Introduction

Subjective well-being (SWB) in school refers to students’ subjective cognitive evaluations and emotional experiences in their school lives based on their own standards (Tian 2008). Extant research has revealed significant connections between school-aged children’s SWB in school and their current and future school behavior, school expectations, and educational outcomes (Huebner and Gilman 2006; Suldo et al. 2014; Tian et al. 2015b). According to the report of the Organization for Economic Co-operation and Development (OECD 2017), successful students not only excel in academic performance, they are also satisfied with their school lives, which suggests that a comprehensive education should pay attention to students’ grades and SWB in school. Notably, the elementary school years are a critical period, and students’ positive experiences during this time serve as a foundation for their current and later sense of belonging, engagement, and achievement in school (Gruman et al. 2008; Miller et al. 2013; Tian et al. 2016d). Therefore, it is essential to understand the determinants of elementary school students’ SWB in school, which might help students to build a good foundation for further development as early as possible.

Schools are not just places where children acquire academic skills; they are also places where children develop their social skills, both of which might influence their SWB in school. Previous studies have mainly focused on the influence of academic achievement on SWB in school (Bücker et al. 2018; Yang et al. 2018a), rarely exploring the effects of social skills. Notably, social skills are developing rapidly during the elementary school years (Mahatmya et al. 2012). Several studies have demonstrated that prosocial behavior represents one kind of important social skill (Fligstein 2001; Gülay 2011). Moreover, the elementary school years are regarded as an important period for shaping prosocial behavior (Battistich et al. 2000). The sustainable happiness model in particular posits that individuals’ SWB is facilitated by their prosocial behavior (Lyubomirsky et al. 2005). Thus, we explored the effects of prosocial behavior on SWB in school. Although previous researchers have explored the relations between prosocial behavior and SWB from both theoretical and empirical aspects, they have rarely examined the specific psychosocial mechanisms through which prosocial behavior affects SWB. Hence, it seems warranted to investigate the potential, precise psychosocial mediators that link students’ prosocial behavior to their SWB in school.

According to the social and personal standards approach of prosocial behavior (Penner et al. 2005), engaging in prosocial behavior can help individuals fulfill their needs (Omoto and Snyder 1995) and promote positive self-images (Schwartz and Howard 1982). Such need satisfaction and positive self-images in turn contribute to SWB. Therefore, we explored possible mediational variables from two perspectives: The satisfaction of psychological needs and the self-evaluation of individuals. Taking into account that school-aged children’s prosocial behavior tends to promote positive interpersonal relationships (Greener and Crick 1999), we expected that the satisfaction of relatedness needs at school should serve as a potential mediator. In addition, self-esteem reflects students’ positive overall evaluations of themselves. Children who display prosocial behavior may be praised and valued by others, and such positive evaluations from others contribute to their evaluations of themselves (Miller et al. 1981). Thus, we expected that self-esteem would also serve as a potential mediator. According to sociometer theory (Leary and Baumeister 2000), the satisfaction of relatedness needs is considered a determinant of individual differences in self-esteem. Therefore, we attempted to uncover the psychosocial mechanisms in the relation between prosocial behavior and SWB in school by exploring the potential mediating roles of students’ satisfaction of relatedness needs and self-esteem.

Subjective Well-Being in School

The conceptualization of SWB proposed by Diener (1994) consists of partially separable cognitive (i.e., life satisfaction or domain satisfaction) and affective components (i.e., frequency of positive and negative affect) (Diener et al. 1995; Diener et al. 1999). Based on Diener’s SWB theory, Tian (2008) extended the theory to the school context, articulating a SWB in school theoretical model comprised of two separate components, also including a cognitive component (i.e., school satisfaction) and an affective component (i.e., affect in school). School satisfaction represents students’ cognitive evaluations of their school lives. Affect in school involves students’ self-reported frequencies of experiencing positive and negative emotions while at school. Empirical support has been reported for the SWB in school model among Chinese children and adolescents (Tian et al. 2014a; Tian et al. 2013; Liu et al. 2015).

Prosocial Behavior and Subjective Well-Being in School

Prosocial behaviors have been defined as socially accepted, friendly behaviors enacted for the purpose of helping others, which are beneficial to society as well as individuals (Feng 2009). Moreover, prosocial behaviors play an important role in children’s overall social development (Eisenberg 1986; Eisenberg and Mussen 1989). In recent years, researchers have paid increasing attention to the functions and positive outcomes associated with prosocial behaviors, particularly investigating their effects on individuals’ SWB (Meier and Stutzer 2008; Tian et al. 2016a).

The sustainable happiness model (Lyubomirsky et al. 2005) assumes that happiness can be actively pursued. Moreover, the model points out that individuals’ longer-term (versus momentary) happiness is determined by the three factors of genetic set point, circumstances, and activities. First, individuals’ happiness levels can in part be determined by their set point (genetics, personality traits), but not completely because happiness levels are subject to change. Second, life circumstances (e.g., income, religious affiliation) also serve as predictors of happiness. Nevertheless, because people readily adapt to most relatively stable circumstances in their lives, such circumstantial factors tend to have rather limited long-term effects on happiness levels. Finally, intentional activities, which require some degree of effort to enact some type of cognitive, behavioral, or volitional activities, represent the most promising means of altering one’s happiness level in this model. Because intentional activities can be episodic, variable, and directly counteract adaptation, activity-based well-being changes can be enduring. Therefore, this model suggests that intentional activities offer the best potential route to higher sustainable levels of happiness. Particularly, prosocial behavior (i.e., action intended to benefit others) has been identified as one of the most effective activities that contributes to individuals’ well-being (Lyubomirsky et al. 2005). Additionally, a growing body of evidence supports the notion that prosocial behavior promotes multiple emotional benefits for the helper. For example, in terms of experimental studies, Lyubomirsky et al. (2005) showed that students who were asked to perform five acts of kindness per week over the course of 6 weeks were happier than those in a control group who were not required to perform five acts of kindness and simply completed measures of well-being before and after the treatment. For another example of an experimental study, Aknin et al. (2015) demonstrated that young children displayed more happiness when children gave their own candy away as opposed to an identical treat that did not belong to them (d = .30). Examples of cross-sectional research included Yang et al. (2018b), who revealed that prosocial behavior positively related to SWB (r = .44) and Tian et al. (2016a), who revealed that prosocial behavior was also positively related to school satisfaction (r = 0.62), positive affect in school (r = 0.54), and negative affect in school (r = −0.28) among elementary school students.

Most of the aforementioned findings have been derived from studies focused on different, general indicators of well-being, rather than domain-specific indicators of SWB (e.g., SWB in school). However, as Sarason (1997) noted, “Subjective well-being judgments always occur within environmental contexts, such as relationships, family, and school” (p. ix). For children, schools represent a major life domain and their perceptions of their school experiences likely have important implications for their lifelong SWB. Thus, it seems warranted to explore the association between prosocial behavior and domain-specific subjective well-being; that is, subjective well-being experienced in particular contexts, such as the school. Additionally, the above study on SWB in school (i.e., Tian et al. 2016a) was cross-sectional, limiting the consideration of temporal processes. Therefore, we used a longitudinal approach to investigate the relation between students’ prosocial behavior and SWB in school.

The Mediation Role of the Satisfaction of Relatedness Needs at School

Based on basic psychological needs theory (BPNT; Ryan and Deci 2000), Tian et al. (2014b) extended BPNT to the school setting. The need for relatedness at school is one of students’ three basic psychological needs in school, which refers to students’ desires to experience a sense of school belonging, including a sense of connection with teachers and classmates. This need is satisfied when students perceive themselves as emotionally close to their peers and teachers. During elementary school, children tend to show increasing prosocial behavior intended to enhance positive relations with their important others, such as peers (Greener and Crick 1999). Kou and Wang (2003) also claimed that prosocial behavior is thought to impact relatedness needs through promoting closeness with others in interpersonal interactions. Helping others is thought to be an essential capacity for individuals to maintain mutually rewarding relationships (Caprara and Steca 2005). This notion has been supported by a study showing that participants who engaged in kind acts displayed an increase in relationship satisfaction (Alden and Trew 2013). Furthermore, students’ prosocial behaviors are significant determinants of elementary school students’ relationships with their teachers and peers (Caputi et al. 2012; Greener and Crick 1999; Wang 2009), both of whom frequently interact with students throughout their school lives (Danielsen et al. 2009; Malecki and Demaray 2003; Reeve et al. 2008). Based on such findings, we hypothesized that prosocial behavior will increase elementary school students’ satisfaction of relatedness needs at school.

With regard to the relation between the satisfaction of relatedness needs and SWB, cross-sectional studies have shown positive relations between the two variables among adolescents (r = 0.68, Tian et al. 2016b; r = 0.68, Tian et al. 2016c). Furthermore, longitudinal studies (e.g., Véronneau et al. 2005) have revealed that the satisfaction of relatedness needs predicted concurrent (β = .17, p < .05) and subsequent positive affect 6 weeks later among children and adolescents. King (2015) suggested that students’ sense of relatedness with teachers (β = .217, p < .001) and peers (β = .199, p < .001) was positively associated with their initial level of positive affect. In addition to the studies of the direct relations among these three variables, the extant literature also has provided some indirect support for the notion that the satisfaction of relatedness needs may play a mediator role in the relation between prosocial behavior and SWB in school. For instance, Piliavin and Siegl (2007) investigated positive effects of volunteering on psychological well-being and self-reported health using all four waves (i.e., 1964, 1975, 1992, and 2004) of the Wisconsin longitudinal study among participants who graduated from Wisconsin high schools in 1957. One of the results showed that the association between volunteering and well-being was mediated by mattering, which refers to the subjective experience of being noticed, cared for, and valued by others. Based on the aforementioned literature, we hypothesized that the satisfaction of relatedness needs at school will mediate the effects of prosocial behavior on SWB in school.

The Mediation Role of Self-Esteem

Self-esteem refers to the positivity of one’s overall evaluation of self (Rosenberg 1965). High levels of self-esteem indicate that one considers herself worthy, whereas low levels imply self-rejection, self-dissatisfaction, and self-contempt (Rosenberg 1965). For children, experiences in elementary school play a crucial role in developing self-esteem (Lingren 1991). Empirical evidence has shown that prosociality is statistically significantly related to self-esteem (Zuffianò et al. 2014). For example, Miller et al. (1981) demonstrated that children’s sharing with needy children was positively correlated with self-esteem whereas children’s lack of sharing (i.e., retaining tokens for themselves) was negatively correlated with self-esteem. For another example, a longitudinal study also revealed that prosocial behavior directly predicted subsequent self-esteem (Fu et al. 2017). In addition, prosocial behavior may enhance self-worth through others’ gratitude and acknowledgment and also provides a means for bolstering feelings about the self. For example, Grant and Gino (2010) observed that individuals experienced a feeling of social worth when they received targets’ gratitude for their performance of prosocial behavior. In this way, prosocial behavior may foster self-worth and more global self-esteem. Finally, children’s self-esteem tends to be influenced by social acceptance from others, and prosocial behavior could help children gain acceptance from important others in school (Flynn et al. 2006). In view of this, prosocial behavior likely exerts an impact on self-esteem. According to the above point of view, we hypothesized that elementary school students’ display of prosocial behaviors will predict higher levels of self-esteem.

As for the relation between self-esteem and SWB, previous studies have suggested that positive self-esteem is a determinant of individuals’ SWB. For instance, Kong et al. (2013) revealed that self-esteem is related to the different components of SWB, such as life satisfaction (r = .39), positive affect (r = .35), and negative affect (r = −.34). Additionally, Cheng and Furnham (2003) showed that self-esteem had a direct effect on happiness (β = 0.49, p < .001). Regarding longitudinal evidence, Liu et al. (2013) demonstrated that children’s self-esteem at baseline positively predicted their life satisfaction 6 months later (β = .18, p < .001), after controlling for initial life satisfaction. In addition, students who engage in more prosocial behavior, such as actively helping their classmates who are unable to do homework, likely enhance their sense of competence and value in school, yielding more positive evaluations of themselves (Aronson et al. 1978). In turn, such higher levels of self-esteem should contribute to students’ psychological adjustment and more frequent positive school experiences, such as well-being (Jin 2015). Therefore, we hypothesized that self-esteem will mediate the effects of prosocial behavior on SWB in school.

The Chain Mediation Role of Satisfaction of Relatedness Needs at School and Self-Esteem

Extant literature provides some support for the notion that the satisfaction of relatedness needs at school and self-esteem may both function as mediators of the link between prosocial behavior and elementary school students’ SWB in school. Furthermore, Sociometer Theory (Baumeister and Leary 1995; Leary and Baumeister 2000) asserts that maintaining social connections and a sense of belonging represent people’s basic needs, and self-esteem serves as a subjective monitor of the degree to which individuals are accepted or rejected by partners or group members. When perceived as being liked and accepted by others, individuals’ needs for relatedness are satisfied, which in turn promotes positive self-esteem. Also, previous studies have revealed that children who are satisfied with their peer and teacher-student relationships have higher self-esteem (Bishop and Inderbitzen 1995; Li et al. 2008). Some empirical studies have also suggested that satisfaction of the need for relatedness predicted individuals’ self-esteem (β = .109, p < .05, Mabekoje and Okubanjo 2009; β = .121, p < .05, Ümmet 2015). Thus, it would be reasonable to assume that elementary school students’ prosocial behavior will influence their satisfaction of relatedness needs at school, which in turn will increase their self-esteem, and which subsequently will increase their SWB in school.

In order to develop a comprehensive understanding of the relation between prosocial behavior and SWB in school, it seems necessary to consider the mediation roles of the satisfaction of relatedness needs at school and self-esteem simultaneously. Compared with a simple mediation model, a multiple mediation model allows for simultaneous examinations of multiple mechanisms linking antecedent variables to consequent variables, which may offer deeper insights into how prosocial behavior is related to elementary school students’ SWB in school. As such, the multiple mediation model may explain not only the mechanisms behind the relations, but also enhance the existing theory and research base, also yielding significant theoretical and practical implications for promoting students’ well-being (Preacher and Hayes 2008). We thus proposed a multiple mediational model to test the multiple mediating effects of the satisfaction of relatedness needs at school and self-esteem in the relation between prosocial behavior and SWB in school.

The Current Study

Based on the extant research, we used structural equation modeling (SEM) to test a model with the satisfaction of relatedness needs at school and self-esteem as potential mediators of the association between prosocial behavior and SWB in school (see Fig. 1). We formulated three hypotheses: (1) Prosocial behavior at Time 1 will positively predict SWB in school at Time 4; (2) the satisfaction of relatedness needs at school at Time 2 and self-esteem at Time 3 will play a mediating role in the relation between prosocial behavior at Time 1 and SWB in school at Time 4 separately; (3) the satisfaction of relatedness needs at school at Time 2 and self-esteem at Time 3 will play a chain mediating role in the association between prosocial behavior at Time 1 and SWB in school at Time 4, namely, prosocial behavior at Time 1 → the satisfaction of relatedness needs at school at Time 2 → self-esteem at Time 3 → SWB in school at Time 4.

Fig. 1
figure 1

The conceptual model of the proposed chain multiple mediation. PB Prosocial Behavior, SRNS Satisfaction of Relatedness Needs at School, SE Self-Esteem, SWBS Subjective Well-Being in School

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Method

Participants

The convenience samples used in the present study were from two elementary schools located in the urban area of Guangzhou city, Guangdong province, China. Based on the information obtained from education authorities in the locality, the two schools showed no significant differences in key characteristics (e.g., the quality of students,Footnote 1 school size,Footnote 2 class size,Footnote 3 and teachers’ teaching abilityFootnote 4). At the baseline assessment (Time 1), 1058 students (Mage = 9.44, SD = 0.97, ranging from 8 to 12 years) from Grades 3–5 participated. Five hundred seventy-five participants were male. According to the information provided by the schools, these students did not change classes during the course of the four measurements, except for 2–3 students in some classes who transferred for personal reasons. Furthermore, the class teacher of the students did not change across the four measurements.

At Time 1 (T1), 1058 students participated. However, not all students participated during the following three occasions (6 months apart). Specifically, 918 (86.77%) at Time 2 (T2), 913 (86.29%) at Time 3 (T3), and 947 (89.51%) at Time 4 (T4) of the T1 participants were retained, respectively. The attrition rate were 13.23% at T2, 13.71% at T3, and 10.49% at T4. The number of students in each grade level during each year of data collection is shown in Table 1. The reasons for attrition were moving out of the school district or being absent from school at one time or another. A total of 776 students participated in the study on all four occasions. Previous longitudinal studies supported that our rate attrition was acceptable (e.g., Cortes-Garcia et al. 2019; Zhu et al. 2019).

Table 1 The number of students in each grade-level at each year of data collection
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We conducted the Missing Completely at Random (MCAR) test (Little 1988) on all variables included in our study. These analyses revealed a normed χ2/df of 1.60, which indicated that the pattern of the missing data was not materially different from a pattern of missing at random (Bollen 1989). In addition, ANOVAs on age, prosocial behavior, SWB in school, satisfaction of relatedness needs at school, and self-esteem were analyzed to evaluate attrition bias, comparing the participating students who provided complete data across all four waves and those who had missing data in at least one wave. There were no statistically significant differences between the two groups in age (F(1, 1056) = 0.004, p > .05), prosocial behavior (F(1, 953) = 1.40, p > .05), satisfaction of relatedness needs at school (F(1, 897) = 0.48, p > .05), self-esteem (F(1, 881) = 3.70, p > .05), or SWB in school (F(1, 931) = 3.63, p > .05). A chi-square test (χ2 = 1.17, df = 1, p > .05) was not significant indicating that there was no difference between the two groups for gender. Therefore, we applied Full Information Maximum Likelihood (FIML) to the subsequent analyses (Little and Rubin 2002). FIML estimates model parameters using all available information, irrespective of whether that information comes from cases with incomplete data or not (Little and Rubin 2002).

Measures

Prosocial Behavior

Prosocial behavior was measured by The Primary School Upper Grade Students’ Prosocial Behaviors Questionnaire (PSUGSPBQ; Feng 2009) at T1. The scale includes 30 items and four subscales, which tap altruistic behaviors (e.g., “I am willing to help my classmates who are unable to do homework.”), behaviors abided by rules (e.g., “I will protect the environment.”), social behaviors (e.g., “I will not interrupt other people.”), and otherness behaviors (e.g., “I am willing to discuss the things about class affairs with others.”). Participants were asked to rate the frequency of behaviors on a 5-point scale (1 = never to 5 = always). Higher scores indicated more frequent prosocial behavior. The PSUGSPBQ has shown adequate psychometric properties with Chinese pupils (Tian et al. 2016a; Wang 2011). The internal consistency of the PSUGSPBQ was observed to be adequate in our T1 sample (alpha = 0.94).

Satisfaction of Relatedness Needs at School

To assess the extent to which students experienced relatedness psychological need satisfaction during their school experiences, we used the Need for Relatedness Subscale from the Adolescent Students’ Basic Psychological Needs at School Scale (ASBPNSS; Tian et al. 2014b) at T1 and T2. All five items are positively phrased (e.g., “Teachers and classmates care about me at school.”). Participants were asked to respond on a 6-point scale (1 = strongly disagree to 6 = strongly agree). Higher scores represented higher levels of relatedness needs satisfaction at school. The applicability of ASBPNSS in Chinese elementary school students has been demonstrated (Tian et al. 2018). In our current study, the Cronbach’s alpha internal consistency coefficients for the Need for Relatedness subscale were 0.82 at T1 and 0.87 at T2, respectively.

Self-Esteem

Rosenberg’s Self-Esteem Scale (Chinese Version) (Wang et al. 1999) was used to assess self-esteem at T1 and T3. The scale includes ten self-report items (e.g., “I take a positive attitude toward myself”), all of which are answered on a 4-point scale (1 = strongly disagree to 4 = strongly agree). Higher scores represented higher levels of self-esteem. The Chinese version of the self-esteem scale has demonstrated good reliability and validity (Tian 2006). The Cronbach’s alpha coefficients in our current study were 0.85 at T1 and 0.89 at T3 respectively.

Subjective Well-Being in School

The Brief Adolescents’ Subjective Well-Being in School Scale (BASWBSS; Tian et al. 2015b) was used to assess subjective well-being in school at T1 and T4. The scale includes two subscales: School Satisfaction (SS) and Affect in School (AS). The SS subscale includes six items (e.g., “I perform well in school.”). Items were answered on a 6-point scale (1 = strongly disagree to 6 = strongly agree). The subscale of AS includes two items. One item assessed the frequency of positive affect (PA) in school, and the other item assessed the frequency of negative affect (NA) in school. The PA item was worded as “In school, the frequency of my pleasant feelings is…”. The NA item was worded as “In school, the frequency of my unpleasant feelings is…”. Both items were rated on a 6-point scale with response options ranging from 1 (never) to 6 (always). The score for the SS subscale was computed by averaging the responses to the six items. The score for the AS subscale was computed by subtracting the NA from the PA score. Finally, the SS and AS subscale scores were summed to create a total BASWBSS score. This procedure for calculating the total score has been used in previous studies (e.g., Eryilmaz 2012). Tian et al. (2016d) have suggested adequate psychometric properties for the instrument with Chinese elementary school students. Specifically, the BASWBSS displayed acceptable internal consistency reliability (SS, r = 0.78) and test-retest reliability across a 6-week interval (SS, r = 0.62, p < 0.01). In this study, the Cronbach’s alpha reliability coefficients for the SS subscale were 0.76 at T1 and 0.85 at T4 respectively.

Covariates

Given prior research reporting that children’s gender and age were correlated with SWB in school (Kaye-Tzadok et al. 2017; Liu et al. 2016), we controlled for these variables in the statistical analyses. Gender was a dichotomous variable (1 = male; 0 = female). Age was measured by the participants’ age in years. These data were collected at T1.

Procedure

We conducted the study after obtaining approval from the Human Research Committee of South China Normal University. Informed consent was acquired from participants’ parents, and assent was acquired from participants. Led by trained graduate assistants in regular classroom environments, the students completed different measures at different time points. Specifically, all four measures and demographic questions were administered at T1; the Need for Relatedness subscale was administered at T2; Rosenberg’s Self-Esteem Scale was administered at T3; and the BASWBSS was administered at T4. Across all four occasions, the participants received identical verbal and written instructions from the trained graduate assistants. They were also informed of the nature of the study and confidentiality of their responses. Participants were allowed to take as much time as needed to complete the questionnaires, and they could refuse to participate at any time.

Data Analysis

First, descriptive statistics and Pearson correlation were analyzed by SPSS 21.0. Second, the measurement model and the longitudinal mediation model were evaluated using Mplus 7.0. Considering that the inflated measurement error caused by multiple items for latent variables may lead to data analysis bias in SEM, three-item parcels were created for self-esteem using the item-to-construct balance approach (Little et al. 2002). Then, we tested our hypotheses with a longitudinal mediation model among the 4-wave follow-up samples. In order to circumvent possible bias of estimation of conditional indirect effects, we controlled for initial levels of satisfaction of relatedness needs at school, self-esteem, and SWB in school at T1. In addition, participants’ age and gender also served as control variables in the structural model.

The fit of the measurement and structural models was evaluated with multiple indicators: the comparative fit index (CFI), the Tucker-Lewis Index (TLI), and the root mean square error of approximation (RMSEA). For both CFI and TLI, values above 0.90 indicated adequate fit to the data (Marsh et al. 2004). For the RMSEA, values less than 0.06 were considered indicative of good fit (Hu and Bentler 1999).

Finally, the bias-corrected (BC) bootstrap procedure has shown higher statistical power compared with other methods for testing mediating effects (Fritz and MacKinnon 2007; Preacher and Hayes 2008; Wen and Ye 2014). Moreover, previous studies have shown that the most effective method to test multiple mediation effects is the bootstrapping method (Cheung 2007; Lau and Cheung 2012). Thus, BC bootstrapping, employing 5000 samples, was used for testing the significance of the mediated effects and to produce bias-corrected percentile confidence intervals. If the 95% confidence interval for the indirect effect estimate did not include zero, it was concluded that the indirect effect was statistically significant at the 0.05 level. The size of the mediating effect was also calculated.

Results

Descriptive Analyses

Two indicators were employed to evaluate the normality of data. Values for univariate skewness greater than or equal to 2.0 and values for kurtosis greater than or equal to 7.0 indicate non-normality (Curran et al. 1996; Muthén and Kaplan 1985, 1992). As shown in Table 1, the scores on the relevant variable thus reflected normal distributions. Descriptive statistics and correlation coefficients are also displayed in Table 2.

Table 2 Descriptive statistics and correlations for the main variables
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The Measurement Model and Structural Model

The Measurement Model

The measurement model included four latent factors (i.e., T1 prosocial behavior, T2 satisfaction of relatedness needs at school, T3 self-esteem, and T4 SWB in school) and 14 observed variables. A preliminary test of the measurement model demonstrated good fit: χ2/df= 3.64, p < .001; CFI = 0.98; TLI = 0.97; RMSEA = 0.05 (90% CI of the RMSEA = 0.043–0.057). The loadings of measured variables on the latent factors were all statistically significant (p < .001), suggesting that all the latent factors were well represented by their indicators.

Additionally, correlation coefficients among the four latent variables are presented in Table 3. The directions of all correlation coefficients were consistent with the respective hypotheses and provided support for further evaluation of the hypothesized model.

Table 3 Correlations for the latent variables
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The Structural Model

The test of the structural model consisted of two parts. First, the direct effect of the predictor variable on the criterion variable was tested. After controlling the T1 level of SWB in school, the direct path coefficient from T1 prosocial behavior to T4 SWB in school in the absence of mediators was significant (β = 0.15, p < .01). Second, the structural model considering all the paths from T1 prosocial behavior to T4 SWB in school was examined with the T1 level of all variables, with age and gender controlled. The results (see Fig. 2) showed acceptable fit: χ2/df= 3.98, p < .001; CFI = 0.94; TLI = 0.93; RMSEA = 0.05 (90% CI of the RMSEA = 0.050–0.056).

Fig. 2
figure 2

The mediation model. P1 altruism behaviors, P2 behaviors abided by rules, P3 social behaviors, P4 otherness behaviors, R1-R5 five items of the satisfaction of relatedness needs at school, SE1-SE3 three parcels of self-esteem, AS Affect in School, SS school satisfaction, PB Prosocial Behavior, SRNS Satisfaction of Relatedness Needs at School, SE Self-Esteem, SWBS Subjective Well-being in School, T1 Time 1, T2 Time 2, T3 Time 3, T4 Time 4. Age and gender are entered as control variables. These control variables are not presented in the figure for clarity. *p < 0.05, ** p < 0.01, *** p < 0.001. →significant path; — → non-significant path

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Mediating Analysis

As shown in Table 4, the total effect from T1 prosocial behavior to T4 SWB in school was statistically significant (95% CI = 0.140 [.045, .236]). The total indirect effect from T1 prosocial behavior to T4 SWB in school was significant (95% CI = 0.090 [.034, .147]), which accounted for 64.29% of the total effects. In the serial mediation model, the mediating effect of T1 prosocial behavior on T4 SWB in school through T2 satisfaction of relatedness needs at school was statistically significant (β = .060, BC 95% CI [.023, .097]), accounting for 42.86% of the total effects. Furthermore, the chain mediating effect of T1 prosocial behavior on T4 SWB in school through T2 satisfaction of relatedness needs at school and T3 self-esteem was also significant (β = .018, BC 95% CI [.006, .031]), accounting for 12.86% of the total effects. However, the mediating effect of T1 prosocial behavior on T4 SWB in school through T3 self-esteem was not significant (β = .012, BC 95% CI [−.026, .050]).

Table 4 Bootstrap analyses of the magnitude and statistical significance of indirect effects
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Discussion

Using a four-wave longitudinal design, we examined the relation between prosocial behavior and SWB in school, as well as the mediating role of both the satisfaction of relatedness needs at school and self-esteem with a sample of Chinese elementary school students. Some of our hypotheses were supported, and the major findings provided valuable insights into how prosocial behavior may relate to subsequent higher levels of SWB in school. More importantly, these findings emphasized the importance of both social (i.e., the satisfaction of relatedness needs at school) and psychological (i.e., self-esteem) variables in understanding the pathways from prosocial behavior to SWB in school.

Prosocial Behavior and Subjective Well-Being in School

As hypothesized, prosocial behavior positively predicted subsequent SWB in school in the absence of mediators, which was consistent with the sustainable happiness model (Lyubomirsky et al. 2005) and the emotional benefits of prosocial behavior among children as suggested by Tian et al. (2015a). However, after controlling for the two mediators, prosocial behavior no longer affected subsequent SWB in school. That is, although prosocial behavior positively predicted SWB in school, it appeared to influence individuals’ SWB in school, indirectly through the satisfaction of relatedness needs at school and level of self-esteem. Such a finding offers new insights into the literature by revealing the possibilities of other pathways in explaining the relation between prosocial behavior and SWB in school and highlights the crucial roles of the two mediating variables.

The Mediation Roles of the Satisfaction of Relatedness Needs at School and Self-Esteem

First, as expected, our finding that the satisfaction of relatedness needs at school played a mediation role in the link between prosocial behavior and SWB in school is in line with previous research demonstrating that prosocial behavior benefits individuals’ well-being via the satisfaction of relatedness needs (Aknin et al. 2013; Martela and Ryan 2016). Given that prosocial behavior is inherently interpersonal, students who are frequently engaged in prosocial behaviors likely interact better with their teachers and peers and thus build intimate social connection with these important others in school, which increases their satisfaction of relatedness needs (Baumeister and Leary 1995; Ryan and Deci 2000). In turn, such enhanced relatedness satisfaction are crucial determinants of SWB (Ryan and Deci 2001). Thus, students engaging in more frequent prosocial behavior are more likely to experience more satisfaction of relatedness needs, which in turn relates to higher levels of SWB in school.

Second, contrary to expectations, our study did not support a mediating role for self-esteem in the link between prosocial behavior and SWB in school. This non-significant result might be explained through the perspective of the statistical procedures employed in our study (see Fig. 2). To be more specific, the direct effect of prosocial behavior on self-esteem was not statistically significant after controlling for the satisfaction of relatedness needs at school (i.e., the first mediator), which perhaps accounted for why self-esteem (i.e., the second mediator) did not play an mediating role in the path from prosocial behavior to SWB in school. This explanation might also help elucidate why this result was inconsistent with the existing research (e.g., Fu et al. 2017), as the prior studies did not consider the mediating role of the satisfaction of relatedness needs at school in the relation between prosocial behavior and self-esteem. However, this result is supported by, as well as may be explained by, the social acceptance model (Twenge and Campbell 2001). According to the social acceptance model, elementary school-aged children’s self-evaluations arise from others’ social acceptance. As we noted earlier, engaging in prosocial behaviors is one way for elementary school students to build good relationships with others by gaining a positive reputation, which increases their experience of a sense of connection with important others in school (Flynn et al. 2006). When elementary school students’ relatedness needs are satisfied, they are more likely to experience the social acceptance and support of others, thereby enhancing their self-esteem. Such chain relations are consistent with our findings discussed below.

Third, the finding that the path of prosocial behavior → satisfaction of relatedness needs at school → self-esteem → SWB in school was statistically significant suggested that prosocial behavior positively predicted the satisfaction of relatedness needs at school, which in turn positively predicted their self-esteem, and which in turn positively predicted their SWB in school. Weinstein and Ryan (2010) demonstrated that prosocial behavior correlated positively with the satisfaction of relatedness needs. Studies have also shown that individuals who experience higher levels of the satisfaction of relatedness needs report higher levels of self-esteem (Rueger et al. 2010; Ümmet 2015). Furthermore, individuals reporting higher self-esteem typically experience higher SWB (Schimmack and Diener 2003; Xu et al. 2005). Therefore, our findings extend beyond previous research to illuminate further the complexity of the linkages between prosocial behavior and SWB in school; specifically, that elementary school-aged children who engage in more prosocial behaviors more readily experience the satisfaction of relatedness needs, which in turn leads to higher self-worth and subsequent SWB in school.

In conclusion, the mediation effect of satisfaction of relatedness needs at school was stronger than the chain mediation effect of satisfaction of relatedness needs at school and self-esteem. One possible interpretation is that the Chinese culture represents one of the prototypical collectivistic cultures that emphasizes group interdependence, harmony in interpersonal relations, and conformity to group norms (Oyserman et al. 2002), which suggests that individuals who live in such cultural backgrounds are more likely to pay more attention to building good relationships with others than on pursuing self-worth.

Nevertheless, self-esteem still play an important role in the chain mediation path from prosocial behavior to SWB in school. Therefore, when understanding the positive effect of prosocial behavior on SWB in school, we not only should pay attention to the role of the satisfaction of relatedness needs at school, but also the role of self-esteem.

Limitations and Future Directions for Research

Compared with the prior literature, our study displayed several merits, including its large sample of Chinese elementary school students and its 18-month longitudinal mediational design. Despite these strengths, there were some noteworthy limitations. First, using self-reporting methods is associated with potential limitations, such as overly positive self-presentations. Future researchers are advised to gather data from multiple sources (e.g., teachers and peers) to increase confidence in the measurements. Second, although prosocial behavior can be conceptualized as multidimensional, we examined the impact of overall prosocial behavior on the SWB in school of elementary school students. Further research could examine how different dimensions of prosocial behavior might vary in terms of the nature and magnitude of their relations to SWB in school. Third, we conducted our study with Chinese elementary school-aged children. Therefore, our results may not be generalized to students from other age groups and cultural backgrounds. Future researchers should test the model among students from other age groups (e.g., adolescents) and cultures (e.g., individualistic cultures). Finally, based on the extant literature and our research interests, we only tested a possible temporal sequence among variables using general SEM. Future researchers should collect data for all study variables on all occasions to test the possibility of alternative temporal sequences using a cross-lagged model. For example, it is worth testing whether there is a reciprocal relation between prosocial behavior and SWB in school.

Implications

Despite the limitations, major findings emerge from our study that yield a more sophisticated understanding of how prosocial behavior relates to Chinese elementary school students’ SWB in school. It should be noted that our study provides strong evidence for the usefulness and importance of satisfaction of relatedness needs at school and self-esteem, as effective factors in Chinese elementary school-aged children’s SWB in school. Therefore, in order to enhance students’ SWB in school, school educators should pay more attention to satisfying students’ relatedness needs at school and improving their self-esteem.

In terms of enhancing students’ SWB in school by promoting their satisfaction of relatedness needs at school, school educators can interact actively and effectively with students as much as possible and encourage students to get along well with their classmates. Furthermore, school educators could also provide some empirically- supported, relevant school-based intervention programs for young school students. For instance, the intervention program of Banking Time (Driscoll and Pianta 2010) might be a good choice. This program involves school educators interacting with students actively by watching, listening, and conveying acceptance and understanding, and thus promoting intimate connections with their students (Driscoll and Pianta 2010).

With respect to enhancing students’ SWB in school by improving their self-esteem, school educators could encourage students to think positively of themselves and help them successfully manage tasks and responsibilities at school. Researchers have suggested that some interventions could improve Chinese elementary school students’ self-esteem. For example, school educators could carry out self-esteem thematic education activities, such as helping students understand themselves, accept themselves and challenge themselves, thereby improving their self-esteem (Sun 2013).

In addition, our findings suggest that school educators should also address students’ relatedness needs satisfaction and self-esteem in interventions together, so as to better promote the students’ SWB in school and subsequently promote their overall positive development in school (Huebner and Gilman 2006).