SDT postulates that both intrinsic and extrinsic motivations influence individuals’ behavior and outcomes [11]. PESE reflects individuals’ confidence in their ability to engage in physical exercise, which significantly affects their motivation and behavior in physical activities [13, 14]. Studies have reported a strong association between PESE and PAE [16, 22]. CE refers to individuals’ knowledge and beliefs regarding physical activities, including their understanding of personal fitness [23]. EE involves emotional responses such as interest and excitement during physical activities [2], whereas BE relates to the frequency and manner in which individuals participate in physical activities [24]. PESE is crucial because it increases participants’ motivation for PAE and improves their fluency experience (FE), which, in turn, enables them to uphold a healthy lifestyle (PEB) through increased PAE [25, 26]. Despite the alleviation of the public health crisis, college students’ PAE remains low [8]. Enhancing their PESE could increase awareness, motivation, and initiative to participate in physical activities [27]. Therefore, the higher PESE of college students may not only improve their PAE but also influence their perceptions of the importance of participating in physical activity [25, 28]. Thus, such college students may participate in physical activity with greater CE, EE, and BE. Consequently, this study proposes the following hypotheses:

H1: PESE positively affects CE in physical activity.

H2: PESE positively affects EE in physical activity.

H3: PESE positively affects BE in physical activity.

As we move toward normative management post-2024, promoting a healthy lifestyle is crucial for achieving SDG-3 [2, 29]. According to engagement theory [17], individuals’ CE, EE, and BE influence their motivation to participate in activities and their outcomes. Physical activity, as a key component of a healthy lifestyle, is associated with positive experiences and health benefits [30, 31]. Functional engagement (FE) in physical activity, which represents a comfortable and enjoyable experience, is linked to improved mood and health outcomes [32, 33].

Students regularly engaging in physical activity such as walking and running tend to have a higher motivation to participate [34, 35], which results in FE, excitement, and pleasure during physical activity [36]. In the current epidemic normalization management, college students have been recognizing the importance of physical activity [37]. Thus, they may feel compelled to participate in physical activities, which can enhance their likelihood of having enjoyable or seamless experiences during these activities [38]. Thus, the CE, EE, and BE of college students in physical activity tend to be associated with a greater FE. Accordingly, following hypotheses are proposed:

H4: CE positively affects FE in physical activity.

H5: EE positively affects FE in physical activity.

H6: BE positively affects FE in physical activity.

With the increasing emphasis on achieving SDG-3, healthy lifestyles and the long-term health benefits of regular exercise have gained prominence [39]. PEB refers to consistent participation in activities like walking, running, and swimming, which is vital for promoting physical health among college students [40]. PEB is vital for college students because it significantly promotes their physical health [41]. Furthermore, college students regularly participating in physical activities with FE, such as excitement and pleasure, are more likely to engage in those activities [42]. Physically active college students tend to have higher participation experiences [43], which motivate them to engage constantly in physical activity and thus exhibit constant PEB [44]. Therefore, FE in physical activity is essential for such students as it allows them to uphold an exercise regimen. Thus, the following hypothesis is proposed:

H7: FE in physical activity is positively associated with PEB.

In total, 900 Chinese college students participated in an online cross-sectional survey conducted using a questionnaire posted on Questionnaire Star platform from July 16, 2023, to August 16, 2023. The participants were selected through convenience sampling, which ensured the inclusion of a diverse demography across various grades, educational backgrounds, and study fields. Among the collected responses, only complete responses and those that fulfilled the inclusion criteria were considered valid for further analysis. Any legally consenting student enrolled in a Chinese university with internet access could participate in the survey. Before the survey was started, the participants were provided with detailed research-related information, including its purpose, potential benefits and risks, duration, and the procedures available for ensuring data confidentiality. The participants had to provide electronic informed consent for affirming their understanding and agreement to participate anonymously. This study was conducted according to the principles of the Declaration of Helsinki and its later amendments. The Ethical Committee of Zhangjiajie College, China, approved the study (ERB No. CLZCJSU-2023-01, Date: January 2023).

A total of 900 questionnaires were collected for this study. After excluding invalid responses, such as incomplete surveys or those completed in less than one minute, 845 valid questionnaires remained, resulting in an effective response rate of 93.9%. Respondents’ background information is detailed in Table 1.

PESE is an individual’s confidence and belief in completing the physical activity [13]. This study adapted Hong and Chan’s [45] self-efficacy scale based on the above definition to measure PESE among college students. The adapted scale in this study had 8 questions. Examples of questions were: “I believe that I can always complete the physical activity if I try hard enough” and “I am confident that I can effectively deal with any problems that arise during physical activity”.

PAE refers to the active cognitive, emotional, and behavioral involvement individuals exhibit when participating in physical activities [2, 46]. Drawing from the above definitions, this study designed 12 questions to assess physical activity engagement (PAE) among college students, based on Fredricks’ (2004) three types of engagement: cognitive (CE), emotional (EE), and behavioral (BE). Example questions for measuring CE in physical activity were: “I plan well in advance before performing physical activity” and “I remind myself to pay special attention to the areas where physical activity tend to be ineffective”. Example questions for measuring EE in physical activity were: “I am willing to improve my physical activity if it is not done in a good way” and “I like to discuss physical activity with my friends”. Example questions for BE in physical activity were: “I actively participate in physical activity” and “I am used to resting after participating in physical activity”.

FE in physical activity, found to be closely associated with positive emotions and health, refers to the feelings of excitement, comfort, and smoothness individuals experience during physical activity [32]. Based on the above definition, the study modified Jackson et al.’s [47] FE scale with 9 questions to measure FE in physical activity among college students. Example questions were: “I feel that everything goes well when I participate in physical activity” and “I am in optimal condition for physical activity”.

PEB is a behavioral manifestation in which an individual consistently exercises while performing physical activity [40]. Based on the above definition, 7 questions were developed to measure PEB among college students in this study. Example questions were: “I will continue to be physically active in the future” and “I will continue to pay attention to content about physical activity”.

Structural equation modeling (SEM), a significant statistical method commonly used in social sciences, is often employed to examine the structure and hypothesized relationships among research variables [48]. Therefore, to investigate the relationships among the variables in the present study, SPSS 25.0 (IBM Corp., Chicago, IL, USA) was used for demographic background, correlation, and reliability analyses. Subsequently, AMOS 24.0 (IBM Corp., Armonk, NY, USA) was used to perform item analysis for each scale as well as to test model fit and conduct path analysis of the hypothesized research model by establishing the structural equation model.

In social sciences studies, first-order confirmatory factor analysis (CFA) provides a better measure of item fitness and rationality of research scales [49]. According to the criteria recommended by statisticians, χ²/df should be less than 5, Goodness of Fit Index (GFI) greater than 0.80, Root Mean Square Error of Approximation (RMSEA) less than 0.1, and item questions with factor loading (FL) greater than 0.500 are statistically significant [50, 51]. Therefore, first-order confirmatory factor analysis (CFA) was conducted to assess the intrinsic validity of the study constructs, and the measured data met the criteria recommended by statisticians. Therefore, after the first-order CFA, measures for PESE were reduced from 8 to 7 questions; measures for CE in physical activity were reduced from 4 to 3 questions; measures for EE in physical activity were reduced from 4 to 3 questions; measures for BE in physical activity were reduced from 4 to 3 questions; measures for FE in physical activity were reduced from 9 to 6 questions; and no deleted questions for PEB measures, as shown in Table 2. The results of confirmatory factor analysis validated the measurement model.

In social statistical analysis, the reliability and validity of each research construct are assessed to evaluate the scientific rigor of the statistical data [50]. Regarding reliability, Cronbach’s $\alpha$ and composite reliability (CR) values greater than 0.7 indicate strong internal consistency within the constructs’ statistics. Table 3 demonstrates that the Cronbach’s $\alpha$ values for the constructs ranged from 0.92 to 0.94, and the composite reliability (CR) values ranged from 0.88 to 0.90, all exceeding 0.7. This indicates that the constructs possess excellent reliability and that the measured data meet the statistical standards [52]. Additionally, factor loading (FL) and average variance extracted (AVE) values greater than 0.5 indicate good convergent validity of the measured data [53]. In this study, FL values ranged from 0.71 to 0.78, and AVE values ranged from 0.50 to 0.61, both exceeding the 0.50 threshold. Furthermore, as shown in Table 4, the square root of the AVE for each construct is greater than its correlation coefficients with other constructs. This indicates good discriminant validity of the measured data [52]. Specifically, each construct shares more variance with its own measures than with other constructs, meeting the recommended criteria for discriminant validity [54]. The results showed that the constructs’ reliability and validity were appropriate.

SEM typically assesses the variance acceptance of the resulting data by evaluating the overall fit of the study model [55]. Good overall fitness is indicated when the value of χ²/df is less than 5; the RMSEA is less than 0.1; the values of Goodness of Fit Index (GFI), Adjusted Goodness of Fit Index (AGFI), Normed Fit Index (NFI), Non-Normed Fit Index (NNFI), Comparative Fit Index (CFI), Incremental Fit Index (IFI), and Relative Fit Index (RFI) are greater than 0.800, and the values of Parsimony-Adjusted Normed Fit Index (PNFI) and Parsimony-Adjusted Goodness of Fit Index (PGFI) are greater than 0.500 [56, 57]. From the measured statistics, the following values were obtained for this study: χ²/df = 3.96, RMSEA = 0.06, GFI = 0.88, AGFI = 0.86, NFI = 0.89, NNFI = 0.91, CFI = 0.92, IFI = 0.92, RFI = 0.88, PNFI = 0.81, and PGFI = 0.75. These results indicated that the models in this study had good fitness and met the criteria recommended by statisticians.

This study proposed seven research hypotheses based on SDT and engagement theory to test the research model. As shown in Fig. 2, PESE had a significant positive effect on CE ($\beta$ = 0.60***; t = 12.15), EE ($\beta$ = 0.65***; t = 14.16), and BE ($\beta$ = 0.70***; t = 14.43); CE ($\beta$ = 0.17***; t = 4.73), EE ($\beta$ = 0.28***; t = 7.73) and BE ($\beta$ = 0.56***; t = 12.26) had a positive effect on FE; and FE had a positive effect on PEB ($\beta$ = 0.84***; t = 19.73). In this context, the triple asterisks (***) indicate that the path coefficients are statistically significant at the p  0.001 level.

Fig. 2.

Validation of the research model. Notes: PESE, physical exercise self-efficacy; CE, cognitive engagement; EE, emotional engagement; BE, behavioral engagement; FE, fluency experience; PEB, persistent exercise behavior, *** p 0.001.

In addition, the values of explanatory power ranging around 0.25, 0.50, and 0.75 indicate that the study model has weak, medium, and strong degrees of explanatory power, respectively [57]. As shown in Fig. 2, the explanatory power was 54% for CE, 63% for EE, 65% for BE, 62% for FE, and 54% for PEB. The aforementioned results indicated that the present study model had a moderate-to-strong degree of explanatory power.

The positive relationships between PESE and the three types of PAE underscore the crucial role of self-efficacy as a motivational factor in promoting physical activity among college students. This aligns with previous research findings indicating that higher PESE is closely related to increased participation in physical activities [22]. For example, Wang et al. [28] reported that college students with higher PESE are more likely to engage in physical activities and exhibit greater awareness. Similarly, Miller et al. [25] found that enhanced PESE improves emotional experiences, leading to increased enthusiasm for physical activity. The findings of the present study support the hypotheses 1, 2, and 3 by validating the significance of motivational factors of PESE in the three PAE types based on the SDT. In the context of promoting a healthy lifestyle and achieving SDG-3, our findings highlight the importance of fostering PESE among college students. Higher PESE motivates students to engage more in physical activity, contributing to their overall health and well-being. This is particularly significant during health crises, such as the COVID-19 pandemic, where maintaining physical activity is essential yet challenging.

Our study found that CE, EE, and BE in physical activity significantly and positively influence fluency experience (FE) among Chinese college students. This finding supports hypotheses 4, 5, and 6 and aligns with engagement theory [17], which posits that these forms of engagement are interconnected and dynamically influence behavioral outcomes. Additionally, these findings are consistent with those of previous research. Mitchell et al. [30] reported that increased engagement in physical activity enhances participation experiences, leading to greater involvement in activities like outdoor sports, swimming, and diving. Similarly, Nagata et al. [34] observed that students with higher levels of engagement in physical activities value their participation, which promotes excitement and pleasure, encouraging them to continue performing these activities. Regular engagement in physical activity enhances participation experiences, increasing motivation to maintain a healthy lifestyle. Based on the SDT, the positive relationship of CE, EE, and BE in physical activity with FE further supports the engagement theory [17], which posits that these forms of engagement are interrelated with the participation processes and pose a dynamic influence on behavioral outcomes.

To achieve the SDG-3, more attention needs to be paid to the influence of healthy lifestyles on health behavior [39]. Our results indicated that the FE in physical activity significantly and positively influences PEB among Chinese college students, supporting Hypothesis 7. This aligns with the findings of previous research indicating that positive participation experiences enhance individuals’ motivation to maintain routine physical activity [41]. For example, Ada et al. [42] reported that students with higher FE are more likely to engage consistently in activities like walking, running, and swimming. Similarly, Han et al. [44] discovered that college students with substantial participation experience remained self-motivated to engage in physical activity even during the COVID-19 pandemic. These findings highlight the importance of fostering positive experiences in physical activity to encourage sustained engagement. By enhancing FE, college students’ PEB can be promoted, contributing to healthier lifestyles and achieving SDG-3 focused on good health and well-being. Applying SDT, the present study enriches the understanding of how motivational factors like FE influence the maintenance of individual behaviors over time. The continued influence of FE on sustaining PEB underscores the need for interventions that enhance participation experiences to support long-term commitment to physical activity.