Equity Measurement of Public Sports Space in Central Urban Areas Based on Residential Scale Data

Urban public sports facilities have captured much public attention because of their close ties to public health. However, few studies have comprehensively assessed the equity of accessibility to various types of public sports space with a fine scale. This study proposed a spatial equity measurement method based on multi-source urban data and GIS network analysis. Residential buildings were taken as the minimum research unit to investigate the equity differences of residents’ enjoyment of urban public sports space accessible by walking and public transportation. Taking Harbin, China, as an example, this study calculated and visualized the proximity of more than 12,000 residential buildings to a variety of public sports space in the central urban area. The results showed that: (1) urban centers enjoy more public sports space resources than border areas, that is, the developed area has more advantages than the emerging area; (2) according to the classification of sports space, their spatial distribution pattern and measurement results are obviously different; (3) the areas with a low walking equity degree also had a low bus equity degree. This study integrated multi-source data into the traditional spatial computing models and provided an important reference for the equitable planning of urban public sports space.

Introduction
As China's urbanization and industrialization accelerate, urban residents do not merely enjoy a higher standard of living, but also face more and more health problems, the most important of which are chronic diseases, weight gain and obesity. According to the Report on Nutrition and Chronic Diseases in China (2020) released by the National Health Commission of the People's Republic of China, deaths caused by chronic diseases accounted for 88.5% of the total deaths in 2019, with more than half of the adult population suffering overweight or obesity and unhealthy lifestyles still prevalent [1]. According to the World Health Organization, active physical activity can remarkably benefit the health of urban residents and prevent and control non-communicable diseases including chronic diseases such as cardiovascular disease, cancer, and diabetes which are often caused by obesity [2]. As the basic media of sports, public sports space is undoubtedly important to residents' health. A number of studies have shown that proximity to sports space is associated with an increase in physical activities and has a positive impact on health [3][4][5][6].
Sports space includes places where people can perform physical exercise, such as parks and squares where leisure activities are the main forms of exercise, fitness centers that focus on strength and shape building, and all kinds of stadiums or facilities where more intense aerobic exercise can be conducted. According to the 2014 National Fitness Report issued by the General Administration of Sport of China, the most popular public sports space for people over the age of 20 includes public stadiums, fitness paths, squares, parks and fitness clubs [7]. The planning and layout of public sports spaces in China generally follows the principles of "fairness, efficiency, convenience, centrality, combination of concentration and decentralization, and layout in combination with residential space structure". The allocation of park green space will be set according to its classification and service population, service radius and per capita indicators. The standard of urban land classification and planning construction land in China (GB50137-2011) also determines that the minimum per capita park green space area is 8 square meters per person. Even so, Harbin only raised the per capita park green space index from 7.5 square meters (2014) to 10 square meters in 2020 and many other cities are still working towards this goal. In addition, as a spatial entity, sports space is influenced by economic, political, and social factors, so it may not be equally enjoyed by all people. Existing studies have pointed out that there is obvious spatial inequity in the distribution of many types of facilities [8][9][10]. At the same time, the results of studies may be different [6]. At present, public sports space is the main place for residents to exercise, but problems remain in the contradiction between the increasing sports demand of the masses and the scarcity of sports facilities and playing field resources.
Spatial equity refers to the degree of equal distribution of services or amenities in different regions and economic, ethnic, and political groups [11]. Its assessment index can be summarized as spatial accessibility and availability, that is, the proximity of people to space and the amount of space available. Many studies have focused on the equity of sports space, mainly on a certain type such as parks [10,11] and sports facilities [8]. Few studies have analyzed the equity of various types of sports space [6,12]. At the same time, there are often differences in the focus and calculation methods adopted in similar studies, which are the key reasons for different results, mainly in the following three aspects.

Computational Models of Spatial Equity
One of the most common and relatively simple approaches is the container approach, which measures the accessibility by determining whether there is space to examine within a particular geographic cluster [6], such as a street, a neighborhood, or a census district. Of course, it can also take a specific walking distance as the range of the container and calculate the value of equity through the amount, area, or percentage of the space examined within the area [13], which is similar to buffer analysis. The container approach is simple but is also open to criticism. First, it only computes the objects within the container, so there are serious boundary problems, especially when based on typical geographic clustering units. At the same time, the analysis results based on different size units may be different. Secondly, the space homogenization of container can be a problem. The container approach assumes that people in containers enjoy equal space equity, which is obviously unrealistic. Especially when the size of containers is too large, the conclusion may lead to serious ecological fallacies.
Kernel density estimation can be regarded as an improved method based on the container approach. It calculates the decreasing value from the target space to the critical distance through the kernel function and the bandwidth, and then fits the result into a smooth cone surface. The advantage of kernel density estimation lies in that it can assign values to all study areas [6] and bring distance attenuation into a fair range of investigation, thus overcoming the spatial homogenization caused by the container approach [12]. However, the biggest problem in kernel density estimation lies in the choice of bandwidth, because bandwidth is the most critical factor to determine the analysis results, and the results calculated by different bandwidth are significantly different. Bandwidth represents the similarity and correlation between kernel density estimation and the container approach.
The improvement of the above two methods is mainly reflected in the introduction of distance as a variable and its influence on the results and the consideration of spatial heterogeneity. Another approach is also based on distance, such as proximity analysis and travel cost approach. They assess the equity of the population to the target space by calculating the cost distance, and the distance is in an inverse relation to the equity degree. However, the results of simple computational logic, such as measuring the distance between a house and the nearest park or calculating the average distance to all facilities within a certain range, are unconvincing [14]. Similarly, the widely applied gravity model incorporates more non-spatial factors, such as facility size and attraction, on the basis of distance attenuation [12]. The distance calculation method has also experienced the transformation from Euclid distance and Manhattan distance to network distance based on the urban road network. With the development of network analysis module of GIS, more and more vector-based road network distance assessment methods have been applied to the study of spatial equity [10,15,16].

Basic Research Unit
The application of the container approach has also aroused attention to the smallest unit of spatial analysis. Since it often uses the smallest integrated unit of data available, such as zip code, community, or census area. In addition to the inconsistency of the analysis results caused by these different unit choices, the general characteristics of the units can not reflect internal differences, and the range of units is still too large for individuals. The larger the unit, the more likely it is to ignore spatial heterogeneity, idealize the results, and draw conclusions that deviate from reality [11,12]. This is due to the limitations of the data itself, and many studies have encountered this problem. However, people are very interested in decisions that are relevant to their fields and directly influence them. As the spatial scale moves from local to regional and eventually national, fewer and fewer people are interested in these issues [17].
It is worth noting that the smallest analysis unit used in previous studies is a single building [11,18], such as a residential building, which can be closer to the real situation of individuals, and the integration results based on this larger area are more reasonable. At the same time, the analysis from a single building also unifies the research scale, and there will not be differences due to the change in countries or regions. However, there is little research on a building as the basic analysis unit, mainly because there are few channels to acquire such data. The advent of detailed, open and accessible multi-source urban data, such as road network data, point of interest (POI) data and building data, has made it easier to conduct studies at a finer scale, providing insight into aspects that were previously difficult to assess [19].

Estimation of Travel Capacity
In this paper, travel capacity refers to the maximum range of people's activities in a certain mode of transportation under the limitation of a certain standard (such as time), which represents the accessibility of the crowd to the target space. For example, the container approach or buffer analysis applies a specific walking distance as the maximum range of units [11,20,21], and targets outside the range are not included in the calculation results. However, there is no unified standard for the setting of people's walking ability or walking distance, 400 m, 500 m, 800 m, 1000 m or even more are adopted, which also makes people question the research. However, many theories or studies have little difference in defining travel times. For example, the new urbanist definition of walkability includes most things within a 10-min walk away from home [22]. In the United States Park Scoring Index, a 10-min walk from home is also used as the assessment standard for urban park access [23]. In China's 2018 Urban Residential Planning and Design Standard, 15-min, 10-min and 5-min life circles were used as step control scales of residential areas [24], and living space was organized based on walking distance. Shanghai, Jinan, and other cities have also launched corresponding planning of 15-min walking living circles. Shanghai has also introduced a 30-min sports life circle, requiring access to a sports venue within 30 min. Moreover, in China, the concept of "life circle" refers to the allocation of various functions and facilities required by residents' basic life based on the walking range within a certain period of time. The walking distance of 10-15 min is equivalent to 800-1000 m, and many studies also use this time or distance as the research basis [10,15,16,25].
Taking time as the standard can unify the research scale and avoid large differences caused by different countries or regions. However, walking as the only mode of travel remains open to problems. The most direct is that walking distance can only be defined as a range. In addition to the boundary effect, it cannot fully represent the travel behavior and ability of the crowd and cannot reflect the real spatial equity situation. Some studies suggest that accessibility should be highly sensitive to modes of travel [26]. There are also more studies that consider multiple modes of transportation to assess spatial equity [27][28][29]. Integrating various modes of transportation can be closer to the real travel situation of people and have a more real assessment of spatial equity.

Research Content
The research problem of this paper is how to effectively measure and evaluate the equity of public sports space in central urban areas. Our objectives include: (1) to provide a simple and detailed method for equity assessment of public sports space in the city; (2) to provide reference for the planning and configuration optimization of public sports space.
The structure of this paper is as follows: the second part is a detailed introduction of research data sources and usage methods. The third part is to carry out the practice and provide the analysis and results of measurement. The fourth part summarizes the main contributions of this study and discusses its application to planning practice. The last part summarizes the results of the survey, which can provide a basis for the policy and practice of sports spatial planning.

Materials and Methods
In order to provide a more effective and applicable spatial equity measurement method and evaluate the urban public sports spatial equity as accurately as possible, this paper takes Harbin city as an example and proposes a comprehensive assessment method of public sports space in central urban area. Our research is based on the concept of lifetime circle, using multi-source urban data and GIS network analysis, taking residential buildings as the basic analysis unit, and combining walking and public transportation modes.

Study Area
This case study area is the central urban area of Harbin, mainly including 4 districts within the Third Ring Road (Figure 1). The 4 urban districts have a permanent population of 4.09 million, with a population density of about 2711 people/km 2 . Harbin, located in the northernmost part of China, is a big city with the highest latitude and lowest temperature nationwide. Harbin has four distinct seasons. Winter is long and cold, summer is short and cool, and the temperature in spring and autumn drastically changes and the time is short. The unique geographical location shapes the prosperous ice and snow culture and ice sports in Harbin, but also makes the daily physical exercise greatly influenced by the climate. Walking and public transportation are equally important. The highway traffic of Harbin city is developed, showing the pattern of "one axis, four rings and eleven lines". The rail traffic construction is still in development, and there are three subway lines. At present, most of the research on the equity of accessibility to sports space in China is concentrated in the south and first-tier cities, but few in cities in cold regions. At the same time, Harbin is also carrying out the 15-min and 30-min fitness circle plan, and the study of urban public sports space equity boasts practical significance and long-term value for the inspection of the existing scheme and future urban planning.

Data Preparation
Our research is to measure the urban spatial situation, so we need to obtain multisource data, including basic geographic information, statistical data, and some emerging big data. This research focuses on the public sports space in central urban areas, i.e., urban sports space open to the public, both paid and free. Some sports spaces open only to a limited number of people are excluded, such as school stadiums which are not open to the public. According to the 2014 National Fitness Report and previous sports space classification [8,18,30], combined with the actual situation of Harbin, this article will divide public sports space into four categories, namely, parks and squares for leisure sports, fitness centers for strength training and body shaping, and all kinds of sports venues and facilities for intense aerobic exercise. The data of parks, squares, fitness centers, sports facilities and bus stations required by the study sourced from the POI data of Amap open platform (https://lbs.amap.com/, accessed on 10 September 2020). The data of residential building were obtained from Baidu Map and vectorized (https://lbsyun.baidu.com/, accessed on 27 November 2020); the information on the urban road network was obtained from OpenStreetMap (https://www.openstreetmap.org/, accessed on 29 November 2020). The final data included 12,548 residential buildings, 1159 sports fields, 1686 bus stops and 7661 roads ( Figure 1 and Table 1). The size and grade of sports space often represent the number of services it can provide. For example, the size of park has been regarded as a key factor influencing the accessibility of parks in previous studies [10,13,29]. Therefore, in order to standardize the analysis, we divided parks and squares into 5 grades (i.e., 5, 4, 3, 2 and 1) according to their area and fitness centers and sports facilities according to their service levels to represent their service capacity. In addition, other features of sports space are also important factors influencing people's access, such as the number of facilities, quality of service and space experience, etc. [4,6], but these factors are difficult to quantify. Dianping (http://www.dianping.com/, accessed on 10 March 2021) is China's leading platform of local information and trading, where people can freely post comments and scores on the places they visit, and the system will generate comprehensive scores of public facilities based on these scores. Facility score can represent the comprehensive evaluation of facilities by the public to a certain extent. We obtained the scores of four types of sports space from Dianping as the comprehensive assessment value of the people for the space (Table 1).

Study Design
After obtaining the required data, we need to import it into ArcGIS software for pre-processing, convert it into spatial data, eliminate invalid information and establish a database. The main method of research measurement is related to the sports space that can be achieved under certain circumstances starting from residential buildings, including the attributes of the sports space itself. The tool adopted in the research is the network analysis module in ArcGIS, and the key control information required for the module operation includes time/distance, speed/mode of transportation, corresponding to 15 and 30 min in the concept of "life circle". At the same time, the mode of transportation also requires attention. Compared with single mode, spatial equity analysis under multi-mode travel can provide more realistic assessment [29] because it takes diverse consideration of travelling ability from the human scale. Therefore, the measurement of public sports space equity in central urban areas in this study includes 2 parts: the sum of calculated values of sports space accessible from residential buildings within 15min (about 1000 m) by walking and within 30min by bus [28]. In this part, we use ArcGIS network analysis module to work out the shortest path from residential buildings to sports space within two-time circles. The overall calculation process is shown in Figure 2 [19,28,30].

Computational Method of Accessibility Equity to Sports Space by Walking
In the concept of 15-min walking circle, we assume that people can walk to the public sports space which is about 1000 m away from home (human walking speed is calculated at 1.2 m/s). Total travel time includes the time from home to the nearest road plus the minimum time along the road to the public sports space. We can calculate the spatial equity in the walking mode in the following formula [19,29]: where A j indicates the equity value of public sports space from residential building j in walking mode; t ij represents the shortest walking time from residential building j to sports space i; t 0 is the maximum time by walking, i.e., 15 min; S i shows the service capacity of sports space i, namely, the level of sports space classified above; P i represents the comprehensive assessment value of sports space i by the people, namely, the score of Dianping; G T ij indicates a simplified Gaussian time decay function, which can represent the change in the influence of the walking time on spatial equity. It should be pointed out that after all of the calculations, we standardized the results according to the categories of sports space, that is, we assumed that the four types of sports space were equally important.

Computational Method of Accessibility Equity to Sports Space by Public Transportation
In the concepts of 15-min walking circle and 30-min travel circle, we assume that people can travel by public transportation to the sports space which can be reached within 15-30min. The calculation of bus travel time includes three parts: the walking time from home to departure bus station (w j ), from departure bus station to destination bus station (p ij ) and the walking time from destination bus station to sports space (w i ). We calculate the spatial equity in the mode of public transportation in the following formula [19,28,30]: where A j is the equity value of public sports space from residential building j in the mode of public transportation; t ij is the shortest bus travel time from residential building j to sports space i; S i and P i have the same meaning as in formula (2); The calculation method of G T ij is the same as formula (2); t 0 is the longest time by bus, i.e., 30 min; N i is the number of bus stations within 400 m of sports space i; w i is the average time to walk to all bus stations within the range; N j is the number of bus stops within 600 m around residential building j; w j is the average time to walk to all bus stops within the range; p ij is the travel time from the departure bus station to the destination bus station. According to the data of Harbin Transportation Bureau, the bus travel speed is calculated at 10 km/h. Similarly, after all of the results were calculated, we standardized the results. Figure 3 shows the visual status of sports space equity in the central urban area as a whole and in different traffic situations. On the whole, there is obvious an inequality of sports space in the inner city which shows a trend of gradual attenuation from the central area to the periphery. The margin of the four districts and the large area in the south of the city are all areas with low spatial equity values. At the junction of Daoli, Daowai and Nangang districts, the spatial equity value is relatively high. Meanwhile, this area is also the city center, with developed transportation and concentrated resources. In addition, the overall equity layout is not a single outward attenuation, the internal changes in the four districts are uneven. Different streets, and even different residential areas, will have noticeable differences in spatial equity.

Spatial Distribution Results
The results of different transportation modes each showed the inequity of sports space, especially parks and squares. Apart from the walking pattern to the park, other spatial equity results also showed a trend of weakening from the city center to the periphery, and the spatial location of the overall distribution was similar to the comprehensive calculation results. Compared with other types of sports space, the change in equity classification of parks is not moderate, and low-value areas account for a high proportion of the total. The high-value regions of all kinds of cases are mainly concentrated at the junction of the three districts, and their distribution ranges are almost the same with minor differences. At the same time, due to the influence of sports space, traffic stations and urban road network distribution, there are discontinuous spatial equity changes in different modes. Compared with the comprehensive calculation results, the calculation results under classification change more obviously, and the spatial transition is not smooth.

Numerical Statistical Results
The spatial visualization results let us know which specific regions in the city have unequal spatial distribution of sports, and we also need to compare the degree of differences of such inequity. As shown in Table 2 and Figure 4, both the overall and classification results showed obvious skewed distribution, with the mean larger than the median. The data with low spatial equity accounted for a higher proportion and had more concentrated distribution. Parks, squares, fitness centers and stadiums averaged 14.8, 20.2, 23.4 and 27.2, respectively. The average, median and high values of parks are relatively poor, but the standard deviation is the lowest, the overall data distribution is the most concentrated, and the internal gap is smaller than other types of sports space. The results of the square category showed obvious differences, with 50% data values lower than 7.9. The internal relative gap was the largest among all types, and the spatial distribution of sports was the most inequitable. The results of fitness center and stadium categories are similar, and the overall data structure is superior to the first two types of sports space. At the same time, the overall performance of the stadium category is slightly better than that of the fitness center category, reflected in larger mean and median. After the integration of the results of the 4 types, although there is still a relatively unequal situation, that is, 25% of residential buildings and the people in them enjoy a high level of sports space, the overall data structure has been improved, the relative gap of spatial fairness in urban areas has been narrowed to a certain extent, and the distribution of data has become more balanced.

Correlation Analysis between Walking and Public Transportation
In this study, sports space equity in walking and bus modes was discussed. As 2 independent variables, they respectively assessed the equity of people to sports space within a short distance (15-min walking) and a long distance (30-min bus travel), and the superposition results also represented the comprehensive situation of space equity. However, the correlation between them as independent variables has rarely been a part of previous studies. We conducted correlation analysis of the equity results in walking and public transportation modes according to classification of sports space and discussed the correlation level of the two traffic modes in central urban areas.
As shown in Figure 5, the correlation results in different categories are different. Apart from parks, all of the other categories and the overall results pass the significance test (p < 0.01), indicating that the spatial equity of the people in the two modes is also closely related. The r 2 of square, fitness center, sports field and overall results were 0.121, 0.228, 0.108 and 0.252, respectively, showing significant correlation between the 2 modes. In other words, the equity of people having access to the sports space is similar in different traffic modes. When the equity value in the walking mode is low, the equity value in the bus travel mode is generally not high. The results of spaces such as parks did not pass the significance test, and the r 2 value was very low, indicating that there was no linear correlation between the influences of the two traffic modes on spatial equity. However, the r 2 value after overall superposition is the largest, indicating that when comprehensively considering multi-type sports space, the results of spatial equity calculated by the two traffic modes are similar. In other words, the spatial configuration of sports space, urban road network, traffic stations and other elements is actually inequitable. If people only reach the sports space by walking and bus, the status quo of inequity cannot be changed.

Discussion
The main contribution of this study is: based on previous studies, the multi-dimensional information is integrated into the classic model, including residential buildings, urban road network, transportation mode, multi-sports space, people's preferences, and the impact of distance attenuation to obtain a more integrated and comprehensive application model. On the data level: POI data provide multiple spatial information of urban sports, which meets people's different needs. Multivariate spatial analysis smooths the large internal gap that is easy to occur in a single type. The calculation results based on residential buildings are more precise and accurate, close to human scale and related to daily life. Dianping data is people's intuitive assessment of sports space, quantifying the comprehensive quality of and people's preference for the sports space. At the level of logical method: according to the concept of "life circle", the equity standard of space equity is proposed to avoid different research scales caused by simple distance. Compared with other distance measurement methods, the network distance calculated on the basis of the GIS network analysis module is more realistic. The addition of distance attenuation function can more scientifically represent the change in spatial equity with the change in distance. Walking and public transportation are travel modes that can be adopted by all residents, which makes up for the shortcomings of single mode in previous studies.
In this study, multi-dimensional visualization results were obtained to objectively show the status quo of sports space equity in central urban areas, which could support scientific planning intervention and decision-making. In the results of this study, squares have the biggest internal gap and the most inequitable overall situation among all of the types. Taking Daoli District as an example, we simply optimized the layout of facilities in combination with the concepts of the existing urban planning and life circle, including transforming existing vacant land, wasteland, garbage dump and other land with low utilization rate into squares and making up for areas with weak public transportation network. The results are shown in Figure 6. After spatial layout adjustment, the mean and median of spatial equity of squares increased significantly, the standard deviation became smaller, the overall distribution change was smoother, and the low value points also decreased significantly. It can be seen that targeted planning intervention can have a direct impact, and the spatial equity of the region has been positively optimized. However, we tend to overlook the problem and think that spatial equity is simply a homogeneous distribution of facilities or services, which can only remain in the ideal planning blueprint. According to previous studies, we need to consider the sports space with different functions and of different types [8,18,31], and different groups of people choose different sports space [1]. The starting point of spatial equity is to take people's demand as orientation. We have obtained the status quo of spatial equity in the central urban area, which needs to be improved. However, before that, we need to understand the actual demand, for example, through the questionnaire of people's demand, so as to make the most scientific and reasonable spatial planning.
There are still some limitations in this study. First, the urban road network is still relatively simple, and more attributes have not been added to it, such as driving speeds on different roads, waiting at junctions and traffic conditions. The assessment of bus travel mode is relatively simple and rough, which is a general estimate of people's travel time. Second, this study only considered walking and public transportation. Adding more travel modes may narrow or increase the gap of spatial equity but will also be closer to reality. Thirdly, this study only calculated the public sports space open to the vast majority of people in urban areas but did not include some public facilities and services only for part of the population, such as sports venues in schools, residential areas, and government office areas, which will also affect the equity. 5 Figure 6. Comparison of the results before and after the spatial planning intervention of sports squares. Asterisks and circles represent outliers.

Conclusions
Taking Harbin as an example, this study presents the equity of public sports space in urban area based on the measurement method of multi-source urban data. The results show that there are significant inequities in the central urban area, the areas with high degree of equity are concentrated in the downtown and the junction of the three districts, and the emerging areas in the south of the city have the lowest degree of fairness. There are differences in the calculation results of different sports spaces. For example, the gap between park sports spaces is large and the overall situation is not ideal, indicating that there may be some problems in the previous park planning. Except for parks, the results of other types of sports Spaces were significantly correlated with the results of walking and bus modes, and the overall correlation degree was the highest. In other words, the areas with low walking equity degree also had low bus equity degree. Therefore, the planning of infrastructure should be considered in many aspects and promoted together to promote the equity of public sports space. In general, residents in urban centers tend to enjoy superior public sports space resources, while those in urban boundaries, the south and emerging areas do not. Therefore, the overall pattern should be optimized according to the distribution of key areas and specific types of sports space. In planning practice, it should also be weighed based on the needs of the population, so as to maximize the resource utilization of public sports space and meet the needs of sustainable development.


Sustainable Engagement and Academic Achievement Under Impact of Academic Self-Efficacy Through Mediation of Learning Agility—Evidence From Music Education Students

The overarching goal of this study was to look into the effects of academic self-efficacy and academic motivation on student long-term engagement and academic achievement. This study also sought to investigate the role of learning agility as a mediator in the relationship between academic self-efficacy and academic motivation. This study examined the impact of student sustainable engagement on student academic achievement as part of our model. A questionnaire technique was used to collect data from 325 music education students studying at various music training institutions in China. The data were analyzed using the Smart-PLS software and a structural equation modeling (SEM) technique. Academic self-efficacy and academic motivation were found to have a positive and significant relationship with student long-term engagement. The academic motivation was also found to have a positive relationship with student long-term engagement. Furthermore, learning agility was found to mediate the relationship between academic self-efficacy and student sustainable engagement. Furthermore, learning agility mediated the relationship between academic motivation and long-term student engagement. Furthermore, student sustainable engagement has a significant and positive relationship with student academic achievement. This paper made a valuable theoretical contribution by investigating the impact of academic self-efficacy and academic motivation on student sustainable engagement, as well as the impact of student sustainable engagement on student academic achievement. Furthermore, this study added to the body of knowledge by investigating the relationship through the lens of cognitive learning theory. In terms of practical implications, this paper would undoubtedly assist educational institutions in maintaining a fair and just learning environment that encourages students to be engaged and perform well. Future research can include other constructs to gain a better understanding of the factors that influence students’ academic engagement and achievement.

INTRODUCTION
Sustainable student engagement in music education has a number of cognitive, interpersonal, and psychological advantages, including emotional regulatory control, self-identity generation, and social interaction improvement (Weinberg and Joseph, 2016). Awareness of the benefits of music education engagement, multiple studies, and reports have found that student engagement in music activities in industrialized countries is small in comparison to certain other school disciplines and that students' value of engagement in music declines over the high school years (McPherson and O'Neill, 2010). The reason for such a disengagement in music education might be the focus placed on teaching Western "classical" music notation in many school music programs which frequently excludes other musical forms and practices (Richmond et al., 2015).
Even if instructors provide a variety of musical forms and activities, students must find these practices personally valuable in order to retain their engagement in music education over time (López-Íñiguez and Bennett, 2020). Effective music engagement emphasizes on participating in a training program by students who have a thorough grasp and appreciation of the practice, out of which they receive a feeling of relevancy, goal, and satisfaction (Chen and O'Neill, 2020). Student engagement is a creative activity that occurs as a result of the ongoing symbiotic association between enthusiasm and discovery learning. Students' active engagement in music activities is influenced by the value attributed to the activity (Fredricks et al., 2016). Student engagement has also been linked to a reduction in criminality, substance abuse, and unhappiness (Wang and Fredricks, 2014;Fredricks et al., 2016). There is evidence that engagement is pliable and receptive to adjustments in educators' and institutions' approaches, which makes it desirable. Therefore, engagement has enormous potential as a significant focus for reforms and is a stated objective of several school development initiatives at the upper-secondary level. According to research, students are more engaged in classrooms in which they have got good relationships with their peers and teachers; where instructors promote students' independence; where instructors have lofty aspirations and provide clear and consistent feedback; or where tasks are varied, daunting, fascinating, and impactful (Fredricks et al., 2016). Various nested settings, such as prosocial organizations, institutions, schools, pedagogical practices, and timescales, have been explored (shorter and longer engagement). As different studies have different definitions of engagement, many academics believe that motivation and engagement remain linked but are distinct notions (Groccia, 2018). The rise in popularity of participation in the study, administration, and practice may be attributed to a number of factors. So, to begin with, engagement is an important factor in students' academic achievement. Student involvement has been connected to the reward system, achievement grades, and education completion rates in an increasing body of information (Wang and Fredricks, 2014).
This pertains to a student's assessment of his or her capacity to engage in and accomplish academic assignments effectively. It can be argued that a sense of self-efficacy enables a person to trust in his abilities to withstand obstacles that prevent him from achieving his goals. The students' academic self-efficacy allows them to achieve their objectives and ambitions (Hussain et al., 2021). Motivation is impacted by some contextual factors: external stimuli, temperament, objective, and instruments for achieving goals. Individuals develop sufficient motivation in order to attain their goals, desires, and inclinations (Mizumoto, 2013). Motivation for academic achievement is particularly important in the case of students. Individuals are motivated to finish an activity, achieve a goal, or get a certificate of competence in their respective careers when they are motivated in this way (Li et al., 2021). Resultantly, motivation explains the reasons for people's actions and dictates why they act in a certain way. Motivation-driven actions are energizing, goaloriented, and long-lasting. Motivation does have a multi-faceted structure in education, and it is linked to learning and academic motivation (Li et al., 2021). Academic motivation and sustainable student engagement, two of the most important examples of better educational behaviors, play a key role in students' academic achievement. As a result, one of the main responsibilities of all successful educators is to increase students' academic motivation and engagement (Peng, 2021).
Learning agility is becoming more universally acknowledged in managing people as a critical component of long-term instructional leadership (Murphy, 2021). Individual learning agility is the best predictor of future performance. Learning agility is described as an individual's capacity and willingness to learn new skills under a variety of circumstances in the first place. Deep learning agility in many settings can provide new experiences (Murphy, 2021). Therefore, we suggested that learning agility could mediate the relationships between academic self-efficacy, academic motivation, and sustainable student engagement, leading to academic achievement. Academic achievement is not itself a determiner of students' performance, while many studies in past have suggested that different kinds of performances refer to the academic achievement of students, such as class performance, test performance, and composite performance as an aggregated result. This cannot be individually evaluated without going into the exploration of contributors to academic achievement (Madigan and Curran, 2021). Several researchers evaluated different indicators and contributors to academic achievement, including grade point averages, class performance, perceptions about evaluation, etc. (Schneider and Preckel, 2017). A lot of other studies revealed the connection between student engagement and academic achievement and also demonstrated that academic achievement is linked to student engagement (Alhadabi and Karpinski, 2020).
It was also suggested that student engagement is linked to several contributing factors, among which motivation is the strongest contributor to students' engagement. Several authors identified that although motivation and engagement are linked, they should be considered distinct concepts (Groccia, 2018). These studies were mostly conducted at college and higher secondary school levels. This whole gap in previous research allowed the authors to find and devise a conceptual model in which relationships between these variables could be studied in the field of music education at higher levels of educational institutions. Some questions were raised: How academic self-efficacy could lead to sustainable student engagement and influence academic achievement? How students' motivation could contribute to sustainable students' engagement leading to academic achievement? and What role learning agility could play in aiding these relationships? This research would help in providing answers to these questions.

THEORETICAL UNDERPINNING
Social Cognitive Theory is undoubtedly the most well-known of the several theories that attempt to describe the factors that control and govern behaviors (Bandura, 1977). According to Social Cognitive Theory, behavior is driven and regulated by a variety of social systems and related personality elements. Self-efficacy (SE) seems to be a fundamental component of these self-influence elements, and it pertains to a participant's assessment of their ability to plan and execute the actions necessary to attain intended results (Bandura, 1997). The impact of self-efficacy on cessation of smoking, nutritional change in behavior, addiction recurrence, job conduct, sports ability and achievement, and academic success has been examined across a range of psycho-social fields (Honicke and Broadbent, 2016). Self-efficacy beliefs, according to Bandura (1997), are self-regulatory and important to human functioning because they give people the ability to influence their own cognitive processes and actions, and hence modify their surroundings.
Self-efficacy is defined as "People's judgments of their skills to plan and courses of action required to achieve specific kinds of outcomes." Self-efficacy is essential for students to continue to perform challenging tasks. SE is usually articulated in academic contexts under the perspective of academic self-efficacy (ASE), which refers to learner assessments of their ability to achieve educational goals (Putri and Prabawanto, 2019). This led us to utilize academic self-efficacy in the context of academic achievement through sustainable student engagement. Almeida (2021) categorized learning approaches into two categories, deep and surface learning approaches, while presenting a valid theory of learning in formal educational settings. Learners who are engaged in the deep learning strategy attempt to integrate new knowledge by connecting it to the individual perspective, background knowledge, and material. In contrast, in surface learning, learners place a greater emphasis on memorization and rote learning rather than appreciating the true significance of themes and theories (Coertjens et al., 2016). Test anxiety or the need to complete course standards in order to pass tests are common motivations for these kinds of learning, and learners aim to achieve these goals with the least amount of work possible (Mahmood et al., 2021). Expectancy Value Theory explains the relationship between self-efficacy and engagement. People's behavioral and emotional engagement is impacted by their degree of self-efficacy (Mahmood et al., 2021). All these theories provide the basis for the inter-connected phenomenon of academic achievement. Academic self-efficacy and motivation leading to sustainable student engagement in music education which in turn leads to academic achievement are goals of this study supported through the above-mentioned theories.

Academic Self-Efficacy and Sustainable Student Engagement
Academic self-efficacy (ASE) refers to a set of attitudes and judgments about a student's efficacy and capacity to carry out specific educational tasks and responsibilities (Fife et al., 2011). Academic self-efficacy is defined by academicians as a student's assessment of his or her ability to achieve academic objectives. Academic self-efficacy has been demonstrated to consistently link favorably with learning achievement and efficient methods of coping, according to a slew of investigations (Paciello et al., 2016). Students with stronger academic self-efficacy have already been observed to handle difficult academic tasks and their educational lives more efficiently (Allari et al., 2020). Children with poor academic self-efficacy are also more susceptible and less eager to execute academic tasks, and being less inspired, avoid school and experience stress and academic disappointment (Bassi et al., 2007).
Although there are few studies on the relationship between academic self-efficacy and study engagement, empirical investigations on students' self-efficacy and other engagement themes exist, and a large number of studies show significant and favorable results (Olivier et al., 2019). ASE and learning engagement are being investigated, and it was found that ASE and learning engagement were linked, according to a previous study (Zhen et al., 2017). Students with ASE reported better academic ambitions by sitting down on assignments and engaging in learning activities, and a similar observation was reported in another research published by Bassi et al. (2007) among teenagers. In a study among university students in Japan (2013), Mizumoto, discovered that students with high academic self-efficacy were more enthusiastic about adopting vocabulary acquisition tactics than those with low to moderate ASE. All the suggested literature allowed us to devise the following hypothesis in our study context. H 1 . Academic self-efficacy shows a connection with sustainable student engagement.

Academic Motivation and Sustainable Student Engagement
Motivation can be thought of as the driving factor which inspires learners to focus on academics and gain better achievements or grades in an academic setting. The academic motivation was classified into two parts by researchers: internal motivation and external motivation. Internal motivation is a relatively high element wherein identity, ambition, and pleasure guide conduct. Motivation can be described as behavior that is motivated by other objectives or incentives other than the activity itself. Within that case, the achievement of a specific activity is linked to external incentives or penalties, rather than the task itself or the individual. Whenever people do not really anticipate anything else in return for their actions, this is referred to be a motivating situation (Urdan and Bruchmann, 2018). Engagement, along with motivation, is seen as critical for improved learning outcomes for all the students in the literature. Student engagement in learning is considered a pre-requisite and a vital part of motivation (Schlechty, 2000). Engaging students in education is not just a means to an end. This is a goal in and of itself, even though it is a means to an end of students getting good academic results. It is significant since genuine engagement can contribute to better academic performance during a student's academic career (Ryan and Deci, 2009). If instructors would like to know how to solve the challenges that young kids face, as well as make education more interesting, they must first listen to what students have to say about their classrooms and professors (Saeed and Zyngier, 2012). There are a few studies in the past that looked into the relationship between academic motivation and student engagement in different contexts (Peng, 2021). Therefore, the authors suggested the following hypothesis.
H 2 . Academic motivation shows a connection with sustainable student engagement.

Learning Agility
Learning agility is an essential component that blends efficacy and motivation into engagement in music education as a mediator between the ASE, academic motivation, and long-term student engagement. Humans live in a time when knowledge is shifting from predetermined skills and background information to optimal learning environment agility in unfamiliar circumstances using a variety of experiences plus technology instruments. Lombardo and Eichinger (2000) invented the phrase "learning agility." This has been characterized as the motivation and capacity to learn through knowledge and then apply acquired information in new settings for good achievement as an educational technique based on past experience. This is defined as the capacity to learn new things on the move and the desire to put what you have learned into practice. It consists of three key elements: capacity, ambition, and adaptation (De Meuse et al., 2010).
Highly adaptable students can take the proper learning from their past experiences and use them in unfamiliar circumstances. Agile learners, according to De Meuse et al. (2010), can assess difficulties rapidly and precisely, synthesize knowledge, and grasp diversity. Learners are open to opportunities and situations, and their problem-solving methods are adaptable. Seemingly, agile learners are ready to learn, test hypotheses, and recognize learning in addition to increasing their abilities to deal with problems. Such learning agility will also be required to deal with problems in education and in future work environments (Murphy, 2021). Learning agility, as per De Meuse et al. (2010), is a rather stable notion that is independent of race, gender, or nationality. This is due to the fact that learning agility is a better predictor of good success than cognitive or behavioral traits (Connolly, 2001). As a result, prior experiences with using and efficacy beliefs in students' learning and lives have a role in modulating the impacts of ASE, academic motivation, and long-term student involvement as measured by learning agility. When students are faced with unclear situations, learning agility allows them to adapt and establish new values (Connolly, 2001). Previously, a few scholars evaluated different relationships in connection to learning agility as mediators, such as learning culture and work engagement (Saputra et al., 2018), and employee engagement through the learning culture of organizations (Tripathi and Sankaran, 2021). It indicated that learning agility being a mediator between ASE, academic motivation, and sustainable student engagement along with being an influencer of sustainable student engagement could be utilized, and we formulated the following hypothesis.
H 3 . Learning agility could be a mediator between academic selfefficacy and sustainable student engagement.
H 4 . Learning agility could be a mediator between academic motivation and sustainable student engagement.
H 5 . Learning agility could lead to sustainable student engagement.

Association of Student Engagement With Academic Achievement
Academic achievement has previously been considered a key result of student engagement. While there has been a large number of investigations on the topic, the findings have been divided. This connection may be seen from two different angles. For instance, Alhadabi and Karpinski (2020) discovered a considerable and reasonably strong link between the academic achievements of students and their engagement, while King (2015) discovered that academic achievement was favorably connected with emotional and behavioral engagement. A few researchers discovered a link between academic achievement and cognitive engagement (Pietarinen et al., 2014). Student engagement is thought to improve school achievement, which in turn encourages learners to participate in such activities, producing a "vicious circle of education" (Xu and Qi, 2019).
According to several experts, the positive relationship between behavioral engagement and achievement is stronger than between cognitive and emotional involvement. The findings of these studies suggest that various measures of student engagement show varying associations to academic achievement when considered altogether (Furrer and Skinner, 2003). Many investigators, on the other hand, did not achieve the same results, and in several investigations, there was no substantial link between academic achievement and student engagement. Shernoff and Schmidt (2007), for instance, discovered that among African-Americans, student participation did not predict grade point average. In addition, Konold et al. (2018) discovered no link between student academic achievement and engagement. Shernoff and Schmidt (2007) also said there was no link between students' proactive emotional engagement and overall achievement levels in English and Maths. According to Appleton et al. (2006), the relationship between intellectual engagement and academic achievement is minimal. This literature suggested formulating the hypothesis for evaluating the relationship between sustainable student engagement and their academic achievement in the context of music education. Therefore, the authors proposed the following hypothesis. H 6 . There is a strong association between sustainable student engagement and their academic achievement.
The following conceptual model (Figure 1) has been formed based on the above findings and hypotheses.

METHODOLOGY
The current study took a quantitative method with a deductive approach, in which hypotheses were formed and analyzed to see how specific variables affected other variables. This methodology is used by researchers to ensure that there is no bias. Selfadministered surveys were utilized to obtain data for the analysis of this quantitative study. The music students from different institutes in China worked as the study's target group. The convenience sample strategy was used to collect data from respondents via physically distributed questionnaires in this study. The data collection and process completion took 2-3 months. The overall number of questionnaires circulated was approximately 500, and we received 350 responses, resulting in a 70% response rate; out of those 530 responses, 325 were viable and used for data analysis. Because the data gathering procedure was delayed at the beginning of the study, reminders were sent to the selected responders to speed up the process. The students of music education in China served as our study unit of analysis.

Statistical Tool
The Smart-PLS 3 was used to analyze the data in this study. The method used in our study was structural equation modeling. Partial least square is widely used in management and social sciences, because it is a variance-based structural equation modeling technique (Nitzl et al., 2016). Furthermore, PLS-SEM is a causal modeling technique whose goal is to increase the explained variance of latent dependent constructs. PLS-SEM is viewed by researchers as a "silver bullet" for dealing with empirical findings with small sample size. Smart-PLS is simple to use and has a plethora of advanced features (Garson, 2016). Furthermore, the Smart-PLS technique is best suited for research studies with complex equations (Wong, 2013). To precisely calculate the values of beta, reliability, and standard error, this study adheres to the recommendations of Wong (2013), and ensures that all of those indicators are part of their respective latent variables with outer loadings of 0.7 in the reflective outer model evaluation.

Measurement
To record respondents' responses, a five-point Likert scale ranging from strongly agree to strongly disagree was used in this study. The Cronbach's alpha value should be greater than 0.7 when checking the reliability of each variable (Hair et al., 2019). We have included the measurement and the Cronbach's alpha values in the following text:

Academic Self-Efficacy
This study utilized the scale of Wang et al. (2022), which is a single-dimension three-item scale. The value of Cronbach's alpha is 0.826, which is acceptable when compared to the benchmark value.

Academic Motivation
The academic motivation was measured by using the scale of Vallerand and Blssonnette (1992) which consists of 14 items. The value of Cronbach's alpha is 0.919, which is well above the required value.

Learning Agility
In this study, learning agility was measured by using a five-item scale by Gravett and Caldwell (2016). The Cronbach's alpha value of learning agility is 0.905, which is acceptable as compared to the benchmark value.

Student Sustainable Engagement
This study measured student sustainable engagement by utilizing the scale of Briggs and Towler (2005), which consists of five items. The Cronbach's alpha is 0.919, which is well above the benchmark value.

Student Academic Achievement
This study utilized student academic achievement by using the 19-item scale of Topor et al. (2010), while our study adopted 15 Frontiers in Psychology | www.frontiersin.org items for the purpose of our study. The Cronbach's alpha is 0.92 which is acceptable.

Demographic Analysis
The demographic profile of the respondents who took part in the survey is presented in Table 1. There were 325 people in total that took part in the study, with 189 men and 136 women. Bachelor's degree holders made up 65% of the overall number of participants, while undergraduates constituted 35%. To acquire data in a cost-effective and time-saving manner, respondents were chosen using the convenience sampling technique. Table 2 displays the overall variation explained for each of the variables studied using single-factor analysis. It discusses the usual technique bias or the questionnaire's bias. For one item, the percent of variance must be less than 50% (Yong and Pearce, 2013). Because the total variation explained in this study is less than 50%, there is no bias in the data.

Measurement Model
The algorithm for the output measurement model is depicted in Figure 2. This diagram shows the effect of independent variables on the dependent variables of the study.
The table below shows the factor loadings for each study construct, namely, academic self-efficacy, academic motivation, learning agility, student sustainable engagement, and student academic achievement. Along with the VIF values, the table displays the composite reliability and average variance extracted (AVE). The factor loading explains an item's contribution to the variable, and its value must be greater than 0.60 (Jordan and Spiess, 2019). The factor loadings for all the items in this study are greater than 0.60, indicating that the factor loadings are fair. The variation inflation factor (VIF) validates the model's collinearity problems. The outer VIF result for the current study is also less than 5 (ranging from 1.804 to 4.211), indicating that there is no collinearity in the model. Furthermore, the current inner VIF result is less than 5 (between 1.508 and 2.475). Table 3 shows that the AVE values are greater than 0.60, indicating the presence of convergent validity (Ahmed and Azmi bin Mohamad, 2016). The composite reliability was greater than 0.70, putting it within the range of highly satisfactory values (Peterson and Kim, 2013).
The HTMT ratio and the Fornell and Larker criteria were used to assess discriminant validity (see Tables 4, 5). These tests determine whether or not there is a difference between the variables. According to Jordan and Spiess (2019), the HTMT rati should be less than 0.90 to ensure a variable's discriminant validity. The HTMT ratio for the current study was less than 0.90, indicating that discriminant validity exists. The Fornell and Larker criteria are met if the value at the top of the column is greater than the value below that column (Henseler et al., 2015). An R-square value greater than or close to 0.50 indicates that the model is substantial and good (Archer et al., 2021). The R-square values for the current study's variables are close to or greater than 0.50, indicating that the model is good. The crossvalidated redundancy should be greater than zero as measured by q-square (Henseler et al., 2015). The Q-square values for the current study's variables are greater than zero, indicating that the model is significant as shown in Table 6.

Structural Model
After successfully analyzing the measurement model, which includes the establishment of constructs and indicator reliability and validity, in the next step, a structural model was assessed to measure the coefficient of determination (R 2 ), significance of path coefficient, and relevance of path coefficient (see Figure 3).
R-square explains the chance in endogenous variables happened due to exogenous variable. Recommended value of (R 2 ) should be greater than 0.10. R-square value criteria proposed by Hair et al. (2013) includes 0.75, 0.50, or 0.25 for endogenous latent variables and can, as a rough rule of thumb, be described as substantial, moderate, or weak, respectively. R-square value of learning agility is 0.636, which shows that 63% of changes in the learning agility are accounted for because of academic self-efficacy and motivation. Similarly, R-square value of student engagement is 0.738 and academic achievement is 0.473, which shows that 73% variance in student engagement and 47% variance in academic achievement are accounted for because of exogenous variable in the model. Q-square is predictive relevance and measures whether a model has predictive relevance or not (>0 is good). Q 2 values of all the endogenous constructs are greater than 0, which shows the predictive relevance of the model.
In the next step, the significance of the path coefficient and relevance of the path coefficient were measured to investigate the hypotheses of this study. The bootstrapping procedure was applied by using 5,000 bootstrap samples for the assessment of the path coefficient. Table 7 shows the direct effects of the variable under study, while Table 8 shows the indirect effects of the variable under study. These tables show whether the hypotheses were accepted or rejected based on the p-values that were less than 0.05 (Andrade, 2019).
Hypothesis 1 (H1) proposed that there is a relationship between self-efficacy and student engagement. The results show that if self-efficacy increases by one unit of standard deviation, then the student engagement increases by 0.575 standard deviation units (B = 0.575, T-value = 9.890, p = 0.000). H2 proposes that there is a relationship between academic motivation and student engagement. The results indicate that academic motivation does not show a significant impact on student engagement at P > 0.005. Hence, H2 is rejected. H5 proposes that learning agility has a positive and significant impact  on student engagement. The results show that learning agility has a positive and significant impact on student engagement (B = 0.277, P = 0.000) Hence, H5 is accepted. Moreover, H6 proposes that a relationship exists between student engagement and student academic achievement. The results reveal that student engagement has a positive and significant impact on student academic achievement. As student engagement increases by one standard deviation unit, the academic performance also increases by 0.688 standard deviation units. Hence, H5 of this study is accepted. In this study, mediation analysis was performed by using the method proposed by Preacher et al. (2016). H3 proposes that learning agility mediates the relationship between selfefficacy and student engagement. The results show that learning agility partially mediates the relationship between selfefficacy and student engagement, as both direct and indirect effects are significant. H4 evaluates whether learning agility mediates the relationship between academic motivation and student engagement. The result shows that learning agility fully mediates the relationship between academic motivation and student engagement, as the direct effect between academic motivation and student engagement was insignificant, as shown in the Table 8.

DISCUSSION
The focus of this study was to evaluate the missing link between academic self-efficacy (ASE), academic motivation, and sustainable student engagement. The study also focused on evaluating the direct impact of sustainable student engagement on academic achievement, which was the ultimate goal of the research. This study also evaluated the mediator of learning agility between ASE, academic motivation, and sustainable student engagement.
According to the definition, ASE refers to different attitudes and behaviors about the self-efficacy of students for performing specific tasks related to education (Fife et al., 2011). It is defined by Elias and MacDonald (2007) as a method to assess the ability of students to perform and attain their goals and academic objectives. Previously, it has been considered for evaluating the academic achievements of the students and has shown a consistent link with coping mechanisms (Paciello et al., 2016). It was also observed that students having stronger academic self-efficacy were able to handle challenging academic tasks (Allari et al., 2020), whereas students with weak academic selfefficacy were less oriented to execute academic tasks (Bassi et al., 2007). Similarly, our results indicated that students who were more goal-oriented have greater academic self-efficacy, which contributed significantly toward sustainable student engagement in music education. These results are also in agreement with some of the previous investigations in similar contexts. It was evident from the literature review that there are a few studies on the relationship between academic self-efficacy and study engagement. Previously, the theme of the relationship between self-efficacy and student engagement does exist, indicating significant association (Olivier et al., 2019). Studies on ASE and learning engagement indicated that these two variables were linked (Zhen et al., 2017).
The second hypothesis of the current study examined the association between academic motivation and sustainable student engagement. Although some of the previous investigations indicated that students' motivation is an indicator of student engagement, results of this study revealed contrasting results that academic motivation is not associated with sustainable student engagement. The possible reason for such outcomes lies in the fact that previously student engagement was assessed in a normal educational context, while this research evaluated the academic motivation in the context of music education and students could not be referred to as sustainably engaged   in this context. It indicates that music could not establish its worth in educational institutes, even though sustainable student engagement has a lot to offer in music education, such as cognitive, interpersonal, and psychological advantages, including emotional regulatory control, self-identity generation, and social interaction improvement (Weinberg and Joseph, 2016). The other direct relationship between student engagement and academic achievement was also tested in this study, which proved that there was a significant association between sustainable student engagement and academic achievement. Academic achievement has previously been supposed as a promising indication of student engagement. Considering this fact, it was observed that there has been a large number of investigations on the topic. This kind of relationship was also studied by Alhadabi and Karpinski (2020) who identified a strong and considerable connection between the academic achievements of students and their engagement. However, some contrasting results were also produced where no connection was found between academic achievement and students' engagement (Konold et al., 2018). The indirect and mediating results of the current study revealed that there was a mediation of learning agility between ASE, academic motivation, and sustainable student engagement. The results proved their significance in a way that learning agility has been a helping tool in the education sector along with working scenarios of different organizations. This could be understood by the phenomenon of learning agility, according to which highly adaptable students can take the proper learning from their past experiences and use them in unfamiliar circumstances.
It is supported by the fact that learners who are agile in learning have the ability to assess the challenges quickly and from previous knowledge could adapt to the changes. This is also supported by the fact that the problem-solving nature of agile learners keeps them engaged, which ultimately leads to academic achievement (De Meuse et al., 2010). Therefore, similar results were obtained in evaluating the relationship of learning agility  with students' sustainable engagement. Some of the previous scholars also evaluated learning agility as a mediator in different contexts (Saputra et al., 2018;Tripathi and Sankaran, 2021). These scholars found the significant mediating role of learning agility in their studies.

Practical Implications
This study provides several important recommendations for public policymakers and academic institutes which help to improve student engagement, which ultimately impacts student academic achievement. Teachers should provide positive moral inspiration to support students' academic self-efficacy. Teachers should exhibit a favorable attitude in order to motivate students in the institutions. The curriculum should be designed by looking at the consideration of student motivation and selfefficacy. Special seminars and sessions should be conducted to boost student motivation and self-efficacy. The institution's administration should pay attention to making academic institutions more collaborative and innovative to motivate students both intrinsically and extrinsically, which would further help to foster student engagement. The academic level of selfefficacy and academic motivation both contributed positively to the prediction of academic performance, according to the findings. As a result, students are expected to acquire experiences in school that will help them increase their academic drive and self-efficacy. Digital natives must be encouraged to identify suitable methods to use digital technology for academic success, rather than focusing solely on learning how to use digital technologies. As a result, digitally enhanced education for college students should presume that students can use technology to discover, analyze, produce, and share information, which should be employed in the context of academic problem-solving. Students' future careers and quality of life will be influenced by their hands-on experience integrating digital technology with academic work.

Theoretical Contribution
The findings imply that in order to achieve meaningful use of digital technology in academic life, students must make an effort to study and apply gained knowledge as agile learners in a digitally enriched environment. The findings support earlier research reports about the importance of motivation and self-efficacy in the student's academic carrier. This study contributes to the body of research by exploring the two key predictors which lead to increased student engagement and academic achievement. This study also explores the mediating role of learning agility between motivation, self-efficacy, and sustainable student engagement. The findings on knowledge and skills and student engagement, in particular, suggest that digital competence has a favorable influence on student involvement, which is further connected to crucial outcomes, such as grades, perseverance, and college completion. Literature shows that limited studies explore the concept of learning agility. This study makes a unique contribution by exploring two important predictors which help to foster learning agility. Along with this, this study provides valuable insights for researchers and scholars to explore more antecedents that play a critical role in fostering student engagement, which impacts their academic performance and has a long-lasting impact on their careers.

Limitations and Future Recommendations
This study found several shortcomings that must be addressed. One limitation of this study is that it included 325 students from varied backgrounds, including various professions, genders, and grade levels. The background of these students may indicate variations in student academic achievement. Second, our samples come from a particular area, so there is some issue of biasness here. To improve study generalizability, it would be preferable to increase the sample size; for example, future research may include students from several institutions in different cities to obtain a better model fit toward data and R-squared values for outcome variables. Third, data of this study were collected from only one single source, which may raise the risk of common method bias. So, future studies should collect data from multiple sources in order to avoid the risk of common method biasness. It is plausible that a number of limitations influenced the research findings, such as difficulties in assessing the student's level of motivation, including a small proportion of students from few institutions without taking into consideration students from different countries, and including a small sample presented by students from a limited geographical area without giving due consideration to students from other countries. As a result, future research should collect data from other countries and do comparison analyses. They were equally significant in interpreting the results and planning future study possibilities.
In this regard, it should be mentioned that while this study took into consideration previously acquired competencies as well as the observed outcomes of the e-learning course, modeling of the overall result was mostly dependent on the data provided by research participants themselves. This could have had an external validity. Even though the research did not take into account students' specialization and attempted to provide as many similar contexts for respondents as feasible, future work of this type will give relevant comparisons.

CONCLUSION
The prime objective of this study was to assess the key predictors that may help to facilitate student sustainable engagement and academic achievement. This study also investigated whether learning agility mediates the relationship between academic selfefficacy and student motivation on student engagement. Data for this study were collected from undergraduates and graduates studying in various colleges and universities in China. This study adopts the convenience sampling technique for the collection of data. A partial least square method was adopted for data analysis.
Results reveal that intrinsic and extrinsic motivation is a prerequisite for any student to set a career target and make their efforts to achieve it. If students have a strong belief in their skills and capabilities, then they will be more involved in academic activities and skill enhancement, which not only leads to an increase in their engagement with learning and education but also has a long-lasting impact on their future careers.

DATA AVAILABILITY STATEMENT
The original contributions presented in this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

ETHICS STATEMENT
The studies involving human participants were reviewed and approved by Henan University of Economics and Law, China. The patients/participants provided their written informed consent to participate in this study. This study was conducted in accordance with the guidelines of the Declaration of Helsinki.