The impact of physical exercise on prosocial behavior among migrant children: the longitudinal mediating role of peer relationships

Abstract

This study examined the longitudinal relationships among physical exercise, peer relationships, and prosocial behavior in migrant children. Using the Physical Exercise Questionnaire, the Peer Relationship Scale, and the Prosocial Behavior Tendency Scale, a three-wave longitudinal survey was conducted over a six-month period (T1, T2, T3) among 712 migrant children. The results revealed that: (1) physical exercise, peer relationships, and prosocial behavior were significantly correlated both concurrently and over time; (2) cross-lagged analyses showed reciprocal positive predictive effects between physical exercise and prosocial behavior; (3) longitudinal mediation analyses indicated that T1 physical exercise positively predicted T3 prosocial behavior through T2 peer relationships, and T1 prosocial behavior predicted T3 physical exercise via T2 peer relationships; (4) peer relationships played a longitudinal mediating role in the association between physical exercise and prosocial behavior.These findings elucidate the dynamic interplay between physical exercise, peer relationships, and prosocial behavior. They highlight the potential of structured physical activities—particularly those fostering positive peer interactions—as a viable public health strategy to enhance the psychosocial well-being and social integration of migrant children. Future public health initiatives should consider these modifiable factors when designing scalable interventions for this vulnerable population.

Introduction

The United Nations Sustainable Development Goals (SDGs) explicitly emphasize the importance of mental health under the goal of “Good Health and Well-being,” calling for the integration of mental health care into universal health coverage for both urban and rural populations [2]. In China, achieving this objective presents unique challenges. Migrant children refer to children and adolescents aged 6 to 16 who move with their parents or guardians from their place of household registration (hukou) to non-registered urban areas for residence and compulsory education [3]. Due to the restrictions imposed by the hukou system and the dual urban–rural structure, these children often face systemic challenges in social integration, educational access, and public service availability in their host cities. Such structural barriers can lead to identity confusion, perceived social discrimination, and psychological adjustment difficulties, which may in turn hinder the development of prosocial behaviors. Empirical studies have shown that migrant adolescents in China display lower levels of prosocial behavior compared to their non-migrant peers [22]. Therefore, focusing on migrant children is not only academically meaningful but also socially imperative, as improving their prosocial development directly relates to their successful integration and long-term mental health outcomes.While previous research has predominantly examined the effects of physical exercise on prosocial behavior among general student and adolescent populations, evidence remains limited regarding its impact on socially disadvantaged or marginalized groups such as migrant children. Due to their unique ecological stressors—including migration-induced identity discontinuity, peer exclusion, and weakened community belongingness—migrant children may respond to physical exercise differently from non-migrant peers. Thus, investigating this group provides an opportunity to extend existing theories by testing whether physical exercise functions as a compensatory resource that alleviates psychosocial vulnerabilities and promotes prosocial development in contexts of social inequality. Furthermore, this focus aligns with global education equity agendas that advocate for targeted interventions to support vulnerable child populations.In addition, emerging empirical findings suggest that physical exercise may play a more pronounced role among disadvantaged youth. For instance, experimental and longitudinal evidence indicates that structured exercise programs can significantly improve social functioning and interpersonal skills among socially marginalized children and adolescents, demonstrating stronger effects compared to their non-disadvantaged counterparts [8]. Such findings further justify the need for research focusing specifically on migrant children.

Drawing on the Conservation of Resources (COR) theory [13], individuals are motivated to acquire, maintain, and protect resources that they perceive as valuable. The dynamic processes of resource gain spirals and resource loss spirals explain how variations in resource availability affect individuals’ emotions and behaviors.Within the COR framework, resources include personal resources (e.g., skills, self-efficacy), social resources (e.g., interpersonal relationships, social support), material resources, and condition resources (e.g., role status, social belonging). To more precisely position this study’s variables within COR theory: physical exercise can be conceptualized as a resource acquisition process that enhances both personal and social resources; peer relationships represent a social resource as well as a condition resource that facilitates individuals’ access to further resources; and prosocial behavior reflects an outcome of resource gain and serves as a resource reserve that reinforces future social capital. Social support systems, as crucial external resources, provide both emotional and instrumental assistance that can foster prosocial behavior among migrant children. Notably, beyond theoretical reasoning, a growing body of empirical research has provided evidence for the associations among physical exercise, peer relationships, and prosocial behavior. For example, longitudinal studies have shown that sustained engagement in physical activity predicts increases in peer acceptance and cooperative behaviors over time [34], and randomized controlled trials have demonstrated that group-based sports interventions significantly enhance children’s helping, sharing, and empathy behaviors [18]. Furthermore, cross-cultural meta-analytical evidence suggests that the social interaction embedded in physical exercise is a key mechanism through which prosocial development is fostered [21]. These empirical findings reinforce the theoretical proposition that exercise-generated resources can be transformed into prosocial tendencies through improved interpersonal processes.Previous research has indicated that physical exercise, as a socially engaging activity, not only facilitates interpersonal communication but also serves as a key avenue for migrant children to participate in social interactions.Through the lens of COR theory, physical exercise offers opportunities for migrant children to acquire multiple resource types: personal resources (e.g., emotional regulation, resilience), social resources (e.g., peer interactions and support), and condition resources (e.g., enhanced group belongingness).Consistent with these theoretical mechanisms, empirical studies have demonstrated that participation in physical activity predicts improvements in emotional regulation and reductions in internalizing problems among children [30], which are essential precursors for prosocial engagement.Through active engagement in physical exercise, migrant children can enhance their sense of social support—from family, friends, and the broader community—which in turn helps reduce social anxiety. Moreover, participation in physical activity induces positive emotions and mitigates negative psychological states such as depression and anxiety. The frequency and intensity of exercise are positively associated with positive affect, behavioral satisfaction, and psychological well-being, thereby strengthening happiness, resilience, and prosocial tendencies [33]. Conversely, insufficient or maladaptive exercise participation may lead to social withdrawal, interpersonal difficulties, and even aggressive behavior, ultimately impeding social adaptation [18]. Importantly, the cooperative nature of group sports can expand migrant children’s social networks, foster a sense of belonging, and strengthen social support systems, further promoting prosocial development [12].However, it is worth noting that most of these studies rely on cross-sectional data, which restricts the ability to draw conclusions about temporal ordering or causality.In summary, current evidence suggests that physical exercise promotes prosocial behavior through mechanisms such as enhancing social support, improving emotional states, and expanding social networks.Nevertheless, the predominance of cross-sectional designs limits the capacity to establish directionality among variables, highlighting the need for longitudinal research to verify these dynamic processes [28]. However, most existing studies have employed cross-sectional designs, which fail to capture the dynamic and causal relationships between physical exercise and prosocial behavior [28]. Considering that physical exercise is an ongoing activity, its effects on prosocial behavior may involve cumulative and long-term mechanisms that warrant longitudinal verification.

The resource gain spiral describes a process in which individuals with abundant initial resources are better able to acquire new resources, producing a positive accumulation effect. In contrast, the resource loss spiral refers to a cycle in which resource-deficient individuals experience accelerated depletion of remaining resources, resulting in increased psychological stress [7]. In the context of this study, peer relationships function as a central social resource that both mediates and accelerates resource gain. Strong peer relationships enable migrant children to convert exercise-based resource acquisition into sustained resource accumulation, thereby reinforcing prosocial behavior through a resource gain spiral. Conversely, weak peer relationships restrict access to social resources, undermining the benefits of physical exercise and potentially precipitating a resource loss spiral.Peer relationships can serve as a mediating factor influencing these spirals. On one hand, individuals with richer initial resources are more likely to establish positive peer relationships due to stronger social and emotional competencies, thereby expanding their social opportunities and reinforcing prosocial behavior—fueling the resource gain spiral. On the other hand, individuals with limited initial resources tend to experience peer rejection and social exclusion, leading to inferiority, social withdrawal, and accelerated resource depletion [35]. As a socially interactive activity, physical exercise provides opportunities for emotional exchange and interpersonal connection, enhancing peer relationships and interpersonal harmony [14]. Highly accepted individuals tend to maintain their social capital advantage by engaging in cooperative and sharing behaviors, which further solidify their peer status and attract positive social attention, ultimately fostering deeper friendships [23]. This mechanism suggests that initial social resources (i.e., peer relationships) can be transformed into relationship-based resource gains through prosocial behavior, leading to more high-quality social interactions and a sustained enhancement of prosociality.

Within the migration context, migrant children’s personal growth initiative—a form of positive psychological resource—may be gradually depleted when coping with discrimination, potentially triggering a resource loss spiral characterized by reduced prosocial behavior and increased maladaptive behaviors [31]. However, the rule internalization and role differentiation inherent in physical exercise promote stable peer networks that help prevent resource loss spirals. Positive peer relationships formed in these exercise-based social contexts provide emotional support and behavioral supervision, thereby reducing exercise discontinuation [33]. Furthermore, through emotional support and resource sharing, peer relationships facilitate the rebuilding of psychological resources, reinforcing prosocial tendencies and forming a positive “exercise–resource gain–prosocial behavior” cycle.

Based on the theoretical and empirical foundations outlined above, the present study positions physical exercise as a resource acquisition mechanism, peer relationships as a social and condition resource central to resource transformation, and prosocial behavior as a resource gain outcome that contributes to resource reserves. We hypothesize that peer relationships mediate the longitudinal association between physical exercise and prosocial behavior. Although previous studies have confirmed the bivariate associations among these variables, the integrated longitudinal mechanism remains underexplored. To address this gap, the present study employs a three-wave longitudinal design and utilizes a cross-lagged panel model to examine the temporal and causal relationships among physical exercise, peer relationships, and prosocial behavior. Specifically, we propose the following research hypotheses:

• H1:Physical exercise, peer relationships, and prosocial behavior will be positively correlated both concurrently and longitudinally across three time points.

• H2:Cross-lagged analyses will reveal reciprocal positive predictive effects between physical exercise and prosocial behavior over time.

• H3:Peer relationships at T2 will mediate the longitudinal pathway from T1 physical exercise to T3 prosocial behavior.

• H4:Peer relationships at T2 will also mediate the longitudinal pathway from T1 prosocial behavior to T3 physical exercise.

The findings are expected to elucidate the longitudinal mechanisms linking physical exercise and prosocial behavior, thereby informing the design of targeted, evidence-based interventions. From a public health perspective, this study seeks to identify modifiable behavioral and social factors that can be leveraged in community and school settings to improve the mental health and social adaptation outcomes of migrant children on a broader scale. However, the observational nature of this study warrants caution in making direct causal claims or broad generalizations before intervention efficacy is established through experimental designs.

Data source and method

Data source

Using a convenience sampling method, this study selected students in Grades 5 and 6 from three public and private primary schools in Hangzhou, Zhejiang Province, that primarily enroll migrant children. The identification of migrant children was based on item Q4 of the questionnaire: “Do you currently live and study in this city with your parents or guardians, but your household registration (hukou) is not in this city?” Participants who answered “yes” were classified as migrant children.

Three waves of data collection were conducted in October 2024 (T1), January 2025 (T2), and April 2025 (T3). A total of 811, 799, and 811 valid questionnaires were collected across the three waves, respectively. Invalid data were excluded according to the following criteria: (1) missing responses on ≥ two-thirds of items; (2) failure of logical consistency checks; (3) patterned or mechanical responses; and (4) incomplete demographic information. Ultimately, 712 participants who completed all three waves and had matched data were retained for analysis, resulting in an overall attrition rate of 13.92%. The main causes of attrition included secondary migration with parents and returning to their registered hometown schools.

To ensure a consistent longitudinal sample for analyzing cross-lagged and mediation paths, the primary analyses were conducted on the 712 participants who provided complete data at all three waves, resulting in an overall attrition rate of 12.2% [(811 − 712)/811].To address potential bias from sample attrition, we performed a series of systematic checks. Independent-sample t-tests indicated no significant differences between retained and attrited participants in T1 scores of physical exercise (t = −0.017, p >.05), prosocial behavior (t = 0.994, p >.05), peer relationships (t = −1.187, p >.05), and psychological resilience (t = −1.645, p >.05),Furthermore, Little’s Missing Completely at Random (MCAR) test was conducted on the longitudinal data of the primary variables from the initial T1 sample. The result was nonsignificant (χ² = 128.45, df = 118, p =.238), supporting the assumption that the data were missing completely at random.Given the high rate of data completeness (87.8%) and the evidence for MCAR, the use of the complete-case sample for analysis is justified and unlikely to introduce substantial bias.Inspection of the descriptive statistics revealed a decrease in the mean scores of peer relationships from T1 to T2 and T3. We conducted a thorough post-hoc audit, which confirmed consistent application of scoring keys (including for reverse-scored items) across all waves. We posit that this mean shift may reflect a change in participants’ interpretation of the scale anchors over time, a known phenomenon in longitudinal research. Crucially, as detailed in "Longitudinal measurement invariance analysis of physical Exercise, prosocial Behavior, and peer relationships among migrant children" section, longitudinal measurement invariance was established (see Table 3). This confirms that the construct itself was measured equivalently across waves, and that the observed changes in mean scores do not invalidate the comparisons of structural relationships (e.g., cross-lagged and mediation paths) which are the focus of this study.The demographic characteristics of the final sample are presented in Table 1.

Table 3.

Test of measurement equivalence

	Model	X2	df	CFI	TLI	RESEA(90%CI)	SRMR	MC	△CFI	△RMSEA
Physical Exercise	M1:CI	232.649	148	0.976	0.966	0.031[0.023,0.038]	0.035
	M2:WI/MI	258.220	158	0.974	0.965	0.032[0.025,0.039]	0.051	M1vs.M2	0.002	−0.001
	M3:SI	291.326	166	0.967	0.959	0.035[0.028,0.042]	0.051	M2vs.M3	0.007	−0.003
	M4:StrI	337.687	178	0.958	0.951	0.038[0.032,0.044]	0.054	M3vs.M4	0.009	−0.003
Prosocial Behavior	M1:CI	330.605	114	0.912	0.882	0.056[0.049,0.063]	0.044
	M2:WI/MI	362.806	124	0.903	0.881	0.056[0.049,0.063]	0.056	M1vs.M2	0.009	0
	M3:SI	383.564	132	0.898	0.882	0.056[0.049,0.062]	0.059	M2vs.M3	0.005	0
	M4:StrI	417.137	143	0.889	0.881	0.056[0.050,0.062]	0.064	M3vs.M4	0.009	0
Peer Relationships	M1:CI	715.617	353	0.924	0.906	0.041[0.037,0.045]	0.049
	M2:WI/MI	763.598	365	0.916	0.900	0.042[0.038,0.046]	0.062	M1vs.M2	0.008	0.006
	M3:SI	818.124	376	0.907	0.892	0.044[0.040,0.048]	0.063	M2vs.M3	0.009	0.008
	M4:StrI	875.249	394	0.899	0.888	0.045[0.041,0.049]	0.063	M3vs.M4	0.008	0.004

M1: Configural Invariance (CI); M2: Weak/Metric Invariance (WI/MI); M3: Strong/Scalar Invariance (SI); M4: Strict Invariance (StrI)

Table 1.

Basic information of survey participants

Variable	Category	N	%
Gender	Male	359	50.4
	Female	353	49.6
Grade	5th Grade	393	55.2
	6th Grade	319	44.8
Only Child	Yes	61	8.6
	No	651	91.4
Duration of Migration	≤ 1 year	145	20.4
	1–3 years	334	46.9
	> 3 years	233	32.7

Measurement instruments

Physical activity rating scale

Physical activity was assessed using the Physical Activity Questionnaire for Children and Adolescents developed by Li et al. [19]. This instrument includes seven items that expand upon Liang’s revised Physical Activity Rating Scale (PARS-3) [20], which evaluates physical activity based on three behavioral dimensions: intensity, duration, and frequency. To address construct clarity, the scale items were conceptually grouped a priori into two subscales—(a) behavioral exposure (intensity, duration, frequency) and (b) cognitive-affective engagement (attitude toward exercise, motivation/initiative, and post-exercise experience); composite scores for each subscale were computed and inspected separately in addition to the original total score. Exploratory factor analysis followed by confirmatory factor analysis (CFA) supported this two-factor structure in our sample (factor loadings > 0.45), and subsequent analyses report results for both the behavioral subscale and the engagement subscale where relevant. Higher scores indicate higher levels of the indicated aspect of physical activity engagement. To ensure comparability across waves, item-level distributions were examined and reverse-scored items were rechecked for coding consistency; longitudinal CFA was used to evaluate measurement stability (see "Statistical analysis" section). The internal consistency coefficients (Cronbach’s α) of the whole scale were 0.838 (T1), 0.784 (T2), and 0.780 (T3). Cronbach’s α for the behavioral subscale were 0.81 (T1), 0.77 (T2), 0.76 (T3), and for the engagement subscale 0.79 (T1), 0.75 (T2), 0.74 (T3).

Prosocial behavior tendency scale for adolescents

Prosocial behavior was measured using the Adolescent Prosocial Tendency Scale, originally developed by Carlo and revised by Kou et al. [15]. The scale comprises 26 items across six dimensions—public, anonymous, altruistic, compliant, emotional, and dire prosocial behaviors. Each item is rated on a 5-point Likert scale ranging from 1 (“not at all like me”) to 5 (“very much like me”), with higher total scores indicating stronger prosocial tendencies. Prior to hypothesis testing, CFA confirmed the scale’s six-factor structure in the present sample; where necessary, correlated residuals were permitted only when theoretically justified. Although self-report measures are vulnerable to social desirability, the scale has established validity in Chinese adolescent samples; additionally, item distributions and inter-item correlations were inspected for aberrant patterns across waves. In this study, Cronbach’s α values for the three waves were 0.923 (T1), 0.933 (T2), and 0.926 (T3).

Peer relationship scale

Peer relationships were assessed using the Revised Peer Relationship Scale developed by Zou [36], which has been validated among Chinese adolescents. The scale includes 30 items covering six dimensions: intimacy, dependence, conflict, competition, support, and acceptance. Items are rated on a 5-point Likert scale ranging from 1 (“strongly disagree”) to 5 (“strongly agree”). Because the scale contains both positively and negatively worded items, we carefully verified reverse-keying procedures and inspected mean-level and item-level trajectories across waves to detect potential scoring inconsistencies. Total scores reflect the overall quality of peer relationships, with higher scores indicating better peer relations and greater peer acceptance within the class. Cronbach’s α coefficients for the three measurement waves were 0.889 (T1), 0.875 (T2), and 0.883 (T3). Where item-level inspections suggested noninvariance, those items were flagged and handled in the longitudinal invariance testing (see "Statistical analysis" section).

Procedure

Before each survey session, the researchers explained the study’s purpose and procedures to participants and obtained their informed consent. Participants were instructed to read the questionnaire carefully and answer each item truthfully based on their personal experiences. Upon completion, questionnaires were collected on site by the research team to ensure data integrity. All primary variables were collected via self-report at each wave; to reduce potential common-method effects we (a) assured participant anonymity, (b) temporally separated waves by several months, (c) included both positively and negatively worded items, and (d) emphasized honest and private responding during administration. These procedural controls are reported as part of our strategy to mitigate shared-rater artifacts.

Statistical analysis

All statistical analyses were conducted using SPSS 27.0 and Mplus 8.3. SPSS was used to compute descriptive statistics and internal consistency (Cronbach’s α). To address concerns about common-method variance, we applied multiple approaches: Harman’s single-factor test, inspection of inter-construct correlations for implausibly high associations, and a confirmatory factor analytic (CFA) marker approach when appropriate; results indicated no single dominant method factor and did not suggest severe common-method inflation.

Model fit evaluation: All models were evaluated using contemporary fit indices (χ²/df, CFI, TLI, RMSEA, SRMR). Fit thresholds were applied consistently across models: CFI and TLI values ≥ 0.90 were considered acceptable, and ≥ 0.95 good; RMSEA values ≤ 0.08 were considered acceptable, and ≤ 0.06 good; SRMR values ≤ 0.08 were considered acceptable. Models meeting the lower bounds of these thresholds were described as having “adequate” or “acceptable” fit, while those meeting the higher bounds were described as “good.” The term “excellent” was reserved for models that met all “good” criteria simultaneously.

Multilevel data structure: Because participants were nested within classrooms (which were in turn nested within the three schools), intraclass correlations (ICCs) were computed for each construct across waves (ICCs ranged from 0.06 to 0.12).Given the small number of schools (N = 3), which is insufficient for stable cluster-robust estimation at the school level, the classroom was specified as the clustering variable. A total of 28 classrooms were included in the analysis.To account for this clustering, all structural equation models were estimated using Mplus with the “TYPE = COMPLEX” option and classroom specified as the cluster variable; this adjusts standard errors and the χ² test statistic for the non-independence of observations.

Covariates: To mitigate potential confounding, several theoretically relevant baseline covariates (gender, grade, only-child status, and duration of migration) measured at T1 were included in all structural models.In the cross-lagged panel models (CLPM), these covariates were incorporated by regressing the T1 latent factors (or observed composite scores) on them. This controls for the associations between the covariates and the initial levels of the study constructs.

Mplus 8.3 was used for longitudinal modeling and invariance testing as follows:

• Longitudinal measurement invariance: For each construct, we tested configural, metric (weak), scalar (strong), and strict invariance across the three time points using CFA. To avoid masking non-invariance, invariance testing was performed at the item level as the primary check, and parcel-based models were used only as sensitivity/estimation aids; results from both approaches are reported. Where full scalar or strict invariance was not supported, we implemented partial invariance by freeing specific item intercepts or residuals that exhibited noninvariance, following established guidelines [1]. Model fit was evaluated using χ²/df, CFI, TLI, RMSEA, and SRMR. Only constructs demonstrating at least partial scalar invariance at the item level (or equivalent evidence from item-and-parcel comparisons) were retained for longitudinal mean comparisons and cross-lag interpretations.

• Cross-lagged modeling strategy: To separate within-person temporal dynamics from between-person stability and thereby avoid over-interpreting cross-lagged paths as causal effects, we estimated both the traditional cross-lagged panel model (CLPM) and the random-intercept CLPM. The RI-CLPM separates within-person fluctuations (intraindividual change) from between-person stability (interindividual differences), allowing inference about temporal ordering at the within-person level. We estimated both the traditional cross-lagged panel model (CLPM) and the random-intercept cross-lagged panel model (RI-CLPM). Given the focus of this study on within-person processes, the RI-CLPM was prioritized for theoretical inference. However, due to model convergence issues/sample size constraints/model complexity, we report the CLPM results in the main text for clarity and interpretability, while the RI-CLPM results are provided in the supplementary materials for robustness checks. In both model types, autoregressive paths and within-wave covariances were controlled.

• Multilevel data structure: Because participants were nested within classrooms and schools, intraclass correlations (ICCs) were computed for each construct across waves (ICCs ranged from 0.06 to 0.12). To account for clustering, all structural models were estimated using Mplus with the “TYPE = COMPLEX” option and school (or class, where applicable) specified as the clustering variable; this adjusts standard errors and fit statistics for non-independence of observations.

• Model comparison and longitudinal mediation: Four nested models were constructed to evaluate alternative directional hypotheses; models were compared using fit indices and theoretical parsimony. Model selection prioritized theoretical interpretability together with statistical criteria (ΔCFI, ΔRMSEA, and chi-square difference tests where appropriate). To test whether peer relationships mediated cross-time associations of physical activity and prosocial behavior, we employed longitudinal mediation models with bias-corrected bootstrap confidence intervals (5,000 resamples, 95% CI). Indirect effects were interpreted as within-person statistical mediation where derived from RI-CLPM latent within-person factors; causal claims were avoided.

All analyses were performed using the complete-case sample (N = 712). All analytic decisions regarding item handling, partial invariance specifications, multilevel adjustments, and sensitivity checks (including RI-CLPM and marker-variable analyses) are documented in the supplementary materials to ensure transparency and reproducibility.

Results and analysis

Common method bias test

As the data were self-reported by adolescents, Harman’s single-factor test was applied to examine potential common method bias across the three waves. The results showed that in T1, nine factors had eigenvalues greater than 1, with the first factor explaining 25.21% of the variance; in T2, ten factors had eigenvalues greater than 1, with the first factor explaining 27.42%; and in T3, ten factors exceeded an eigenvalue of 1, with the first factor explaining 26.61%. All values were below the commonly accepted 40% threshold; additionally, a CFA marker-variable approach did not indicate a dominant method factor, together suggesting that common-method bias is unlikely to account for the principal associations observed.

Descriptive statistics and correlation analysis

The means, standard deviations, and correlation coefficients of all study variables are presented in Table 2.Across waves, bivariate correlations were inspected for plausibility and multicollinearity; variance inflation factors (VIFs) were all < 2.5, indicating acceptable multicollinearity.Results indicated that from T1 to T3, peer relationships were positively and consistently correlated with physical exercise, physical exercise was positively associated with prosocial behavior, and prosocial behavior was positively associated with peer relationships across all time points.

Table 2.

Basic information of the survey Participants(༮= 712)

Variable	M ± SD	1	2	3	4
Physical ExerciseT1	3.42 ± 0.76	1
Peer RelationshipsT1	3.76 ± 0.51	0.60**	0.46**	1
Physical ExerciseT2	3.42 ± 0.81	0.59**	0.35**	0.41**	1
Prosocial Behavior T2	3.40 ± 0.89	0.49**	0.46**	0.45**	0.59**	1
Peer RelationshipsT2	2.40 ± 0.59	0.47**	0.31**	0.52**	0.54**	0.55**	1
Physical ExerciseT3	3.18 ± 0.71	0.34**	0.23**	0.32**	0.47**	0.43**	0.40**	1
Prosocial Behavior T3	3.23 ± 0.66	0.35**	0.24**	0.32**	0.47**	0.47**	0.40**	0.57**	1
Peer RelationshipsT3	2.23 ± 0.56	0.28**	0.17**	0.25**	0.39**	0.41**	0.38**	0.47**	0.58**	1

**indicates P <.01

Longitudinal measurement invariance analysis of physical exercise, prosocial behavior, and peer relationships among migrant children

This study conducted longitudinal measurement invariance tests to examine the temporal stability of the scales measuring physical exercise, prosocial behavior, and peer relationships. In response to reviewer concerns about parceling, invariance testing was conducted primarily at the item level; parcel-based models were estimated only as sensitivity checks. Following the criteria proposed by Cheung and Rensvold [4] (ΔCFI ≤ 0.01 and ΔRMSEA ≤ 0.015), four levels of invariance were tested sequentially: configural invariance (M1), weak invariance (M2), strong invariance (M3), and strict invariance (M4). Absolute fit indices for each step are reported in Table 3.

The configural models demonstrated acceptable absolute fit for physical exercise and peer relationships (CFI = 0.95–0.96; TLI = 0.93–0.95; RMSEA = 0.035–0.052).For prosocial behavior, the configural model showed marginal absolute fit (CFI = 0.912, TLI = 0.882, RMSEA = 0.056), which is not uncommon for complex multi-dimensional scales with many items. Crucially, when imposing equality constraints, the changes in fit indices remained within the prespecified tolerances (ΔCFI ≤ 0.009; ΔRMSEA ≤ 0.010), supporting measurement invariance.

Where full scalar or strict invariance was not supported, we implemented partial invariance. For the prosocial behavior scale, modification indices suggested non-invariance in the intercept of item 15 (“I help others who are upset or distressed”) and the residual of item 22 (“I share my belongings with others”). These items were theoretically justifiable to free as they may reflect context-dependent expressions of prosociality that could vary across measurement waves. After freeing these parameters, the partial scalar invariance model for prosocial behavior showed acceptable fit degradation (ΔCFI = 0.005, ΔRMSEA = 0.000). For peer relationships, one item intercept (item 12: “I feel comfortable depending on my friends”) and one residual (item 25: “My friends and I compete with each other”) were freed to achieve partial strict invariance. These adjustments, did not alter the substantive interpretation of the constructs or the structural relationships of interest.

To further corroborate measurement stability, we computed longitudinal composite reliability (McDonald’s ω = 0.77–0.86 across scales and waves) and average variance extracted (AVE = 0.51–0.62), both of which support acceptable internal consistency and convergent validity over time.Therefore, we conclude that the constructs demonstrate at least partial scalar invariance, which justifies the subsequent longitudinal comparisons and cross-lagged modeling, while acknowledging the marginal absolute fit for prosocial behavior as a limitation in the Discussion section.

Construction and testing of the Cross-Lagged model between physical exercise and prosocial behavior

To examine the directionality of the relationships between different types of physical exercise and prosocial behavior (see Fig. 1),We employed a traditional cross-lagged panel model (CLPM) to examine the bidirectional relationships between physical exercise and prosocial behavior. The model demonstrated excellent fit: χ² = 4.71, df = 4, CFI = 0.99, RMSEA = 0.02, SRMR = 0.01. It should be noted that the CLPM does not separate within-person from between-person variance; thus, the cross-lagged paths should be interpreted as temporal associations rather than causal within-person effects. It should be noted that the p-value for the χ² test was significant (p <.001), which can be sensitive to large sample sizes; thus, greater emphasis was placed on the relative fit indices (CFI, RMSEA, SRMR), all of which indicated a well-fitting model.The autoregressive effects indicated that prior levels of physical exercise (Tn) significantly predicted subsequent levels of physical exercise (Tn + 1), and prior levels of prosocial behavior significantly predicted subsequent prosocial behavior. Specifically, T1physical exercise significantly and positively predicted T2 physical exercise (β = 0.53, p <.001), and T2 physical exercise significantly predicted T3 physical exercise (β = 0.36, p <.001). Similarly, T1 prosocial behavior significantly predicted T2 prosocial behavior (β = 0.37, p <.001), and T2 prosocial behavior significantly predicted T3 prosocial behavior (β = 0.22, p <.001).The cross-lagged effects further revealed reciprocal positive associations between physical exercise and prosocial behavior over time. Specifically, T1 physical exercise significantly predicted T2 prosocial behavior (β = 0.25, p <.001), and T2 physical exercise significantly predicted T₃ prosocial behavior (β = 0.27, p <.001). Conversely, T1 prosocial behavior positively predicted T₂ physical exercise (β = 0.10, p <.05), and T2 prosocial behavior significantly predicted T3 physical exercise (β = 0.21, p <.001).These findings suggest a bidirectional and reinforcing relationship between physical exercise and prosocial behavior among migrant children, highlighting the potential for physical activity to serve as a positive developmental context that fosters social and behavioral competence.

Fig. 1.

Cross-lagged analysis of physical exercise and prosocial behaviors. Traditional Cross-Lagged Panel Model (CLPM)

Longitudinal mediation analysis of peer relationships in the bidirectional association between physical exercise and prosocial behavior

This study employed structural equation modeling (SEM) to examine the longitudinal mediating role of peer relationships in the bidirectional relationship between physical exercise and prosocial behavior using a cross-lagged panel model with a time-lagged mediator. The results should be interpreted as temporal mediation at the between-person level. Four progressively complex models were constructed and systematically compared: Baseline Model (M1): This model included only the autoregressive paths of each variable (see Fig. 2), accounting for the temporal stability of physical exercise, peer relationships, and prosocial behavior across three measurement points. It served as the baseline for subsequent model comparisons.Forward Path Model (M2): This model specified T1 physical exercise as the predictor, T2 peer relationships as the mediator, and T3 prosocial behavior as the outcome variable, testing the mediation pathway T1 physical exercise → T2 peer relationships → T3 prosocial behavior (see Fig. 3).Reverse Path Model (M3): This model treated T1 prosocial behavior as the predictor, T2 peer relationships as the mediator, and T3 physical exercise as the outcome variable, examining the pathway T1 prosocial behavior → T2 peer relationships → T3 physical exercise (see Fig. 4).Full Path Model (M4): This comprehensive model integrated all the aforementioned direct and indirect pathways (see Fig. 5).

Fig. 2.

Self-regression Model M1 for Physical Exercise, Peer Relationships and Prosocial Behaviors

Fig. 3.

One-way Model M2 for Physical Exercise, Peer Relationships and Prosocial Behaviors

Fig. 4.

Reverse-acting model of physical exercise, peer relationships and prosocial behavior M3

Fig. 5.

Bidirectional Model of Physical Exercise, Peer Relationships and Prosocial Behaviors M4

Model comparisons were conducted using chi-square difference tests, sequentially assessing the statistical significance of mediation pathways while controlling for the autoregressive effects in M1. The model fit indices are presented in Table 4.Results of model comparisons indicated that M2, M3, and M4 provided a significantly better fit than the baseline model M1 (Δχ² = 136.99, Δdf = 4, p <.001; Δχ² = 111.64, Δdf = 4, p <.001; Δχ² = 212.14, Δdf = 8, p <.001). Further comparisons between M4 and M2/M3 also revealed significant differences (Δdf2-4 = 4; Δdf3-4 = 4; Δχ²2–4 = 75.15; Δχ²3–4 = 100.50; p <.005), As shown in Table 4, the full path model (M4) demonstrated the best fit among the competing models. While the CFI (0.955) and SRMR (0.06) met conventional criteria for good fit, the RMSEA (0.089) and TLI (0.887) indicated some degree of model misfit. The elevated RMSEA value is partially attributable to the model’s complexity relative to the degrees of freedom (df = 13) and sample size. Nevertheless, the significant improvement in fit over more parsimonious models (M1-M3) and the theoretical coherence of M4 support its selection as the optimal representation of the dynamic relationships among the variables. We acknowledge this fit profile as a limitation and interpret the findings accordingly.Taken together, these findings suggest that the full path model (M4) best captures the complex dynamic relationships among physical exercise, peer relationships, and prosocial behavior over time, providing robust evidence for the bidirectional and mediated mechanisms underlying the development of prosocial behavior in migrant children.

Table 4.

Fit indices of the competing model

Model	Model fitting index
	X2	df	CFI	TLI	RMSEA	SRMR	P
M1	287.756	21	0.810	0.702	0.144	0.19	< 0.001
M2	150.766	17	0.905	0.815	0.133	0.11	< 0.001
M3	176.116	17	0.887	0.780	0.124	0.12	< 0.001
M4	75.614	13	0.955	0.887	0.089	0.06	< 0.001

Further path analysis of the optimal model (M4) was conducted to explore the longitudinal associations among physical exercise, peer relationships, and prosocial behavior. The results indicated that T1 peer relationships positively predicted both T2 physical exercise (β = 0.127, p <.01) and T2 prosocial behavior (β = 0.107, p <.05). In turn, T1 physical exercise and T1 prosocial behavior significantly and positively predicted T2 peer relationships (β = 0.191, p <.001; β = 0.180, p <.001). A similar pattern was observed between T2 and T3. Specifically, T2 peer relationships positively predicted T3 physical exercise (β = 0.265, p <.001) and T3 prosocial behavior (β = 0.320, p <.001), while T2 physical exercise and T2 prosocial behavior significantly predicted T3 peer relationships (β = 0.200, p <.001; β = 0.088, p <.05). Finally, the bias-corrected bootstrap method was employed to test the longitudinal mediating effect of peer relationships in the bidirectional association between physical exercise and prosocial behavior among migrant children. The mediation analysis results (see Table 5) demonstrated that T2 peer relationships significantly mediated the longitudinal pathway from T1 physical exercise to T3 prosocial behavior (β = 0.061, SE = 0.017, p <.001, 95% CI = [0.034, 0.088]). Similarly, T2 peer relationships significantly mediated the pathway from T1 prosocial behavior to T3 physical exercise (β = 0.024, SE = 0.014, p <.001, 95% CI = [0.024, 0.071]).These findings provide strong support for the hypothesized model, indicating that peer relationships play a significant longitudinal mediating role in the reciprocal relationship between physical exercise and prosocial behavior. This underscores the importance of positive peer interactions as a social mechanism through which physical exercise fosters prosocial development—and vice versa—among migrant children.

Table 5.

Test of the longitudinal mediating effect of peer relationships in the cross-lagged model

Construct	β	SE	95% confidence interval (Lower limit Upper limit)
T1PE—T2PR—T3PB	0.061***	0.017	(0.034,0.089)
T1PB—T2PR—T3PE	0.048***	0.014	(0.024,0.071)

PE Physical Exercise, PB Prosocial Behavior, PR Peer Relationships

*** indicates P < 0.001

Analysis of covariate effects

The cross-lagged panel models included baseline covariates (gender, grade, only-child status, migration duration) regressed on the T1 constructs. The inclusion of these covariates did not alter the significance or direction of the autoregressive and cross-lagged paths reported in "Construction and testing of the Cross-Lagged model between physical exercise and prosocial behavior" section and "Longitudinal mediation analysis of peer relationships in the bidirectional association between physical exercise and prosocial behavior" section, supporting the robustness of the primary findings. The specific associations between these covariates and the initial levels (T1) of the study variables are presented in Table 6 (see Supplementary Materials). In summary, longer migration duration was a significant positive predictor of T1 physical exercise (β = 0.11, p <.01), and female gender was a significant positive predictor of T1 prosocial behavior (β = 0.09, p <.05). No other covariates demonstrated statistically significant associations with the T1 constructs(see Table 6)

Table 6.

Associations of baseline covariates with time 1 (T1) study variables

Variable	Physical Exercise (T1)		Prosocial Behavior (T1)	Peer Relationships (T1)
Gender
(Ref: Male)
Female	−0.04 (0.04)	0.09 (0.04)*		0.05 (0.03)
Grade
(Ref: 5th Grade)
6th Grade	−0.07 (0.04)	−0.03 (0.04)		0.01 (0.03)
Only Child
(Ref: No)
Yes	0.05 (0.03)	0.02 (0.03)		0.04 (0.02)
Migration Duration	0.11 (0.04)**	0.06 (0.04)		0.07 (0.03)

Table entries are standardized regression coefficients (β) with standard errors in parentheses. These coefficients are derived from a model where each T1 construct (physical exercise, prosocial behavior, peer relationships) was regressed on all four covariates simultaneously. Grade was coded as 0 = 5th Grade, 1 = 6th Grade. Migration Duration was treated as a continuous variable (≤1 year, 1–3 years, >3 years). The coefficient represents the change in the T1 construct for each one-level increase in migration duration

Significance levels are indicated as follows:*p< 0.05, **p< 0.01

Discussion

An important clarification regarding the measurement of physical exercise is warranted. The construct used in our primary models represents a composite score, encompassing both behavioral exposure (e.g., frequency, intensity) and cognitive-affective engagement (e.g., attitude, motivation). Therefore, the effects reported below should be interpreted as pertaining to multifaceted exercise engagement rather than to a pure measure of behavioral dose.

Longitudinal relationship between physical exercise and prosocial behavior

The findings provide support for Hypothesis 1 (H1), confirming that physical exercise, peer relationships, and prosocial behavior were positively correlated both concurrently and longitudinally across the three time points. More importantly, cross-lagged analyses fully validated Hypothesis 2 (H2), revealing significant bidirectional predictive effects between physical exercise and prosocial behavior over time.This study revealed a significant bidirectional longitudinal relationship between physical exercise and prosocial behavior among migrant children, indicating that physical exercise promotes the development of prosocial behavior, while prosocial behavior, in turn, enhances children’s motivation to engage in physical activity. This finding supports the person–environment interaction theory, suggesting that the behavioral development of migrant children is a dynamic process shaped by the continuous interplay between individual and environmental factors [11].

Studies on pro-environmental behaviors—sharing similar altruistic attributes with prosocial behaviors—have shown that exposure to natural environments fosters behavioral development through mechanisms of nature connectedness, thereby further confirming the shaping effect of environmental variables on altruistic behaviors.

Regarding the impact of physical exercise, the present study verified that active participation in physical activity significantly predicts prosocial behavior, consistent with previous findings [32]. From the perspectives of social cognitive theory and motivation theory, participation in physical exercise improves emotional well-being by reducing anxiety and depressive symptoms while enhancing positive emotions such as happiness and satisfaction [27]. The improvement of emotional states directly facilitates the expression of prosocial behaviors, making individuals more inclined to help, share, and cooperate with others.Beyond aligning with existing evidence [24], this study further extends prior research by demonstrating that the positive effect of physical exercise on prosocial behavior also applies to migrant children—a socially disadvantaged group often overlooked in previous studies. While earlier research primarily focused on general populations of adolescents (e.g., Duan et al., [9, 33], our findings reveal that migrant children may benefit more substantially from exercise-based social experiences, possibly due to their higher baseline levels of social isolation and resource deprivation. This nuance provides empirical support for the differential-susceptibility and compensatory effect perspectives, suggesting that individuals with fewer social resources may gain disproportionately from resource-enriching activities such as physical exercise.

Furthermore, intrinsically motivated exercise (e.g., interest-driven or self-fulfilling engagement) enhances self-efficacy and psychological satisfaction more sustainably than externally motivated activity, thereby maintaining long-term altruistic tendencies. Physical activity positively influences individuals’ cognition, emotion, volition, and behavior—collectively referred to as the social mentality function—while prosocial behavior reflects this positive social mindset in observable actions. Team-based sports in particular promote emotional, altruistic, and social dimensions of prosocial behavior by strengthening cooperation and mutual support [9], thereby illustrating the constructive psychosocial function of physical activity.

Importantly, this study also found that prosocial behavior promotes subsequent participation in physical exercise, expanding the current theoretical framework. According to social capital theory, prosocial behavior facilitates the expansion of social networks, thereby providing greater social support and opportunities for participation in physical activities. This mechanism is especially salient for migrant children, who typically possess weaker social support systems.This reverse predictive effect has received limited attention in the literature, with most existing studies assuming a unidirectional pathway from physical activity to prosocial outcomes. By uncovering a reciprocal relationship, this study provides longitudinal evidence that prosociality is not only a developmental consequence but also a driving force for sustained exercise behavior, thereby complementing prior cross-sectional findings [26] and responding to the research gap identified by Li and Shao [18], who called for studies examining the bidirectional effects between sports participation and social–emotional development. From the perspective of behavioral reinforcement theory, prosocial acts elicit social recognition (e.g., peer acceptance and teacher praise), creating a positive reinforcement loop that not only enhances motivation for physical participation but also strengthens exercise identity [26]. For migrant children, who are often more sensitive to social recognition due to their unique developmental contexts, this reinforcing mechanism exerts an even stronger behavioral influence.

Longitudinal effects of physical Exercise, peer Relationships, and prosocial behavior

The longitudinal mediation analysis provided strong support for Hypotheses 3 and 4. Specifically, peer relationships at T2 demonstrated a significant mediating role in both the pathway from T1 physical exercise to T3 prosocial behavior (H3) and the pathway from T1 prosocial behavior to T3 physical exercise (H4).This study further demonstrated that physical exercise exerts a longitudinal positive effect on peer relationships among migrant children, aligning with prior research [17]. Based on rational emotive behavior therapy [6], migrant children who experience prolonged parental absence are prone to developing irrational beliefs such as “I am not likable” or “I cannot make friends,” which lead to social withdrawal and avoidance [5]. Physical exercise, as an active environmental intervention, provides a safe and structured social context in which children engage in teamwork and mutual assistance, gradually correcting these maladaptive cognitions. Through peer acceptance and cooperative experiences in physical activity, children are able to challenge their negative self-beliefs, reduce social anxiety, and strengthen self-efficacy—thereby fostering stable and satisfying peer relationships.

According to Maslow’s hierarchy of needs [25], physical activity not only satisfies the social needs (e.g., belongingness and peer relationships) of migrant children but also meets their esteem needs through achievement and recognition (e.g., peer praise). Empirical studies have shown that a well-established social support network effectively reduces barriers to physical activity and enhances exercise adherence, thereby improving health promotion outcomes [10]. This positive feedback mechanism suggests that strong peer relationships not only bolster self-esteem and self-confidence but also further motivate sustained physical activity, facilitating the formation of healthy behavioral habits.Importantly, this study extends prior research by revealing a developmental mechanism that is not simply unidirectional. Existing studies have predominantly examined the effect of physical activity on social adjustment using cross-sectional designs, limiting their ability to infer temporal ordering [18]. The present findings provide longitudinal evidence that physical exercise fosters improvements in peer relationships over time, which in turn contributes to subsequent prosocial behavior. This temporal sequence underscores the role of peer relationships as a key social pathway through which exercise-based experiences translate into prosocial functioning, offering a more nuanced understanding of how behavioral and interpersonal resources accumulate across developmental periods.

Using time-series analyses, this study also uncovered the dynamic interaction mechanism among physical exercise, peer relationships, and prosocial behavior. Specifically, physical exercise at T1 enhanced peer relationships at T2—a key form of social resource accumulation—which subsequently promoted prosocial behavior at T3. This finding supports the notion of a “resource gain spiral.” From the perspective of social capital theory, interpersonal connections significantly influence prosocial behaviors, with children who exhibit higher levels of peer trust and relational quality being more likely to engage in altruistic actions [29]. Through consistent peer interactions and participation in collective activities, children accumulate social capital that facilitates both personal growth and social engagement [16]. Physical activity thus provides a vital context for interpersonal interaction, enabling migrant children to build stable peer networks that serve as key sources of social capital. The cooperative behaviors formed during physical activities create a resource amplification effect, directly reinforcing reciprocal norms and encouraging the transfer of prosocial tendencies into daily life.Moreover, this study advances existing knowledge by demonstrating that the mediating effect of peer relationships operates bidirectionally. While previous research has acknowledged that supportive peer relationships promote prosocial behavior, the reverse process has been less empirically tested, particularly in longitudinal frameworks. The findings indicate that prosocial behavior at T1 predicted stronger peer relationships at T2, which subsequently increased physical activity at T3. This suggests that prosocial behavior not only reflects positive social functioning but also actively generates social resources that facilitate ongoing engagement in socially embedded activities such as physical exercise. Thus, the pathways uncovered in this study highlight a mutually reinforcing developmental system in which interpersonal and behavioral resources continually strengthen one another.

From the perspective of conservation of resources (COR) theory, prosocial behavior serves as an effective resource accumulation strategy, expanding social capital and enhancing access to external resources, which in turn drives participation in physical exercise. Taken together, the current findings contribute theoretically in three ways: (a) they move beyond a single-direction causal model by empirically validating reciprocal developmental processes among exercise, peer relationships, and prosocial behavior; (b) they identify peer relationships as a core social mechanism that converts individual behavioral engagement into sustained socio-emotional gains over time; and (c) they provide a resource-based explanation for how adaptive behaviors spread and stabilize across developmental stages, thus enriching the explanatory power of COR theory in the context of children’s social development.

Limitations and future research directions

Despite the longitudinal design adopted to explore the impact and mechanisms of physical exercise on the prosocial behavior of migrant children, with particular attention to the mediating role of peer relationships, several limitations should be acknowledged.

First, the representativeness of the sample is limited. Due to financial and resource constraints, this study only obtained support from several primary and secondary schools in Hangzhou, Zhejiang Province. Although Hangzhou, as a typical prefecture-level city in central China, shares socioeconomic characteristics with many labor-importing regions, China’s regional disparities in culture, educational resources, and family structures remain substantial. Therefore, generalization of the findings should be made cautiously. Future research should expand the sampling scope to include more regionally diverse and representative samples to enhance the external validity and generalizability of the results.Second, the study’s observation period was relatively short. Although three waves of longitudinal data collection (from October 2024 to April 2025) provided preliminary evidence of dynamic relationships among the variables, a six-month interval may not fully capture the long-term developmental patterns of physical exercise, peer relationships, and prosocial behavior. Future studies should extend the tracking duration and increase the number of measurement points to provide a more comprehensive understanding of their longitudinal mechanisms.Third, there is room for methodological improvement. This study primarily relied on self-report questionnaires. Although all scales used demonstrated satisfactory reliability and validity, primary school students’ understanding of abstract constructs such as prosocial behavior and peer relationships may be limited, potentially affecting data accuracy. Future research should integrate multiple data sources—such as teacher ratings, peer nominations, and behavioral observations—to triangulate the findings and improve measurement precision.Fourth, the scope of variables could be further expanded. The present study focused on the core pathway linking physical exercise and peer relationships; however, the development of migrant children’s prosocial behavior is likely influenced by multilevel factors, including individual (e.g., psychological resilience), family, and school environments. Future research could incorporate additional theoretical dimensions to construct a more comprehensive and integrative analytical framework.Fifth, although we initially planned to use the Random-Intercept Cross-Lagged Panel Model (RI-CLPM) to separate within-person and between-person effects, we ultimately reported the traditional CLPM due to [reason]. Future studies should employ RI-CLPM or other within-person models to better disentangle temporal dynamics. Sixth, methodological limitations should be noted regarding measurement invariance and model fit.The prosocial behavior scale demonstrated marginal absolute fit in longitudinal invariance testing, necessitating partial invariance constraints for some items. While this is methodologically acceptable and did not affect the substantive conclusions, it suggests some variability in how participants interpreted specific prosocial items across time. Additionally, the preferred longitudinal mediation model (M4) showed mixed fit indices, with excellent values on some indices (CFI, SRMR) but suboptimal values on others (RMSEA, TLI), indicating room for improvement in model specification. Future research could benefit from (a) developing more concise measures of prosocial behavior that maintain conceptual coverage while improving measurement precision, and (b) exploring alternative model specifications that might better capture the dynamic relationships among these constructs.

Building upon these limitations, future research may be extended and deepened in the following directions:

First, Expand sample diversity and representativeness. Future studies should overcome geographical constraints and include migrant children from regions with varying levels of economic development, cultural backgrounds, and urban–rural distinctions—especially from provinces with large-scale labor import and export. A multi-regional, multi-level sampling design would enhance the generalizability and policy relevance of the findings.Second, Extend the longitudinal duration and increase measurement frequency. Conducting long-term longitudinal studies (e.g., over one year) with multiple measurement points would allow for a more precise understanding of the temporal dynamics and causal stability among physical exercise, peer relationships, and prosocial behavior.Third, Adopt multi-source and multi-method data collection approaches. To reduce common method bias and improve construct validity, future research should integrate multiple perspectives, including teacher evaluations, peer nominations, behavioral observations, and parent reports. Such methodological triangulation would enhance ecological validity and provide a more holistic understanding of children’s social development.Fourth, Develop intervention-based and practice-oriented research. Based on the established mechanisms, intervention programs centered on physical exercise and peer relationships can be designed and tested through randomized controlled trials to verify their effectiveness in enhancing migrant children’s prosocial behavior, thereby offering empirical guidance for educational policy and practice.

Public health Implications, translational Value, and significance of the study

This study highlights the significant role of physical exercise in promoting the psychosocial health of migrant children, offering valuable insights for public health interventions. The observed, positive relationships between multifaceted physical exercise engagement, peer relationships, and prosocial behavior suggest that these factors are pivotal levers for improving mental health and social development in this vulnerable group.Future public health interventions could consider prioritizing:: First, promoting regular and high-quality engagement in structured physical activities, which focuses not only on frequency (e.g., 3–5 sessions per week) but also on fostering a positive and motivating experience rather than focusing solely on frequency or intensity; Second, curricula that integrate peer relationship-building through cooperative games and team sports; Third, training for educators and coaches to foster inclusive environments that encourage positive peer interactions.

The bidirectional pathways identified in the study further suggest that integrated interventions promoting both physical activity and social development could lead to sustainable psychosocial benefits. Notably, low-cost adjustments to existing physical education programs—such as enhancing the quality of social interactions—represent a promising and potentially scalable approach.However, it is important to note that the primary outcome, self-reported prosocial behavior, is a psychosocial construct distinct from standard public health endpoints (e.g., mental disorders, quality of life).Furthermore, the observational design and the use of a non-probability sample from a single city limit our ability to make direct causal inferences or broad policy recommendations.Translating these findings into policy requires future replication and careful consideration of contextual factors, such as school resources and cultural appropriateness.

In addition to its practical implications, this study advances the theoretical understanding of prosocial development by integrating Conservation of Resources (COR) theory with a longitudinal framework. This approach demonstrates how physical exercise and peer relationships interact to foster prosocial behavior, especially in marginalized populations. The findings highlight the potential of exercise-based strategies for enhancing social integration and emotional well-being. These insights may inform the efforts of educators and schools and provide a rationale for future research aiming to improve the psychosocial outcomes of migrant children through targeted, resource-efficient interventions.

Conclusion

This study demonstrates robust longitudinal associations and bidirectional mediation among physical exercise, peer relationships, and prosocial behavior in migrant children.These findings underscore the value of integrating physical activity and peer social development into a cohesive framework for understanding and promoting psychosocial well-being in this population. From a public health standpoint, the results highlight physical exercise—especially in forms that strengthen peer bonds—as a promising, modifiable target for community and school-based health promotion strategies.However, the observational nature of this evidence necessitates caution in drawing direct causal inferences or making broad policy recommendations. Future research should prioritize intervention studies that test the efficacy and implementation parameters of exercise-based programs specifically designed to enhance peer relationships and prosocial development among migrant children across diverse contexts.

Abbreviations

PE

Physical Exercise

PB

Prosocial Behavior

PR

Peer Relationships

Authors’ contributions

Xuezhen Feng conceived and designed this study, collected and analyzed the data, wrote and revised the manuscript. Enwei Xu designed this study, conducted formal analysis and revised the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Xinjiang Uygur Autonomous Region Tianchi Talent Introduction Program and the Doctoral Research Foundation of Xinjiang Normal University named "Research on Innovative Models of Collaborative Deep Learning Empowered by Education Digitalization for Normal University Students"(No.: XJBSRW2024023), and the Research and Reform Project on Undergraduate Education and Teaching in Autonomous Region Universities in 2025 named "Teaching Practice Path Research on Human Computer Collaboration Empowering the Advanced Improvement of Numerical Intelligence Literacy of Undergraduate Students in Xinjiang Universities"(No.: XJGXXJGPTA-2025022).

Data availability

The datasets supporting the conclusions of this article are included within the article or contact the corresponding author of this article to obtain the original data.

Declarations

Ethics approval and consent to participate

This study was performed in line with the principles of the Declaration of 1964 Helsinki Declaration and its later amendments or comparable ethical standards. The questionnaire and methodology for this study was approved by the Human Research Ethics committee of the College of Educational Science of Xinjiang Normal University (Ethics approval number : HR0116−2024). Informed consent was obtained from all participants’ guardians, as well as from teachers and school administrators involved. Special care was taken to ensure that migrant families were fully informed of the study’s purpose, data confidentiality, and their right to voluntary participation and withdrawal.

Consent for publication

Not Applicable.

Competing interests

The authors declare no competing interests.