty of elderly joining their children, have contributed to a steady annual increase in the number of migrant elderly people in Hangzhou. By 2022, they accounted for 11.21% of the total migrant population, exceeding the national average. For this research, we selected the JR community, a relocation housing area located in the central urban district of Hangzhou, as the research sample. Considering the larger residential compensation provided during relocation compared with the original living space required by residents, this area provides abundant rental housing at low prices, attracting a significant migrant population. Residents aged 55 and older comprise 19.87% of the total population in the community, among whom 293 are accompanying elderly migrants, constituting 10.46% of the total migrant population (

Table 1. Summary of the migrant and resident population data for the sample communities.

Age Group	Mobile Population		Total	Proportion	Resident Population		Total	Proportion
	Men	Women			Men	Women
<55	1239	1269	2508	89.54%	510	510	1020	63.67%
55–59	54	74	128	4.57%	60	70	130	8.11%
60–64	31	49	80	2.86%	49	56	105	6.55%
65–69	29	31	60	2.14%	71	65	136	8.49%
70–74	4	8	12	0.43%	39	43	82	5.12%
75–79	2	4	6	0.21%	28	28	56	3.50%
80–84	2	2	4	0.14%	7	19	26	1.62%
85–89	1	2	3	0.11%	10	23	33	2.06%
90–94	/	/	/	/	5	6	11	0.69%
95–100	/	/	/	/	1	1	2	0.12%
>100	/	/	/	/	/	1	1	0.06%
Total	1362	1439	2801	100.00%	780	822	1602	100.00%

). This highlights the sample’s dual characteristics of aging and mobility.

Because daily behavior at the community scale is relatively small and big data research methods are inapplicable [51], this study adopts a small-sample, one-on-one research design to gain a deeper understanding of individuals’ real daily activity spaces and behavior patterns. Based on the primary migration motivations of elderly migrants, this study categorizes them into two types: one is family reunion-motivated accompanying elderly migrants (FR-AEMs), whose main motivation for migration is to live with their children; the other is caregiver-oriented accompanying elderly migrants (CO-AEMs), whose main motivation is to take care of their grandchildren. These two types of elderly migrants exhibit significant differences in their lifestyles and migration motivations, and this classification is made to better reflect their needs and behavioral characteristics. Based on the distribution characteristics of the local elderly population and accompanying elderly migrants in the sample community, 26 subjects were selected, encompassing 18 local elderly residents, 3 FR-AEMs, and 5 CO-AEMs. The sample comprises individuals aged 55 to 70, all of whom were selected for their comparably good mobility to eliminate the impact of physical differences in mobility on the results.

Community life circles are typically considered to be the spatial domain of the daily activities of individuals. Nonetheless, considering that the life circle model does not fully align with the travel characteristics of the elderly and the differences in spatial management methods and governance entities across Chinese cities, the current research builds upon life circle theory and incorporates these two factors. This study defines the spatial scope of daily activities into three areas (Figure 3).

Area A: Closed residential communities are the predominant form of residential area development in China [52]. These communities are defined by both physical boundaries, such as walls or commercial buildings that separate them from the surrounding city, and governance boundaries created by different governance entities. The space within these boundaries is referred to as Area A.

Area B: While the life circle model may deviate from the actual travel range of distinct groups, it serves as a governance concept to facilitate top-down unified construction and management [53]. Thus, Area B is defined as the space outside the residential community but within a 15-min life circle. To reflect the actual reachable space for individuals within the real urban road network, the actual travel range is calculated based on real travel paths, resulting in an irregularly shaped life circle.

Area C: Although the life circle model is based on individuals’ basic needs, it cannot fully encompass all individuals’ daily activities, given the increasing individual mobility and diversification of needs [54]. From the pre-processed data, it can be observed that spaces outside the life circle are still frequently used. Therefore, we define the C area as a space frequently used outside of the life circle. Due to the high level of uncertainty in the distribution of these high-frequency travel locations (for example, some participants visit a temple that is nearly 20 km away every day), the C area theoretically refers to all spaces outside the life circle, without a defined boundary.

3.3. Data Collection and Semantics Extraction

The spatiotemporal trajectory of the daily activities of individuals serves as a crucial data foundation for spatiotemporal behavior analysis [55,56]. Considering the highly personalized nature of these activities, their typically short duration, and their tendency to be forgotten [57], traditional methods of subjective data collection, such as activity logs and questionnaire interviews, are not suitable. Therefore, to accurately and comprehensively capture the spatiotemporal trajectories of individuals, this research employed a handheld GPS tracking device with high spatiotemporal precision—the Unistrong G635—as the primary data collection tool (Figure 4A). The experiment was conducted during autumn (October–November), a period of time when elderly people in Hangzhou typically travel more frequently. The trajectory data of each participant were collected for no less than five days to ensure that the data volume met the basic requirements for trajectory analysis. Considering the limited battery life of the device, the position data storage interval was set to store data every 3 s. The device automatically generated trajectory files in GPX format containing multi-dimensional geographic information, encompassing longitude, latitude, time, instantaneous speed, and elevation. A total of 157,304 raw data points were identified in the exported files. After applying a Kalman filter to clean up the errors caused by signal interference, 108,234 valid data points were retained.

Stay points, as a core element in spatiotemporal trajectory analysis, were the first to be identified and extracted in this research (Zheng, 2015) [58]. Time geography posits that individual stays are regarded as situations where a certain amount of time is spent within a given spatial range. Thus, stay points are segments of a trajectory comprising a series of continuous GPS points, characterized by two key features: concentration within a certain spatial range and a long time span. This work integrates spatial and temporal elements, using Python 3.8 programming with the GPS Track Editor v.1.04 to identify stay points with a walking speed of less than or equal to 0.8 m/s (Figure 4B). Nonetheless, some low-speed movements may be misidentified as stay points. The study further eliminates trajectories with slow, linear movement characteristics using DBSCAN (density-based spatial clustering of applications with noise) to exclude the possibility that individuals are either staying or wandering within a specific spatial range or moving slowly over a small area. In total, 1451 stay points were identified. By using the origin and destination of each stay, travel paths were divided, resulting in 867 origin-destination trajectories.

Stay points function as a concrete representation of geographic spatial information and contain rich semantic data, which are crucial for understanding group movement patterns. To extract the daily activity characteristics reflected by these stay points, this research explores their functional and behavioral semantics.

Functional semantics: This study eliminates material differences, such as the specific form and quality of spaces, focusing instead on functional characteristics that reflect individual needs. Traditional research typically defines the functional types of stay points based on their spatial relationship with points of interest (POIs). However, because POIs are abstracted as point-like objects with no physical area, errors are easily introduced during semantic attribution. Therefore, this study adopts areas of interest (AOIs), which better represent the actual spatial locations of these points, as the basis for comparison. By detecting the overlap between the stay points and their corresponding AOIs, the spatial correlation between the two is established, thereby improving the accuracy of the functional semantics of stay points (Figure 4C).

This research defines the functional types of daily activity spaces based on basic living needs and existing urban infrastructure construction standards. Spaces with specific functions are classified according to their urban infrastructure type, encompassing public service facilities that provide basic living services, commercial facilities that offer commercial services, and transportation facilities that meet basic mobility needs. Some spaces do not have clearly defined functions, such as elevated areas, green spaces, or structures within residential communities; these are considered independent types in this study. Additionally, certain special public spaces, such as temples or tourist attractions, which individuals frequently visit in daily life, are recognized as independent types of spaces. The specific types of spaces, their spatial distribution characteristics, and photos of typical spaces are shown in Figure 5.

Behavioral semantics: In the daily lives of the elderly, numerous instances of informal use of urban spaces occur [59]. To capture the actual behaviors within the stay points, this study first extracted a library of possible behaviors in different spaces through tracking observations. Then, by filling out activity logs at 30-min intervals, elderly participants were asked to recall the spaces that they visited and the behaviors that occurred throughout the day, thereby achieving an accurate correlation between space, time, and behavior. Drawing on the concepts of freedom and choice from everyday life theory, which reflects individual behavioral patterns, and focusing on the core needs of the elderly, this work seeks to elevate the relevance of behavioral classification results for this group [60]. As this research primarily focuses on daily activities outside the individual’s residential space, behaviors such as eating and sleeping, which occur at home, are not differentiated and are collectively referred to as “indoor behaviors.” Based on the degree of autonomy in elderly people’s behavior, other activities are categorized into three types (

Table 2. Classification of behavior types based on the characteristics of elderly people.

Behavior Type		Specific Behavior	Behavior Type	Specific Behavior
Indoor		Eat, sleep etc.	Household Duties	Pick up grandchildren
Self-care	Health- Promoting	Exercise		Take care of grandchildren
		Medical treatment		Entertain grandkids
		Physical therapy		Take grandkids for educational training
		Dispense medication	Daily Tasks	Access community services
	Leisure	Take up hobbies
		Casual chat		Access daily life services
		Walk the dog
		Worship		Take bus
		Play cards		Grocery shopping
		Dine out		Shopping
		Worship		Take subway
		Study		Take express delivery

): activities related to caring for their grandchildren are defined as household duties, activities that meet their own needs are defined as self-care, and activities necessary for daily life are defined as daily tasks. To better reflect the core needs of the elderly, self-care behaviors are further subdivided into two categories: health-promoting behaviors that promote physical well-being, and leisure activities that fulfill mental and emotional needs.

3.4. SIP Assessment Process

3.4.1. Optimization of the SIP Model

Based on patterns of social interaction and an understanding of social integration theory, this study proposes two optimization measures for the existing SIP model. First, while traditional research has primarily focused on the role of the community environment in promoting social interaction, this study additionally considers the “support-constraint” effect of personal lifestyle habits and behavioral preferences on social interaction. Second, building on traditional spatiotemporal co-occurrence analysis, this study emphasizes the interaction between spatiotemporal behaviors, reflecting the similarities in travel and activity preferences among different groups through their co-occurrence relationships and the degree of co-occurrence (Figure 6).

3.4.2. “Support-Constraint” Effects Based on Spatiotemporal Behavioral Characteristics

As discussed in the literature review, the time element plays a central role in this analysis. This work prioritizes the spatiotemporal characteristics of stay points as the core of semantic analysis, selecting the time allocation and rhythm across distinct spaces and behaviors to describe the social characteristics of the accompanying elderly migrants and local elderly populations.

In the “space–time” dimension, an individual’s activity space comprises nodes, paths, and areas. The number, location, stay duration, and dynamic changes of these elements reflect the spatial usage characteristics of different groups in urban spaces [61]. In the “behavior–time” dimension, the specific types of behaviors, the time allocation for each type, and the travel time being spent largely reflect the temporal and spatial constraints that influence these behaviors [62]. Hence, this research selected the following indicators for analyzing the spatiotemporal behavioral differences between the groups (

Table 3. Space and behavior analysis indicators, based on the temporal dimension.

Dimension	Indicators	Notes
Spatial-Temporal	Spatial distribution of stay points	Dynamic characteristics of the distribution range of stay points in different spaces
	Duration of stay	Time allocation across different spaces
	Rhythm of stay	Time rhythm of space selection across different types of spaces
Behavioral-Temporal	Travel time	Required travel time
	Duration of behavior	Time allocation for different types of behaviors
	Rhythm of behavior	Time rhythm of the occurrence of different types of behaviors

).

3.4.3. Spatiotemporal Behavior Co-Occurrence Types and Degree Assessment

This work determines whether the preconditions for social interaction are present, based on the degree of spatiotemporal behavior co-occurrence. In this research, this mainly refers to the phenomenon where at least two elements (behavior, time, and space) between groups share similar characteristics. This can be categorized into four types: full co-occurrence of all three elements (ATP), time–space co-occurrence (TP), time–behavior co-occurrence (AT), and space–behavior co-occurrence (AP). The first two types more strongly suggest the possibility of face-to-face social interactions between groups, while the latter two mainly reflect the similarity in travel characteristics between groups. Due to the subtle differences in the connotations of the four types of co-occurrence relationships, this study calculates the degree of co-occurrence separately for each type.

In the current research, computational approaches have been constructed to measure the degree of spatiotemporal co-occurrence, based on the “exposure” measurement approach [63]. The exposure index can be derived by weighting the quantity or proportion of spatial–temporal overlap to obtain a composite value, representing the degree of spatial–temporal co-occurrence of different events or individuals. For example, if a participant spends a longer exposure time in a certain area, and multiple related events occur in that area, the spatial–temporal co-occurrence degree of that participant would be higher. The specific formula is as shown in Equation (1):

$$P_{a\times b}=\sum _{i=1}^n\left({\displaystyle \frac{a_i}{A}}\right)\left({\displaystyle \frac{b_i}{t_i}}\right)$$

(1)

where $a_i$ and $b_i$ represent the population of groups $a$ and $b$ in region $i$, $A$ is the total population of group $a$, and $t$ is the total population of groups $a$ and $b$.

In the context of this study, the analysis of spatiotemporal prisms allows for the direct acquisition of opportunities within the same spatiotemporal domain. Therefore, the formula for the degree of co-occurrence can be simplified from the exposure index, as shown in Equation (2):

$$P_{a\times b}=\sum _{i=1}^n{\displaystyle \frac{a_i{b}_i}{AB}}$$

(2)

where $P_{a\times b}$ is the actual co-occurrence frequency of $i$ space, $u$ time, and $r$ behavior between the two groups. $AB$ is the product of the number of two groups of people appearing in space $i$, which describes the maximum number of co-occurrences that two groups of individuals can produce.

3.4.4. SIP Assessment Principles and Process

Based on the degree of spatiotemporal behavior co-occurrence and spatiotemporal behavior characteristics, this work proposes a principle for evaluating SIP that integrates both factors (Figure 7).

First, we drew conclusions regarding the factors’ supportive and restrictive effects on social interactions, based on a comparison of behavioral and spatial characteristics. Given that some activities are primarily generated by individual entities and do not support social interactions, we must also adjust the impact results based on the specific content of the activities undertaken during the assessment. Subsequently, we assessed the degree of spatiotemporal behavior co-occurrence. K-means clustering was utilized to categorize co-occurrences into three levels. Finally, based on the support and constraint effects obtained from the assessment, the degree of co-occurrence is upgraded or downgraded, resulting in five SIP levels, which represent the SIP levels of space and behavior.

4. Results

4.1. The Spatial and Behavioral Characteristics of Daily Activities

4.1.1. Spatial–Temporal Characteristics

The current work compared the specific spatial locations of the stay points and their relative positions to the study area across distinct time slices to reflect the differences in travel ranges between the accompanying elderly migrants and the local elderly population (Figure 8). The stay points of FR-AEMs are the most concentrated, being primarily located within the residential community, with their activity range slightly expanding between 16:00 and 20:00. CO-AEMs, however, exhibit significant dynamic characteristics. During the two main time periods of caring for grandchildren, from 08:00 to 12:00 and from 16:00 to 20:00, they showed higher levels of activity, with their activity range expanding and approaching that of the local elderly population. During other time periods, the activity range of CO-AEMs was similar to that of FR-AEMs, which was mainly concentrated within the residential area.

This research reveals the dynamic changes in spatial usage and spatial preference differences by analyzing the rhythm of residence time in public spaces (Figure 9a). The population using public spaces, such as green spaces, community service centers, and commercial facilities, changes significantly over time: from 04:00 to 08:00, local elderly residents dominate the usage; from 08:00 to 16:00, CO-AEMs are the primary users; and in the evening, all three groups exhibit high levels of activity. Through an analysis of the average residence time in such spaces (Figure 9b), we found that time periods for all three groups visiting commercial facilities were relatively consistent. Nonetheless, significant differences in time rhythms were observed between the local elderly and CO-AEMs, particularly in spaces such as buildings, green spaces, and elevated floors. The time rhythms of the local elderly and FR-AEMs showed certain similarities, especially in green spaces, where their evening activity periods significantly overlapped. Furthermore, due to large individual differences in public space usage, particularly for non-daily trips to meet specific needs, FR-AEMs and CO-AEMs tend to have shorter stay times that are mainly concentrated within the residential area and nearby spaces, such as green spaces and supermarkets. CO-AEM activity is primarily found in commercial facilities, green spaces, and residential neighborhoods. Local elderly residents tend to use spaces with personalized functions, such as temples, and spaces that meet higher-level needs, such as educational training centers.

4.1.2. Behavioral–Temporal Characteristics

From the analysis of travel time and travel distance (Figure 10), it can be seen that there were no significant differences in travel time for basic daily activities such as grocery shopping, exercising, taking care of grandchildren, accessing community services, and dining out. Given that this study measures the actual travel time of individuals, rather than the ideal travel time from their place of residence, the duration appears longer compared with the travel time defined by the life circle concept. In transactional activities such as grocery shopping, the CO-AEMs and FR-AEMs tended to spend more time traveling compared with the local elderly population. For activities such as collecting grandchildren, receiving medical treatment, getting prescriptions, and running errands, the local elderly population tended to spend more time traveling than the other elderly groups. Some activities, such as religious rituals, which cater to personalized needs, also exhibit similar characteristics, with funeral rites being the most prominent. Individual travel is constrained by the external environment and a result of proactive selection, based on function and space.

From an analysis of the time rhythm of daily activities, it is evident that varying degrees of differences can be identified between the local elderly population and the two types of accompanying elderly migrants (Figure 11). Specifically, the CO-AEMs mainly engage in caregiving tasks between 08:00 and 13:00 and between 15:00 and 19:00, alongside some leisure and health-related activities. Their discretionary free time is relatively limited, mainly occurring in the morning (6:00–9:00) and after dinner, during which periods they mostly engage in transactional activities like shopping and obtaining basic life services, as well as leisure and health activities to satisfy their personal interests and fitness needs. The FR-AEMs tended to be less active than the other two groups. These elderly people are more dependent on family relationships and lack opportunities to establish new social connections. Consequently, their activities primarily involve individual exercise, such as walking or jogging, with active times concentrated in the evening, focused on leisure and health-related behaviors.

4.2. Spatial–Temporal Behavior Co-Occurrence Degree

To reflect differences in the co-occurrence degree between the local elderly population and the two types of accompanying elderly migrants under different co-occurrence patterns, this study summarizes the average values and standard deviations for the four types of co-occurrence degree (

Table 4. The average and standard deviation in degree of the four co-occurrence types.

Group	APT		PT		AP		AT
	Aver.	Std.	Aver.	Std.	Aver.	Std.	Aver.	Std.
FR-AEM & local elderly	0.2484	0.16	0.065	0.04	0.425	0.18	0.0486	0.03
CO-AEM & local elderly	0.2046	0.13	0.0966	0.07	0.3673	0.18	0.0564	0.05

). Among them, the FR-AEMs exhibited higher similarity to the local elderly population. The differences in public space usage patterns between the CO-AEMs and the local elderly population are the main reason for the lower overall co-occurrence level.

Through a horizontal comparison of the spatial distribution of the four types of space–time behavior co-occurrence (Figure 12), it can be observed that the spatial distribution characteristics of PT and AP are quite similar. Compared with the other two co-occurrence types, their distribution range is broader, indicating a clear correspondence between behaviors in public spaces and the time–space usage relationship. Through a longitudinal comparison of the co-occurrence characteristics between the two types of accompanying elderly migrants and local elderly residents, the level and spatial distribution of AP co-occurrence were found to be similar for both groups. For the FR-AEMs and the local elderly population, the level of APT co-occurrence was higher, and the number of spaces with AT co-occurrence characteristics was greater. The CO-AEMs had a higher level of PT co-occurrence, reflecting the finding that both the labor-oriented elderly and local elderly residents showed a greater intensity of use of these spaces.

From the perspective of temporal variation characteristics (Figure 12), the dynamic changes in the four co-occurrence types exhibit similar characteristics, but there are also dynamic primary and secondary relationships in the co-occurrence levels between the two groups during specific time periods. All four co-occurrence types display peaks between 8:00–12:00 and 16:00–20:00, with a distinct trough between 13:00 and 16:00. Among them, the co-occurrence level of APT between the FR-AEMs and the local elderly population was notably higher than that of the CO-AEMs between 17:00 and 21:00, with the two groups being relatively similar at other times. The co-occurrence levels of PT between the CO-AEMs and the local elderly population were significantly higher than those of the FR-AEMs between 7:00 and 11:00.

4.3. SIP Assessment

From the significance of behavior and space differences (

Table 5. Results concerning the significance of behavior and space differences.

Behavior	Group Relationship		The Difference of Mean Values	p Value	Significance
Casual chat			0.2556	0.2446	/
			0.0901	0.789	/
			−0.1655	0.2343	/
Exercise			0.1428	0.531	/
			−0.1813	0.2502	/
			−0.3241	0.0216	*
Grocery shopping			0.31	0.6908	/
			−0.0073	0.9995	/
			−0.3173	0.6163	/
Take up hobbies			1.1323	0.0005	**
			0.0547	0.9753	/
			−1.0775	0	**
Access daily life services			−1.623	0.0336	*
			−1.0675	0.1338	/
			0.5555	0.531	/
Take subway			−0.3983	0.8425	/
			0.3265	0.865	/
			0.7248	0.5373	/
Eat out			−0.195	0.9297	/
			0.1293	0.9299	/
			0.3242	0.7998	/
Take bus			−0.08	0.9814	/
			−0.1171	0.9524	/
			−0.0371	0.9962	/
Shopping			−0.1366	0.9722	/
			−0.9001	0.0801	/
			−0.7635	0.4656	/
Medical treatment			1.1989	0.2185	/
			−1.1446	0.0273	*
			−2.3435	0.0061	**
Dispense medication			1.1625	0.6467	/
			−0.4135	0.7638	/
			−1.576	0.4072	/
Pick up grandkids			1.0008	0.1385	/
Take care of grandkids			−0.6032	0	***
Walk the dog			−0.4731	0	***
Play Cards			−0.5888	0.0817	/
Physical therapy			0.2163	0.5	/
Take grandkids for educational training			−0.1093	0.4062	/
Entertain grandkids			−0.5784	0	***
Take express delivery			−0.682	0.5425	/
A−Green space			−0.0736	0.6587	/
			−0.386	0	***
			−0.3124	0	***
A−Built structure			−1.5028	0.1969	/
			−0.9045	0	***
			0.5984	0.7631	/
A−Elevated layer			1.1698	0	***
			0.9479	0	***
			−0.2219	0.4674	/
A−Commercial facility			0.1093	0.9104	/
			−0.083	0.8759	/
			−0.1922	0.7146	/
A−Residential neighborhoods			0.1533	0.9955	/
			0.3107	0.962	/
			0.1574	0.9935	/
B−Green space			0.7478	0	***
			−0.3134	0.003	**
			−1.0612	0	***
B−Commercial facility			−2.0898	0	***
			−1.6932	0	***
			0.3965	0.2236	/
B−Traffic facilities			−0.2189	0.8282	/
			0.2559	0.7626	/
			0.4748	0.4586	/
A−Medical facility			1.1989	0.2688	/
			−0.7803	0.2147	/
			−1.9792	0.026	*
C−Supermarket			−0.053	0.9974	/
			−0.9961	0.1468	/
			−0.9431	0.3591	/
A−Community service			1.1508	0.3203	/
B−Educational facilities			0.9078	0.2922	/

* p < 0.05, ** p < 0.01, *** p < 0.001. CO-AEM & FR-AEM; CO-AEM & Local elderly; FR-AEM& Local elderly.

), it can be observed that behaviors such as hobbies and medical treatment show that local elderly residents have greater and more personalized demands. The differences with FR-AEMs are primarily seen in interest-based behaviors, while the differences with CO-AEMs are reflected in child-rearing behaviors. Regarding public spaces, significant differences were observed between the local elderly population and CO-AEMs, particularly in areas such as green spaces, built structures, commercial facilities, and elevated floors. There are no significant differences between FR-AEMs and the local elderly population, except in the case of green spaces.

The evaluation results for SIP show that certain groups have relatively greater potential for social interaction, but this potential is not fully supported within the available spaces (

Table 6. Assessment results of the SIP of behavior and space.

Behavior	Local Elderly							Local Elderly
	CO-AEM							FR-AEM
	Duration	Time Rhythm	Interactivity	Effect	APT	AT	SIP	Duration	Time Rhythm	Interactivity	Effect	APT	AT	SIP
Casual Chat	1	1	1		0.8	0.19	Extremely high	1	1	1		0.9	0.37	Extremely high
Exercise	1	1	1		0.81	0.15	Extremely high	0	1	1		0.57	/	High
Grocery shopping	1	1	1		0.28	/	High	1	1	1		0.24	/	Medium
Take up hobbies	1	0	1		0.04	/	Extremely low	0	1	1		0.21	/	Low
Access daily life services	1	1	0		0.1	/	Low	1	1	0		0.14	/	Low
Take subway	0	0	0		/	0.01	Extremely low	0	0	0		/	0.01	Extremely low
Eat out	1	0	0		0.04	0.01	Extremely low	1	1	0		0.02	0.01	Low
Take bus	1	0	0		/	0.01	Extremely low	1	0	0		/	0.01	Extremely low
Shopping	1	1	0		0.04	0.02	Low	0	0	0		0.05	/	Extremely low
Medical treatment	/	/	/		/	/	/	0	1	1		/	0.01	Low
Dispense medication	1	0	0		0.01	0.01	Extremely low	1	1	0		0.02	0.01	Low
Pick up grandkids	0	1	1		0.01	/	Low	/	/	/		/	/	/
Take care of grandkids	0	1	1		0.81	0.15	High	/	/	/		/	/	/
Walk the dog	/	/	/		/	/	/	0	1	1		/	0.1	Low
Play cards	/	/	/		/	/	/	1	1	1		/	0.06	Medium
Physical therapy	/	/	/		/	/	/	0	1	1		0.14	0.01	Low
Take grandkids for educational training	1	1	1		/	0.12	Medium	/	/	/		/	/	/
Entertain grandkids	0	1	1		/	0.03	Low	/	/	/		/	/	/
Take express delivery	1	1	0		0.01	/	Low	/	/	/		/	/	/
Space	Local Elderly							Local Elderly
	CO−AEM							FR−AEM
	Duration	Time Rhythm	Stayability	Effect	APT	PT	SIP	Duration	Time Rhythm	Stayability	Effect	APT	PT	SIP
A−Residential neighborhoods	0	0	1		0.01	/	Extremely low	0	0	1		0.09	/	Extremely low
C−Supermarket	0	0	0		0.04	0.01	Extremely low	0	0	0		0.05	/	Extremely low
B−Commercial facility	0	0	0		0.1	0.03	Extremely low	0	1	0		0.14	0.04	Extremely low
A−Built structure	0	1	1		/	0.45	Medium	0	0	1		/	/	Extremely low
A−Elevated layer	1	1	1		0.2	0.42	Low	1	1	1		0.02	0.27	Medium
A−Green space	0	1	1		0.81	0.82	High	1	1	1		0.74	0.27	Extremely high
A−Medical facility	1	0	1		/	/	Extremely low	1	0	1		/	0.01	Extremely low
B−Traffic facilities	0	0	0		/	0.01	Extremely low	0	0	0		/	0.01	Extremely low
A−Commercial facility	1	1	1		0.28	0.02	Medium	1	1	1		0.24	0.02	High
B−Green space	1	0	1		0.07	0.02	Extremely low	0	1	1		0.21	0.06	Medium
A−Community service	0	0	1		/	0.02	Extremely low	/	/	/		/	/	/
B−Educational facilities	0	0	1		0.01	/	Extremely low	/	/	/		/	/	/
C−Temple	/	/	/		/	/	/	/	/	/		/	/	/
B−Daily service	/	/	/		/	/	/	/	/	/		/	/	/
B−Temple	/	/	/		/	/	/	/	/	/		/	/	/
B−Educational Training Center	/	/	/		/	/	/	/	/	/		/	/	/
B−Medical facility	/	/	/		/	/	/	/	/	/		/	/	/
A−Educational facilities	/	/	/		/	/	/	/	/	/		/	/	/

Optimizable; Support; Constrain; Non-interaction.

). The CO−AEMs and local elderly residents exhibit higher SIP in household duties and daily tasks, while the FR−AEMs and local elderly residents show higher SIP in health−promotion behaviors. However, in terms of spatial distribution, most spaces have low SIP scores. First, the capacity of the space to accommodate different activities affects SIP. Certain spaces, such as the green areas and buildings in Zone A, support behaviors like caregiving and fitness activities, resulting in higher SIP. However, some activities, such as shopping, picking up medicines, and medical visits, are more goal−oriented and lack the basic conditions for social interaction. Second, spaces in different areas possess distinct SIP characteristics. Zone A, for example, provides a stronger sense of belonging, making it easier for individuals to stay there and interact. In contrast, individuals in Zone B are relatively unfamiliar with the space, making it difficult to establish effective contact unless the activity aligns with the space’s function.

5. Discussion

5.1. Spatiotemporal Behavioral Differentiation and the Similarity Between Groups Influence the SIP of the Community Environment

The study, based on an evaluation of SIP across different spaces and behaviors, reveals that the similarities in spatiotemporal behavior within groups form the foundation for social interactions between them. On the behavioral level, as part of the elderly group, migrant seniors and local seniors exhibit strong common characteristics in terms of health care, leisure, and responsibilities. These phenomena align with previous research on the general understanding of elderly needs, reflecting an elderly person’s attention to their physical and mental health [5], as well as the traditional Chinese notion of placing family interests at the core of life [3].

On the spatial level, past research has generally focused on the specific functions of spaces, reflecting group needs [19], but often overlooks the impact of spatial characteristics on group space choices. This study found that spaces exhibiting higher SIP displayed the following characteristics. First, compared to spaces with clear functional purposes, informal urban spaces show greater inclusiveness for daily activities, exhibit higher spatial vitality, and provide rich opportunities for social interaction. Second, the overall SIP shows the trend of being highest in the residential area, then decreases outward. This may be related to the reduced mobility of the elderly [12], as well as the dependency of migrant seniors on the community. Previous studies have generally focused on the community as a unit, emphasizing the construction and optimization of community spaces [35,44]. The results of this study suggest that future research should pay more attention to the role of internal facilities and spaces within residential areas.

5.2. Supplement to the Theory of Social Integration and Social Justice

Based on the description of spatiotemporal behavior, this research shows that different groups exhibit multidimensional differences in their daily activities. Traditional studies often attribute these differences to social segregation, reflecting social inequality [39]. However, this study does not fully support that view. According to the SIP of space and behavior, there is no clear exclusion between groups in most spaces, and community spaces are increasingly inclusive. Although there are differences between groups in terms of some spaces and behaviors, these are mainly due to variations in living habits and spatial preferences. For example, local elderly residents may travel longer distances to meet personalized or higher−quality needs, especially regarding worship activities. This result challenges the traditional view that longer travel distances always indicate social inequity.

The research also shows that spatiotemporal behavior can provide a more detailed understanding of social fairness issues for the elderly. In the spatial dimension, local elderly people have a broader and more evenly distributed activity range, while migrant elderly people tend to have a core−periphery structure to their activity range, centered around their residence. This suggests that migrant elderly people are more dependent on their living area and may fear urban life [20]. Traditional research has often overlooked the temporal dimension [36,37]. This study highlights temporal segregation, showing that while both groups can use the same spaces, their use times and durations are misaligned. Thus, a full understanding of group segregation requires an analysis of the time dimension, in addition to the spatial and behavioral aspects. These findings contribute to theories of social integration and fairness.

5.3. The Optimization of the “Support-Constraint” SIP Model

This study proposes the “support-constraint” SIP model, which combines the impact of spatiotemporal behavior characteristics and co-occurrence degree, providing a more accurate assessment of SIP. Compared to traditional methods [22,31], this model fills the gap found in previous evaluation methods by combining qualitative and quantitative research.

Due to the inclusion of behavioral factors, the optimized SIP not only reflects the contact opportunities emphasized in traditional studies but also highlights the similarity of these groups in terms of lifestyle habits, travel preferences, and other factors. This has led to the discovery of more potential spaces and behaviors that promote social interaction. For example, the degree of spatiotemporal co−occurrence in built structures and elevated layers is not high, but spatial preferences show a high degree of similarity. This feature is also somewhat reflected in the behavior of having casual chats.

Social interactions are influenced by social, economic, and environmental factors, which can prevent some social interactions from occurring. In terms of space, medical and traffic facilities, due to their functional nature and short stay duration, offer fewer opportunities for social interaction. In terms of behavior, factors such as personal stay time and the degree of contact affect the occurrence of interactions, supporting the view that social interaction is influenced by activity content [43].

5.4. Community Governance and Spatial Optimization Strategies Under the SAT

Working according to the SAT [30], this study proposes strategies to enhance SIP. First, since accompanying elderly migrants often face time and space constraints, spatial allocations for functions and community activities must consider the usage habits of diverse groups while avoiding excessive interference. Second, for behaviors and spaces that limit social interaction, optimizing the environment and adding interactive activities can create more opportunities for social engagement. Finally, for behaviors and spaces with high SIP, actual social interaction can be promoted further by organizing specific social events or by providing interactive platforms. Based on the evaluation results of this study, the specific optimization methods are as follows.

At the level of community governance, daily tasks can serve as a catalyst, enabling social relationships within groups to form quickly. With health as a common goal, the social boundaries between groups can gradually be broken down. Efforts should focus on daily activities, such as household chores and caregiving, to help accompanying elderly migrants establish initial social connections through shared tasks. Given the common needs of elderly people for fitness and recreational activities, effective spatial support should be provided to help them gradually overcome their social boundaries and build connections with local elderly residents.

In terms of spatial construction, the focus should be on shaping informal spaces that attract the elderly to nearby parks and green areas, allowing them to explore and adapt to the urban environment more freely. Efforts must be made to seamlessly connect residential areas with surrounding public spaces, fostering a more open and inclusive environment for social interactions and activities. Implementing time−based zoning in these spaces will help optimize their utilization, providing more opportunities for different groups to share spaces while catering to the specific needs of the elderly, thereby enhancing the inclusivity and vitality of the community.

6. Conclusions

This study explores how optimizing community design can improve the social integration and mental well−being of elderly immigrants. It offers practical suggestions to help enhance their quality of life and social adaptation. Elderly immigrants face challenges due to aging and mobility, which can lead to isolation and negatively impact their mental health. The study focuses on how community environments can help them connect socially and improve their well−being. This research demonstrates that the community environment plays a crucial role in the social integration of elderly immigrants. Providing more public spaces and community activities that promote social interaction is an effective way to enhance the social integration of elderly immigrants. In terms of methodology, the study takes into account the support and constraints of individual spatiotemporal behavior characteristics on social interaction. This framework overcomes the limitations of traditional SIP models that rely solely on quantitative spatiotemporal co−occurrence calculations, making SIP assessments more accurate. Through SIP evaluation, this study identifies more potential community environments that can promote social interaction and proposes a layered strategy for optimizing community environments, providing practical guidance for future community planning and urban design.

As an exploratory study on the social integration of accompanying elderly migrants, this research focuses only on the external time–space behavior characteristics of individuals. Nonetheless, daily activities are the result of an individual’s internal needs when interacting with the external environment. The same time–space behavior characteristics may have completely distinct occurrence processes, which correspond to different solutions. Hence, future research may aim to clarify the motivating factors behind individual daily activity decisions to reveal the mechanisms behind these activities. Additionally, local elderly groups have a high degree of individuality. The current work regards this as a core characteristic of the local elderly population but does not further categorize it. Nevertheless, some local elderly individuals are shown to share relatively high similarities with accompanying elderly migrants, which may influence the results of their social interactions. To effectively categorize the local elderly population, exploring the core attributes that affect their daily activity patterns is necessary. Finally, social integration is a sustained and multidimensional topic. By focusing on rebuilding social relationships, this research addresses the most urgent psychological issues of accompanying elderly migrants. Nonetheless, the social integration of accompanying elderly migrants cannot be solved using a single approach. Future research should propose solutions to higher−level dimensions of isolation, such as cultural and psychological perceptions, to achieve urban adaptation and social integration for accompanying elderly migrants.