Commensality and academic performance: measuring peer acceptance among college students

Abstract

Peer relationships play a critical role in academic performance, yet their link in higher education remains underexplored. This study introduces commensality—shared mealtimes—as a novel proxy for peer acceptance and examines its relationship with academic outcomes across student groups. Using 2,717,938 transaction records from 3355 first-year undergraduates at a prestigious Chinese university, we developed “commensality value” metrics to quantitatively measure peer relationships. Regression analyses reveal that peer acceptance, particularly from peers who are more physically distant, is positively correlated with academic performance. This correlation is stronger among male students, politically active students, former class leaders, and those with politically active parents. These findings highlight the potential benefits of strong peer relationships and suggest that promoting environments that encourage peer commensality could be a valuable strategy for universities to explore. By bridging gaps in the literature, this study introduces innovative metrics and advances the understanding of the peer academic success.

Introduction

As students transition into college, the influence of family diminishes, while peer relationships increasingly become a pivotal factor widely believed to shape academic performance¹. Traditional research on peer relationships has predominantly focused on the impact of physical networks—such as those formed within dormitories, classes, and academic majors—on academic outcomes^2,3,4. Yet, these studies fail to grasp the more substantive aspects of peer integration among college students. Notably, in most Chinese universities, for example, dormitory assignments are determined through a random sampling process, which may not necessarily foster genuine peer relationships⁵. The degree of genuine peer acceptance within these relationships, particularly among roommates, is a crucial yet underexplored factor related to academic performance.

Research conducted on primary and secondary school students has consistently shown that peer acceptance contributes to academic progress^6,7. Yet, few empirical studies have extended this inquiry to college students, primarily because traditional methods of measuring peer acceptance—such as the “nomination” method⁸—are more suited to younger students and present challenges when applied to a university context.

The concept of “commensality”, the practice of eating together, while often considered cultural or even religious, provides a novel perspective of empirically measuring peer relationships. This study posits that commensality serves as an innovative and effective technique for studying peer acceptance among college students. By integrating commensality data with rich demographic and academic information, this research aims to open new avenues for understanding the intricate relationship between peer relationships and academic performance in a university context, utilizing big data methodologies.

When students enter university, they become separated from their families, and peers emerge as their primary social contacts. This is a period where the concept of “peer effects,” which encompasses the externalities of human capital, psychological state, and social behavior that arise from interactions within peer groups—is considered to reach its peak⁹. This concept posits that adolescents, in particular, are more susceptible to peer influences than adults, impacting their emotional¹⁰, behavioral¹¹, and academic adaptation¹². This susceptibility is especially pronounced among Chinese college students, where the reduction of CEE (College Entrance Examinations) pressures and increased peer interaction amplify peer influences. The “college friend circle,” comprising dormitories, classes, colleges, and clubs, plays a significant role in the socialization process, shaping students’ psychological characteristics and swaying their major choices¹³, career planning¹⁴, academic performance¹⁵, and behaviors such as smoking¹⁶ and alcohol use¹⁷.

The psychological community has long investigated the role of peer effects on academic performance. As early as 1966, the Coleman Report indicated that students’ grades are closely linked to the educational backgrounds and aspirations of their peers. The report suggested that youth subcultures, distinct from the adult world, exert a stronger influence among peer groups than family or school¹⁸. Subsequent studies have confirmed the presence of peer effects in primary and secondary schools, highlighting their impact on academic performance¹⁹. Yet, research findings on peer effects in higher education present a divided picture.

Some early studies suggest that peer effects positively influence academic performance in college. For instance, Hoel’s study at Reed College found a significant peer effect on academic outcomes²⁰. Similarly, Hasan and Bagde’s research in an Indian engineering college further specified this causal mechanism. They found that the pre-college academic skills of randomly assigned roommates significantly influenced a student’s performance. Crucially, this effect was most potent when there was a match between the roommate’s skills and the student’s courses, e.g., a roommate skilled in math improved a student’s math grades, but not English²¹. Sacerdote’s study at Dartmouth College utilized the random assignment of roommates to isolate peer effects. His findings revealed that it was not the mere presence of a roommate, but rather the specific characteristics of that roommate, that mattered. Specifically, being randomly assigned a roommate with a higher GPA causally led to a significant increase in a student’s own GPA². In China, studies on top Chinese universities, such as Tsinghua, also support these findings, showing a positive impact of dormitory peers on academic performance, with some evidence suggesting this impact grows over time^22,23.

Yet, there are dissenting voices in academia that argue against the positive impact of peer effects on college students’ academic performance. For example, Zimmerman found that college students’ academic outcomes were not substantially influenced by their peers in a study of roommates’ grades and SAT scores at Williams College²⁴. In a panel study at the University of Maryland, Foster similarly found that peer effects on academic performance do not exist. Furthermore, Arum and Roksa argued that peer relationships might negatively affect undergraduates’ achievements in critical thinking, complex reasoning, and writing skills^25,26.

These conflicting findings have compounded the uncertainty in college policy and decision-making. Take China as an example, only a few universities have attempted to assign dormitories based on student characteristics, such as smoking habits, while most continue to use random assignments. The inconsistency in research outcomes stems from two primary issues: the lack of scientific rigor in defining and measuring core peer relationships and the failure to account for the heterogeneity of these dynamics. Studies that focus solely on physical connections, such as shared dormitories or majors, overlook core aspects of peer relationships, including genuine peer acceptance, potentially leading to distorted conclusions about cause and effect. Additionally, the dynamics of peer relationships likely vary across different disciplines, majors, genders, ethnicities, and CEE scores. Although studies have recently begun to recognize the importance of these heterogeneous factors²⁷, there remains a need for comprehensive research that accounts for these variables using reliable, substantial empirical data.

Introducing peer acceptance as a dimension of analysis is pivotal for understanding the link between real peer relationships and academic performance among college students. Previous research on primary and secondary school students has demonstrated that peer acceptance is a positive and protective factor in peer relationships, which can mitigate internalizing and externalizing problems and reduce students’ propensity for maladaptive outcomes²⁸. Consequently, peer acceptance generally exerts a positive influence on academic performance.

Yet, despite the established importance of peer acceptance in earlier educational stages, this concept has been underexplored in the context of college students. A significant challenge lies in the applicability of the traditional “nomination” method, commonly used to measure peer acceptance. This approach typically requires younger students to list their most and least favored classmates, which allows researchers to categorize peer relationships into distinct types, such as popular, rejected, or neglected^8,29. Yet, this method is less suitable for college students, who are generally more mature and for whom such questionnaires cannot reliably capture the nuances of peer acceptance.

To address this gap, we introduce the concept of “commensality” as a novel measure of peer acceptance among college students. Commensality is an interdisciplinary research area that explores the social, psychological, and cultural aspects of shared meals. From a psychological and behavioral perspective, commensality is believed to foster social connections and enhance a sense of belonging, which in turn can positively influence academic performance. Research by Gregory suggests that sharing meals promotes social interaction, enabling individuals to express emotions, share experiences, and build close relationships, thereby enhancing overall well-being³⁰. Additionally, commensality has been shown to alleviate stress and anxiety levels, with shared meals among friends or family reducing psychological stress and facilitating emotional regulation³¹. Furthermore, commensality plays a key role in shaping individual self-identity³².

Regarding the second issue, the conflicting findings on peer relationships and academic performance are not only a matter of heterogeneity; they are symptomatic of a fragmented and unsystematic body of research. The limitations of research samples or the absence of important variables often prevent a comprehensive understanding and lead to contradictory results. To improve the scientific rigor, it is essential to conduct a systematic examination of these factors. Based on the existing literature, this study identifies several key aspects of heterogeneity—first, physical space. Research has shown that different dormitory allocation methods can result in varying peer effects. Globally, dormitory assignments generally fall into three categories: no on-campus dormitory provision, non-random dormitory assignments, and random dormitory assignments. In China, most universities assign dormitories randomly based on students’ majors, creating a natural random sampling of dormitory, floor, and building assignments. In contrast, universities in the United States and other countries often use multi-criteria evaluations for dormitory assignments, resulting in greater variability in standardized test scores among roommates. There is also a higher prevalence of single rooms. The nature of peer relationships is quite different in multi-person dormitories compared to single rooms. Furthermore, Chinese students often bring a competitive mindset into dormitory life, where roommate interactions can be influenced by competition for awards, party membership quotas, and employment opportunities, leading to “utilitarian tendencies and small group phenomena”. In addition, compared to primary and secondary students, college students experience greater physical and social distance, making it necessary to consider dormitory buildings and other spatial elements in peer relationship research³³.

Second, gender. Existing studies indicate that the link between peer relationships and academic performance varies by gender. Some social psychology research suggests that women are more susceptible to peer influence in competitive environments³⁴, a view supported by empirical studies³⁵. Yet, in the context of college students, most research finds that male students are more influenced by their peers³⁶.

Third, family backgrounds. According to Harris, family background provides children with opportunities to build different types of peer networks. Although college students are physically distant from their families, family factors continue to influence peer effects to a great extent. For instance, in China, urban-rural and household registration factors can affect peer acceptance; children of migrant workers are often marginalized in public schools and less likely to be accepted by peers²⁸. Family economic conditions and consumption levels also play a role. Students whose parents share similar educational backgrounds, occupations, and socioeconomic status are more likely to form friendships. For example, Mayer and Puller found that students of the same race, income level, and with at least one parent having higher education are more likely to become friends³⁷. Conversely, students from disadvantaged socioeconomic backgrounds likely face reduced peer acceptance or occupy a marginalized position within peer groups.

Fourth, individual social identity and status. Students’ specific social identities and roles within their communities are also powerfully correlated to peer relationships. Political orientation, for example, influences peer relationships, as students with similar political views are more likely to connect³⁷. Additionally, student leadership experience can affect peer dynamics; those who have held leadership positions tend to have broader peer networks and receive more positive peer evaluations²⁸. Ethnicity is another fundamental aspect of social identity, with studies indicating that it can also shape peer effects^38,39.

Therefore, in this study, we first investigate the relationship between peer interactions among college roommates and academic performance, focusing on how commensality variables that we defined to innovatively measure peer acceptance are linked to academic performance. We then extend the analysis by broadening the categories of peers. In addition to roommates (Category 1), we examine Category 2 peers—classmates living on the same dormitory floor but not sharing a room—and Category 3 peers, who are classmates but live on different floors or in different buildings. This expansion allows us to explore how peer relationships at varying physical distances are associated with academic performance. Finally, we investigate the heterogeneity of these associations across various subgroups, considering how factors including gender, academic background, and family influence moderate the relationship between peer acceptance and academic performance. While this study refrains from making premature causal claims, by robustly mapping the abovementioned relationships, it provides a solid empirical groundwork for future inquiries.

Results

The short-term and sustained links between roommate-peer relationships and academic performance

To begin, we analyzed the short-term association between peer acceptance, as quantified by “commensality” among roommates, and their semester average scores. “Commensality” is operationalized through this: If two students make their first card swipe in the same canteen, on the same day, and during the same meal period, and the time difference between these first swipes is within a specified threshold, this is considered a single instance of them dining together. As a result, each student’s “commensality value” is incremented by 1. As shown in Table 1, there is a significant positive correlation between the value of roommate commensality in the first semester and the students’ average scores at the end of that semester. Specifically, the standardized coefficient was $\beta$= 0.092, with a p value of less than 0.001 and a 95% confidence interval of [0.004, 0.008]. This finding indicates a positive and significant association, where higher peer acceptance among roommates is linked to higher semester average scores in the short term.

Table 1 Regression results of standardized coefficients for roommates’ commensality and average scores

To validate these findings, we replaced the first-semester data with second-semester data and conducted another round of standardized coefficient regression analysis. The results remained consistent, showing that the short-term association remained significant. The commensality value for the second semester was significantly and positively linked to the course average scores at the semester’s end ($\beta$= 0.142, p < 0.001, 95% ${CI}$ [0.016, 0.026]). Moreover, the $\beta$ value for the second semester was 54% higher than that for the first semester, suggesting this link may intensify over time.

To determine whether this is sustained beyond the short term, we examined the link between first-semester roommate commensality on average scores in the subsequent semester. The results indicated that the commensality value from the first semester remained significantly and positively associated with the average scores in the second semester ($\beta$= 0.104, p < 0.001, 95% ${CI}$ [0.006, 0.014]). This suggests that peer acceptance among roommates exerts a sustained impact on academic performance over time.

It is essential to recognize that the current model may be susceptible to omitted variable bias (OVB). While the association with roommate relationships is significant, other peer relationships, not yet accounted for, may also have a crucial link to academic performance. To gain a broader perspective, the subsequent sections will examine the associations with other significant peer relationships.

The short-term and sustained links between multiple peer relationships and academic performance

While the dormitory roommate relationship is one of the most significant peer relationships for college students, it is not the only one. Students often form connections with peers in the same class, dormitory building, and neighboring dormitories on the same floor. Even if students do not share the same floor, classmates may still interact and influence each other for various reasons. To explore the links of different types of peer relationships to academic performance, we draw on the framework established by Back, Schmukle, and Egloff regarding the effects of proximity on interpersonal relationships among college students³³. As detailed in Methods, we categorized peers based on physical distance: second-category peers (students in the same class and on the same dormitory floor, but not roommates) and third-category peers (students in the same class but on different floors or buildings). Additionally, we developed a commensality diversity index based on interactions with peers across these three categories.

We re-examined the short-term associations between peer acceptance with academic performance using these categories. To ensure the robustness of our analysis, we excluded students who did not have all three peer categories simultaneously. The short-term analysis for the first semester is presented in Table 2. The results indicate a positive, though marginally significant, coefficient for roommate commensality ($\beta$ = 0.043, p = 0.051), while the second-category commensality is not significant. In contrast, the third-category commensality demonstrates a significant positive correlation with average GPA ($\beta$ = 0.076, p = 0.002, 95% ${CI}$ [0.027, 0.125]), and the commensality diversity index also shows a significant positive link ($\beta$ = 0.037, p = 0.037, 95% ${CI}$ [0.002, 0.072]). These findings suggest a substantial positive association between peer acceptance and academic performance in the short term.

Table 2 OLS results of standardized coefficients for commensality with multiple categories of peers and average scores

To further rigorously compare the effect sizes, we conducted F-tests on the four independent variables. The results indicate no significant difference between the three categories of commensality behaviors; however, significant differences were observed between: Roommate commensality and the commensality diversity index ($F$(1, 2262) = 4.29, p = 0.0384), second-category commensality and the commensality diversity index ($F$(1, 2262) = 4.24, p = 0.0397), and third-category commensality and the commensality diversity index ($F$(1, 2262) = 4.26, p = 0.0392).

Based on the standardized regression coefficients and F-test results, we conclude that in the short term, the third-category commensality value ($\beta$ = 0.076) has the strongest association with semester average scores, followed by the commensality diversity index ($\beta$ = 0.037). Roommates and second-category peers showed weaker or non-significant links.

After replacing the data with those from the second semester and performing standardized coefficient regression, the results indicate that the short-term links remain significant. Specifically, the regression analysis shows that roommate commensality during the second semester has a positive correlation with semester average scores ($\beta$ = 0.042, p = 0.045, 95% ${CI}$ [0.001, 0.083]). The second-category commensality ($\beta$ = 0.075, p < 0.001, 95% ${CI}$ [0.034, 0.116]), third-category commensality ($\beta$ = 0.134, p < 0.001, 95% ${CI}$ [0.090, 0.178]), and the commensality diversity index ($\beta$ = 0.094, p < 0.001, 95% ${CI}$ [0.061, 0.127]) all show significant positive correlations with semester average scores.

Referring to the meta-analysis by Cheung and Slavin⁴⁰, which found an average effect size of 0.11 across 52 educational projects with sample sizes greater than 2000, the commensality diversity index in this study is close to this benchmark, while the third-category commensality exceeds it. F-tests conducted on pairs of the four independent variables revealed the following: Roommate commensality vs. second-category commensality: $F$ (1, 2784) = 5.73, p = 0.0168. Roommate commensality vs. third-category commensality:$F$ (1, 2784) = 5.60, p = 0.0180. Roommate commensality vs. commensality diversity index: $F$ (1, 2784) = 30.47, p < 0.001. Second-category commensality vs. third-category commensality: No significant difference. Second-category commensality vs. commensality diversity index: $F$ (1, 2784) = 28.96, p < 0.001.

Third-category commensality vs. commensality diversity index: $F$ (1, 2784) = 30.06, p < 0.001.

These results suggest that among the four variables, the third-category commensality value ($\beta$ = 0.134) is most strongly associated with semester average scores, followed by the commensality diversity index ($\beta$ = 0.094), the second-category commensality value ($\beta$ = 0.075), and finally, the roommate commensality value ($\beta$ = 0.042). Furthermore, the coefficient for third-category commensality in the second semester is significantly higher than that in the first semester (0.134 vs. 0.076), which may indicate that the effect size of commensality increases over time.

In the short term, compared to roommate commensality, interactions with peers who are physically more distant (i.e., those not on the same floor or in the same building) present the strongest positive link to academic performance. Specifically, the data indicate that holding other factors constant, an increase in the commensality value for third-category peers by 3.15 (equivalent to approximately three shared meals with one such peer or one shared meal with three such peers) is linked to an increase of ~9.70 points in the student’s total score by the end of the semester.

Is this sustainable? The results show that first-semester commensality with roommates ($\beta$ = 0.064, p = 0.006, 95% ${CI}$ [0.019, 0.109]) and third-category peers (β = 0.133, p < 0.001, 95% ${CI}$ [0.082, 0.184]) are both significantly positively correlated with the average score in the second semester. Yet, the positive correlation between second-category commensality, the commensality diversity index, and the average score was not significant in the first semester. An F-test conducted on these four independent variables revealed that there were no significant differences between the pairs of variables. Consequently, it can be inferred that the third-category commensality value from the first semester is the most substantial predictor of average scores in the second semester ($\beta$ = 0.133), followed by the value of roommate commensality from the first semester ($\beta$ = 0.064). Even when extending the timeframe, the link between peer acceptance among third-category peers and academic performance remains the strongest.

These findings indicate that peer acceptance, as measured by commensality values, is significantly associated with academic performance. Interestingly, contrary to the propinquity effect in social relations, peers who are physically the most distant were found to be the most strongly linked to academic performance.

When the average score was replaced by the failed subject ratio, as shown in Table 3, the results demonstrated that peer acceptance is significantly and negatively associated with the failed subject ratio, both in the short and long term, thereby confirming the robustness of the findings. Expanding the scope of academic performance to include major ranking and the number of failed subjects (see Supplementary Tables 6–11) further supports the findings: peer acceptance negatively correlates with the number of failed subjects and positively correlates with major ranking, both in short-term and sustained analyses.

Table 3 OLS results of standardized coefficients for commensality with multiple categories of peers and failed subject ratio

The heterogeneity of the links between multiple peer relationships and academic performance

The results of this research suggest that peer relationships, particularly peer acceptance, have a nonnegligible positive link to students’ academic performance. Yet, previous studies have shown that the strength of this association or effect can vary widely among different student groups. This variation raises the question: what factors are related to these differences? Many earlier studies were limited by sample size and data availability, which prevented a comprehensive analysis. To address this gap and further refine our findings, we explored the heterogeneity across different groups of students.

To this end, we selected 12 sub-samples across six pairs of student groups for analysis. These groups include:Male and female students^{24,35,36,41,42,43}; Han Chinese and ethnic minorities in China⁴⁴; Students who have served as class leaders in high school and those who have not²⁸; Communist Party members or league members versus non-party members or league members³⁷; Students with elite working parents and those with non-elite working parents; Students with parents who are Communist Party members versus those whose parents are not³⁷. Except for the pair involving elite and non-elite working parents, where no significant differences were found, the other groups demonstrated notable variations in how peer relationships were linked to academic performance.

In the short term, the association between peer relationships and semester average scores was more pronounced for male students compared to female students. Specifically, for male students: First-semester roommate commensality: $\beta$ = 0.064, p = 0.006, 95% ${CI}$ [0.018, 0.11], Second-semester roommate commensality: $\beta$ = 0.049, p = 0.019, 95% CI [0.00811, 0.0899], Second-category commensality: $\beta$ = 0.043, p = 0.049, 95% ${CI}$ [0.000196, 0.0858], Third-category commensality: $\beta$ = 0.072, p = 0.006, 95% ${CI}$ [0.0203, 0.124], Commensality diversity index: $\beta$ = 0.086, p < 0.001, 95% ${CI}$ [0.0524, 0.12].

For female students, while the commensality diversity index was significant in the second semester ($\beta$ = 0.118, p < 0.001, 95% ${CI}$ [0.0605, 0.175]), the links to other variables were less pronounced.

When examining the sustained timeframe, the link between peer relationships and academic outcomes remained stronger for male students. For male students: First-semester roommate commensality: $\beta$ = 0.059, p = 0.009, 95% ${CI}$ [0.0148, 0.103]; Third-category commensality: $\beta$ = 0.115, p < 0.001, 95% ${CI}$ [0.0534, 0.177]; Commensality diversity index: $\beta$ = 0.039, p = 0.036, 95% ${CI}$ [0.00258, 0.0754]. For female students, the third-category commensality value in the first semester was significant ($\beta$ = 0.159, p = 0.027, 95% ${CI}$ [0.0184, 0.3]), but other variables were not. See Supplementary Table 1 for full details.

These findings align with the results of Griffith and Rask³⁶, which found that male students are more significantly influenced by their peers compared to female students. This pattern holds true even when the semester average score is replaced by other performance measures, such as failed subject ratios.

As shown in Table 4, the short-term link between peer relationships to academic performance varies significantly between party members or league members and non-members. For party members or league members, the third-category commensality value in the first semester is strongly correlated with average GPA ($\beta$ = 0.087, p < 0.001), as is the commensality diversity index ($\beta$ = 0.044, p = 0.019). In the second semester, the association remains significant, with second-category commensality ($\beta$ = 0.074, p < 0.001), third-category commensality ($\beta$ = 0.139, p < 0.001), and the commensality diversity index ($\beta$ = 0.108, p < 0.001) all positively associated with GPA.

Table 4 OLS results of standardized coefficients for average scores by political status subsamples

In contrast, for non-party members or league members, the observed associations were less pronounced. For these students, no significant link was found in the first semester, and while the roommates’ commensality in the second semester showed a significant correlation ($\beta$ = 0.197, p = 0.048), other variables did not demonstrate a similar link.

Regarding the sustained timeframe, the link between peer relationships and academic performance continued to be stronger for party or league members. For instance, first-semester roommate commensality shows a significant association ($\beta$ = 0.059, p = 0.016), and third-category peer commensality remains highly strongly correlated ($\beta$ = 0.138, p < 0.001). In contrast, for non-members, no significant sustained associations were found. When other performance indicators, such as the failed subject ratio, are considered, the results remain consistent. See full results in Supplementary Table 2. These findings suggest the link between peer relationships and academic outcomes is stronger for party members or league members compared to non-members.

Table 5 provides further evidence of heterogeneity among students who have previously served as class leaders versus those who have not. For former class leaders, the association with first-semester roommate commensality is significant ($\beta$ = 0.079, p = 0.019), as is the link with third-category commensality ($\beta$ = 0.077, p = 0.026). During the second semester, the link with roommate commensality ($\beta$ = 0.059, p = 0.042), second-category commensality ($\beta$ = 0.071, p = 0.014), third-category commensality ($\beta$ = 0.150, p < 0.001), and the commensality diversity index ($\beta$ = 0.050, p = 0.031) remains significant.

Table 5 OLS results of standardized coefficients for average scores by class leader experience subsamples

In contrast, students without class leadership experience show a significant association only with second-category commensality during the first semester ($\beta$ = 0.067, p = 0.049), while other associations are not significant. Moreover, for this group the link with roommate commensality during the second semester is not significant.

When assessing sustained associations, former class leaders continue to show greater links to peer relationships. Roommate commensality ($\beta$ = 0.086, p = 0.008) and the commensality diversity index ($\beta$ = 0.136, p < 0.001) are more strongly associated with their semester average scores compared to non-leader students, for whom only the third-category commensality remains significant ($\beta$ = 0.126, p = 0.003). Replacing semester average scores with the failed subject ratio yields consistent results; see the details in Supplementary Table 3.

As shown in Table 6, students with parents who are Communist Party members exhibit a stronger link to peer relationships in the short term compared to those without. For students with party member parents, the first-semester roommate commensality ($\beta$ = 0.078, p = 0.011), third-category commensality ($\beta$ = 0.074, p = 0.031), and commensality diversity index ($\beta$ = 0.076, p = 0.003) are all positively correlated with their semester average scores. This pattern persists in the second semester, where the second-category commensality ($\beta$ = 0.079, p = 0.008), third-category commensality ($\beta$ = 0.129, p < 0.001), and the commensality diversity index ($\beta$ = 0.119, p < 0.001) continue to show significant positive links.

Table 6 OLS results of standardized coefficients for average scores by party member parents subsamples

Contrastingly, students whose parents are not Communist Party members show a different pattern. For these students, only the third-category commensality value in the first semester ($\beta$ = 0.098, p = 0.012) shows a significant link, with other variables not reaching significance. In the second semester, while the third-category commensality ($\beta$ = 0.171, p < 0.001) and commensality diversity index ($\beta$ = 0.063, p = 0.013) are significant, other links remain non-significant.

When examining the continuous association, students with Communist Party member parents continue to show stronger links to peer relationships. First-semester roommate commensality ($\beta$ = 0.092, p = 0.005), third-category commensality ($\beta$ = 0.142, p < 0.001), and commensality diversity index ($\beta$ = 0.052, p = 0.049) all show substantial associations with their academic performance. In comparison, for students whose parents are not party members, a significant association is observed only for third-category commensality ($\beta$ = 0.158, p < 0.001), with other variables remaining non-significant.

For students with Communist Party member parents, stronger peer relationships are linked to better academic outcomes. These findings remain consistent even when the semester average score is replaced with other performance indicators, such as the failed subject ratio, indicating the robustness of these observed links; See the details in Supplementary Table 4.

Table 7 advances the understanding of the association between peer relationships and academic performance for Han Chinese students versus Chinese ethnic minorities. Among Han students, peer acceptance is closely linked to academic performance, correlating with their semester average scores, major rankings, and failed subject ratios. Specifically, positive peer acceptance shows a significant positive correlation with higher scores and better rankings, while a lack of acceptance is linked to lower scores, poorer rankings, and higher failed subject ratios.

Table 7 Regression results for average scores by han and minority chinese subsamples

For ethnic minority students, however, the association with peer acceptance is more pronounced in the number of failed subjects rather than for average scores or rankings. This suggests that for these students, peer acceptance is significantly related to the likelihood of passing specific subjects, highlighting that ethnicity may be a key moderating variable in the link between peer relationships and academic outcomes. The link between commensality and academic performance does vary across different student groups.

Discussion

Our study reveals a significant and robust positive association between peer acceptance—innovatively operationalized through commensality (shared meals)—and students’ academic performance. This association holds true across multiple academic metrics, including average scores, major rankings, and the likelihood of failing subjects. We observed that higher commensality values were statistically predictive of better academic outcomes for students at all performance levels, from those struggling to pass to those at the top of their class. Furthermore, these associations appeared to strengthen over the academic year, a pattern consistent with literature suggesting that the influence of peer relationships intensifies with duration^25,45.

It is essential, however, to notice the multifaceted nature of commensality, particularly during the first semester. The initial peak in commensality values during this period might reflect not only genuine social bonding but also social pressure or an intense, potentially stressful phase of social exploration. The observed stabilization of commensality in the second semester could indicate a transition from broad, exploratory interactions to more stable and authentic peer connections. Despite these interpretative complexities, our models consistently reveal a robust positive association. This suggests that, despite the underlying social dynamics, the overall pattern links increased commensality to favorable academic outcomes.

One of the most noteworthy findings is that the strongest positive association with academic performance was observed with commensality involving peers who are physically most distant—those not residing on the same floor or in the same building. Statically, an increase of 3.15 points in G3 Commensality value each week, i.e., for instance, three shared meals with a third-category peer, links to an approximate increase of 9.70 points in a student’s total score by the end of the semester. Moreover, an increase in the commensality diversity index from 0 to 3 correlates with an impressive 4.03-point increase in the average semester score, translating into a considerable cumulative increase of 44.33 points over the semester.

A plausible explanation lies in the random assignment of students to dormitories at University B. By design, dormitory groups are far smaller and more demographically homogenous, particularly in terms of gender, than academic classes. Consequently, the probability of a student encountering influential peers is inherently lower within the confines of the dorm compared to the broader, more diverse pool of classmates. This seemingly counterintuitive finding becomes even clearer when viewed through the social capital theory^46,47,48. We propose that commensality serves as a behavioral proxy for peer acceptance, a social state that, in turn, grants students access to valuable social capital. Specifically, dining with peers—whether roommates or more distant connections—reflects varying degrees of integration into social networks, enabling students to acquire distinct forms of social capital. While roommate relationships are often formed out of convenience due to random assignment and provide essential bonding capital, interactions with more distant peers are more likely to be intentional choices that bridge structural holes in the university’s social network. As predicted by theory⁴⁷, these bridging ties are invaluable sources of unique information and diverse perspectives, thus explaining their powerful effect on academic performance. Beyond access to novel information, additional mechanisms may also be at play. For instance, dining with distant peers might require greater effort and intentionality, potentially signaling higher motivation or social competence, which could independently contribute to academic success. Alternatively, such interactions may expose students to diverse ideas or study habits not available within their immediate circles. Future research is needed to explore these potential mechanisms.

Our analysis also uncovered significant heterogeneity in the strength of these associations across different student subpopulations. We find a stronger association between peer acceptance and academic outcomes among male students compared to female students. This pattern aligns with prior research indicating males may derive a greater sense of social status from broad peer recognition and competitive environments^49,50, whereas females may place greater emphasis on smaller, intimate friendship circles⁵¹.

Communist Party members, Youth League members, and students with leadership experience exhibit a stronger positive association between peer acceptance and academic performance compared to their counterparts. This is indirectly supported by studies showing the value of social integration and political networks in shaping individuals’ academic and social behavior⁵², while the direction of causality cannot be determined from our data.

Students with parents who are party members show a stronger link between peer acceptance and academic outcomes compared to those whose parents are not party members. Conversely, the association was weaker for ethnic minority students compared to their Han Chinese counterparts. This latter finding might be explained by social context. Research by Seuring et al. suggests that in classrooms with a higher proportion of minority students, peer relationships within minority groups tend to be stronger, as the environment provides more opportunities for minority language use and cultural exchange⁵³. In contrast, in classrooms with a lower concentration of minority students, as is the case at University B, where minority students are underrepresented, opportunities for strong in-group bonding are limited. This lack of a robust in-group support network can lead to heightened feelings of social isolation or acculturative stress. These pressures may act as a confounding factor, dampening or overriding the academic benefits that would otherwise stem from broader peer acceptance. Consequently, the link between general commensality and academic performance becomes less pronounced for this group.

This research offers two primary contributions. First, we introduce innovative techniques for measuring peer relationships, particularly peer acceptance. Traditional methods such as “positive nomination” and “negative nomination”^54,55, are not applicable for large, fluid college students, and direct, large-scale observation is quite infeasible, prompting us to apply commensality as a new approach. Commensality offers a fresh perspective and a reliable empirical measure of peer acceptance among college students. Leveraging students’ transactional data and integrating diverse student information, we develop commensality variables and look into the dynamics of varying peer relationships and academic performance. This work utilizes campus card data as an entry point, employing large-scale, real-world transactional data of students to measure commensality as a proxy for peer relationships. The regression estimates from the extensive sample data help obtain more stable effect sizes for the relationship between peer relationships and academic performance. By relying on objective data—such as commensality data and course scores recorded by the university administrative system—we increase external validity compared to traditional survey-based studies.

Second, our research enhances the understanding of how peer relationships, particularly peer acceptance, relate to the academic performance of college students. While the association between peer relationships and individual well-being—such as depression^56,57,58, adjustment outcomes⁵⁹, and decision-making behaviors like prosocial behavior⁶⁰, self-injurious behavior, and risk-taking behavior⁶¹—has been extensively studied, the link between peer acceptance and academic performance at the college level has remained relatively unexplored. We address this gap by providing a comprehensive analysis of how peer acceptance is associated with academic outcomes. Our work refines the understanding of various categories of peers. It expands the exploration of heterogeneity in peer effects, examining the diversity of these associations across factors including physical proximity, gender, political status, leadership experience, and family background. These findings are again powerfully illuminated by social capital theory^46,47. This framework posits that social interactions are not merely social events but are instrumental in building capital that yields tangible returns. In this context, commensality serves as a mechanism for accumulating social capital, which in turn enhances academic performance. Specifically, roommate commensality aligns with bonding social capital⁴⁷, offering emotional support and collaborative opportunities through strong, trust-based ties. In contrast, commensality with more distant peers reflects bridging social capital, granting access to diverse information and perspectives that enhance academic outcomes.

While our work advances the measurement and understanding of peer relationships, we are also cognizant of its limitations. First, the applicability of commensality as a behavioral proxy is context-dependent. Its successful implementation relies on specific institutional infrastructures, such as a high-density residential campus, a centralized payment system, and a cultural norm of on-campus dining. Consequently, this approach may not be directly transferable to higher education systems where such conditions are absent, for instance, the non-residential or commuter models common in many Western countries. This limitation, however, also highlights another unique contribution of this study. That is, it provides a much-needed empirical investigation from an East Asian high-residency context to the global literature. It is not merely a geographic expansion but a methodological and empirical enrichment that highlights the necessity of context-sensitive approaches in understanding peer relationships across diverse educational systems. We encourage future research to replicate and adapt this methodology by tailoring it to the specific conditions of their respective institutions. For instance, alternative behavioral proxies—such as co-presence in library spaces or Wi-Fi logs—could be explored to capture peer dynamics in non-residential learning environments. This adaptive approach will further broaden the applicability of behavioral data in studying social interactions globally.

Second, the use of canteen-level data may introduce a degree of noise from random encounters into our “Commensality” metric. Nevertheless, we are confident this does not undermine the core findings. Most critically, the metric demonstrates strong construct validity, showing a clear, socially intuitive gradient: values are constantly highest with roommates and moderate with other categories of peers, as detailed in Table 8. Such a structured pattern provides evidence that the metric captures meaningful signals rather than random noise. Furthermore, our analytical framework, which applies the standardized coefficient OLS regression, is sensitive to the relative ranking of commensality values rather than their absolute magnitudes. Even if a baseline level of noise uniformly inflates the scores, the metric’s power to predict academic outcomes remains intact, as the variance associated with genuine social interaction is preserved. Finally, the metric’s ability to predict academic performance serves as strong external validation, suggesting it successfully operationalizes a meaningful aspect of student social life. While future research with POS-level data would be valuable, our findings support the ‘Commensality’ metric as a robust proxy for peer acceptance in this context.

Table 8 Descriptive statistics and explanations

Third, while our two-wave longitudinal design helps establish temporal precedence, our findings are not causal. The limitation here is potential self-selection bias, as unobserved characteristics (e.g., motivation, mindsets) may confound the relationship between peer interactions and academic outcomes. This is inevitably relevant for our heterogeneity analyses; for example, the stronger associations for students with Party membership could reflect these pre-existing traits rather than a causal impact of their status. Therefore, future work employing methods designed for causal inference, such as instrumental variables, is needed to isolate the effect.

Fourth, our study utilizes a large amount of objective behavioral data, which, while powerful in scale and accuracy, cannot capture the subjective motivations behind commensality. We are unable to distinguish between interactions driven by genuine affinity versus those motivated by social regulation or peer pressure. Nor could we cover another important aspect of peer relationships—peer rejection⁶² in this study. Future research could benefit from a mixed-methods design, for instance, incorporating qualitative data to provide a richer understanding of the student experience in peer relationships.

Fifth, the duration of the relationships examined. This study focused on the impact of peer relationships over a single academic year consisting of two semesters. Yet, the duration of peer relationships is a core factor influencing peer effects^25,45. Extending the study period to two years or even longer could reveal more about the long-term effects of peer acceptance and interactions.

While our study identifies robust associations rather than definitive causality, the findings suggest potential avenues for university policies that aim to enhance student experiences and academic outcomes. We present the following ideas as exploratory directions that warrant further research, and encourage universities to view these suggestions as starting points for experimentation and collaboration with researchers to build evidence-based strategies.

First, universities might consider fostering environments that facilitate communal activities, such as dining, studying, and relationship-building. For instance, Harvard’s residential system for undergraduates, integrating dining halls and learning spaces, exemplifies structures that encourage such engagement. Drawing on our observed association between commensality and academic performance, universities could also explore initiatives such as offering discounts for shared meals or integrating collaborative projects into their curricula.

Second, structured peer support programs could be an area of exploration. An example is the “mentor program” at MIT’s Department of Physics, which pairs first- and second-year students with trained upper-level students. Given our findings on the positive association between peer acceptance and academic performance, universities may want to investigate whether such programs are effective in their own cases.

Last, our heterogeneity analyses highlight varying associations between peer influence and academic outcomes across different student groups. However, a weaker association for specific groups—such as ethnic minorities or female students—does not automatically indicate a deficit that requires a uniform intervention. Instead, it suggests that the dynamics of peer influence are shaped by numerous factors, such as cultural norms, social capital, or differing access to support systems, and thus, a “one-size-fits-all” approach is likely insufficient. This highlights the need for further research to comprehend the distinct social and academic support networks that various student populations rely on. Instead of prescribing standardized solutions, future policies should be informed by a nuanced understanding of these varying needs, ensuring that any support provided is both relevant and practical while protecting student privacy.

Methods

Data and sample selection

This study received approval from the Ethics Committee of Beijing Institute of Technology (BIT-EC-H-2024275). Since the data did not involve direct interaction with human subjects, informed consent was waived by the Ethics Committee. All data were handled with a high level of confidentiality and used exclusively for this research. The data were obtained from the administrative department of B University in Beijing and could be categorized into three primary categories. The first category consisted of a comprehensive dataset containing 10,285,494 entries, which captured all campus card transactions made by undergraduate students between September 2020 and June 2021. For our analysis, we focused on a subset of 2,717,938 transactions specifically related to first-year undergraduates during the 2020–2021 academic year, spanning 10 months. This subset provided detailed transactional information, including student IDs, locations (for instance, which canteen the transaction happened), and timestamps for each transaction.

The second category comprised the data on first-year students (2020 fall freshmen), detailing a range of demographic and academic variables such as geographical origin, gender, Chinese College Entrance Examination (CEE) scores, educational background, major, dormitory allocation, and family information.

The third category included detailed academic records for the 2020 cohort over one academic year, encompassing course names, grades, and examination formats. To construct our final analytical dataset, the three data categories were first merged using student IDs. This process was conducted within a secure environment to safeguard student information. Upon successful merging, the entire dataset was de-identified. We replaced the original student IDs with randomly generated, unique research IDs, severing any direct link to individual students and ensuring privacy during the analysis phase. The course grade data were preprocessed for the first and second semesters of the 2020–2021 academic year as follows: (1) Grades classified as “Fail/Pass/Good/Excellent” were eliminated due to their qualitative nature. (2) University-level elective courses were excluded because of their low failed subject ratio of only 2.7%, the lowest among all course categories. (3) Grades from resit, retake, and repeat examinations were omitted, as these had a high failed subject ratio of approximately 60%, more than double that of regular exams. (4) Chinese College English Test Band 4 grades were removed, as they do not use a percentage grading scale. After applying these criteria, a total of 93,834 valid course grades remained, with 48,818 from the first semester and 45,016 from the second.

The initial sample included all B University students who had dining experiences in campus canteens, as indicated by their card payment records from September 2020 to June 2021. We excluded students with incomplete data and those who did not use canteen services within the study period. For analyses focusing on roommate interactions, the sample sizes were refined to n₁ = 2782 for the first semester and n₂ = 3355 for the second semester of the 2020–2021 academic year. Further refinement occurred when evaluating broader social interactions, excluding students with less than three defined peer categories. This adjustment resulted in sample sizes of n₃ = 2485 for the first semester and n₄ = 3007 for the second semester.

A notable disparity in sample sizes between semesters was observed, primarily due to the appearance of students in the second semester who lacked canteen transaction data in the first semester. To determine if the absence of transaction data for some students in the first semester was missing completely at random (MCAR), we used CEE scores as a key indicator of academic performance. This allowed for a comparative analysis between students missing one semester’s transaction data and the overall student cohort, providing clues into the randomness of data absence.

In our initial analysis, we subjected both the student subset n₀ (lacking first-semester card transaction data) and the complete student cohort N to the Kolmogorov–Smirnov (K–S) test. The test produced a KS statistic of 0.0565 and a p value of 0.0764, indicating no significant difference at the 0.05 level. This suggests a preliminary similarity between the two data distributions. Yet, the proximity of the p value to 0.05 warrants attention.

Furthermore, Litter’s MCAR test was applied, resulting in a non-significant outcome (χ² = 1.376, df = 1, p = 0.241). Additional K–S tests comparing n₁ to n₂ and n₃ to n₄ yielded statistics of 0.0066 (p = 0.9999) and 0.0112 (p = 0.9948), respectively. In both instances, the p values were not significant, reinforcing the null hypothesis that the data distributions are identical in origin.

A visual inspection via a violin plot (Figure. 1) illustrates these findings; the distributions and statistical properties of n₀ and N, n₁ and n₂, and n₃ and n₄ display substantial similarity, with only minor deviations at the extremes. Consequently, this analysis suggests that the absence of commensality values with roommates in the first semester is random. Therefore, the imputation of these missing transaction records was not implemented.

Fig. 1: Distribution of college entrance examination scores across three sample pairs.

The violin plots visualize the distribution of college entrance examination scores for three pairs of sample groups over two semesters. Each plot shows the density and spread of scores within each group, with the central white dot representing the median and the thick black bar indicating the interquartile range. a compares the distribution of the subset (n₀) that lacked first-semester transaction data with the full sample (N). Both groups display similar score distributions, suggesting that missing data in the first semester was random. b The comparison between students in the first semester (n₁ = 2782) and the second semester (n₂ = 3355) of the 2020–2021 academic year. The distributions are consistent, indicating stable academic performance across semesters. c The distributions after further refinement, excluding students without three defined peer categories. The sample sizes for the first (n₃ = 2485) and second (n₄ = 3007) semesters again show similar patterns, demonstrating uniformity in score distributions after adjusting for peer interaction criteria.

Variables

Overall, our study employs a two-wave longitudinal design that captures data across distinct phases of the students’ first academic year, establishing a clear temporal sequence for our variables. Baseline data was collected through the university’s administrative processes via standard electronic registration forms during student enrollment. This dataset includes time-invariant characteristics such as demographics, family background, students’ pre-college political status, and class leader experience. This can be referred to as the t0 data.

Our primary independent variable, commensality, was measured continuously throughout the first semester based on daily meal card transaction records. These records were then aggregated into a cumulative score representing social integration during this period. We denote this as the Commensality(t1) variable. After this semester, we obtained the students’ official Academic Performance(t1) from university records. The process was repeated for the second semester. Commensality(t2) was calculated from transaction records during this period, and Academic Performance(t2) was collected at the end of the semester.

The concept of “Commensality” is employed as a key for quantifying peer acceptance, operationalized through the “Commensality value.” It is derived from the spatiotemporal analysis of campus card transaction data. When two students’ first card swipes in the same meal period (breakfast, lunch, or dinner) on a given day, and the time difference between these first swipes is within a specified threshold, it is interpreted as a shared meal, incrementing their respective “Commensality value” by “1.” If three students dine together, their values each increase by “2.”

For contexts: the study site, B University, is a large comprehensive university in Beijing consisting of two individual campuses for undergraduates. During the 2020–2021 academic year, the two campuses housed 8 main canteens, half single floored, half 2–3 floored, accessible to undergraduate students. Our card swiping data included location identifiers that distinguished between these eight main individual canteens, and for one canteen, the specific floors. Collectively, these dining facilities contained approximately over 200 distinct Point-of-Sales (POS, i.e., “swiping points”).

We acknowledge that the spatial granularity of our data is overall at the canteen level, which is less precise than individual POS data and could potentially capture incidental co-occurrences. To mitigate this inherent limitation and enhance the signal-to-noise ratio of our “Commensality” metric, we adopted two methodological safeguards. First, we implemented a data-driven approach to establish the temporal threshold, as detailed later in this section, to strengthen the validity of our metric despite the broader spatial resolution. Second, our study design incorporates a multi-level peer analysis through three categories of peers. This allows for an internal validity check of the “Commensality” metric. If the metric were capturing only random noise, we would expect a uniform distribution of values across the commensality values of these socially distinct groups. As we have demonstrated, this is not the case.

We categorized peers based on physical distance into three groups. The gender composition of these groups is determined by the university’s housing policy, which mandates that students residing on the same dormitory floor are of the same gender. Consequently, first category peers (Roommates) are students sharing the same room. They are always same-gender. Second category peers (Floor-mates) are Classmates living on the same dormitory floor but not in the same room. They are also inherently same-gender.

Third category peers (Other Classmates) are classmates living on different floors or in different buildings. This category is therefore composed of both same-gender and mixed-gender peers.

With Python, we grouped students by their non-identifiable research IDs, dormitory building, and room number, and analyzed the time gaps between initial card swipes during different meal periods. This methodology allowed us to calculate each student’s monthly “Commensality value” with their roommates. We expanded the analysis to include Commensality with the second category peers and third category peers. These computations were followed by a fourth variable, the “Commensality Diversity Index.” These four variables serve as a proxy for peer acceptance⁶³. Higher commensality values suggest elevated levels of peer acceptance.

An integral aspect of this approach involved determining the optimal time threshold for defining a commensality event. To this end, we analyzed all card transaction data from a selected month within the academic year, assessing in 10-second intervals to ascertain the most suitable time difference threshold. Figure 2 illustrates a noticeable inflection point around the 120-s mark in the descriptive statistics of roommate Commensality values for the month. Most statistical indicators exhibited a more rapid increase prior to this point, with a deceleration thereafter⁴¹. This pattern indicates that setting a time threshold below 120-s results in a significant rise in commensality occurrences. Yet, a threshold exceeding 120 s, while still contributing to an increase, is likely to capture more incidental commensality events—such as cases where students dine together by chance rather than intent or are influenced by other error factors. As a result, this study selected a 120 s (2-min) threshold for time differences.

Fig. 2: Descriptive statistics of commensality over varying time thresholds measured in seconds.

This figure displays the evolution of seven statistical metrics—maximum (dark brown), 75th percentile (yellow), standard deviation (purple), mean (orange), median (teal), 25th percentile (green), and minimum (pink) of commensality values across different time thresholds, ranging from 0 to 600 s. Each curve represents a specific statistical measure as the time threshold increases. The steep rise early on, particularly for the maximum, indicates a sharp increase in commensality occurrences within the initial 100 s, after which the values plateau, reflecting fewer incremental increases beyond this threshold. The median, mean, and other percentile-based metrics show a more gradual rise, stabilizing at different points. These patterns suggest that setting the commensality time threshold at or near 120 s captures the most substantial occurrences without much-added noise from incidental events.

Finally, we constructed four independent variables related to commensality for each semester: the commensality value of roommates, the commensality value of second-category peers (second-category commensality value), the commensality value of third-category peers (third-category commensality value), and the student commensality diversity index, see Table 8. For the comprehensive list of variables, see in Supplementary Information p.1–4.

By controlling for the comprehensive set of variables, we aim to address homophily⁶⁴ and the reflection problem⁶⁵. See Supplementary Table 5.

The Chinese College Entrance Examination (CEE), also known as the Gaokao, is a nationwide standardized test that plays a pivotal role in determining access to higher education in China. It assesses students in key subjects such as mathematics, Chinese, and a choice between sciences or humanities. CEE serves as a reliable baseline for assessing the academic abilities of Chinese undergraduate students and is used in this study to gauge students’ academic aptitude prior to entering college.

The original Chinese College Entrance Examination scores of the students were processed and converted as follows: the difference between the original score of each student and the mean score of the students from the same province or region was divided by the standard deviation of the college entrance examination scores of the group of students. Since some majors can be applied for across subjects, for example, physics college entrance examination candidates can apply for the history major of University B, the college entrance examination subjects are not distinguished. The calculation formula is based on the research of Huang and Ma⁶⁶, as shown in (1).

$${Z}_{{{cee}}_{{ip}}}=\frac{{{Cee}}_{p}-{\bar{C}{ee}}_{p}}{{{Stdcee}}_{p}}$$

(1)

Zcee is the processed standard score, Cee is the total score of the college entrance examination (original score), and Stdcee is the standard deviation; i and p in the subscripts represent the student and the province of origin, respectively. In addition, the place of origin and class are two dummy variable groups. The place of origin refers to the 35 provinces, cities, or regions in China where the students in the sample took the college entrance examination; class is the class of the first-year undergraduates, totaling 189.

Models

We employed statistical models tailored to the characteristics of our dependent variables to assess the relationship between commensality values and academic performance while controlling for various student and peer characteristics. For continuous dependent variables—such as semester average score, failed subject ratio, and standardized major ranking—we utilized the standardized coefficient Ordinary Least Squares (OLS) regression model. Standardizing the coefficients allowed us to calculate effect sizes, facilitating a direct comparison of the impact magnitude among different independent variables in our analyses.

Standardized coefficient OLS

The study mostly involves three dependent variables: semester average score, major ranking, and failed subject ratio, for which the standardized coefficient OLS model is employed. The model expression is detailed in Eq. (2). Conversely, when analyzing the fourth dependent variable, the number of failed subjects, the negative binomial regression model is utilized, as discussed in detail later.

$${Y}_{{it}}={\beta }_{0}+{\beta }_{1}C1{{Comm}}_{{it}}+{\beta }_{2}C2{{Comm}}_{{it}}+{\beta }_{3}C3{{Comm}}_{{it}}+{\beta }_{4}{{PeerIndex}}_{{it}}+{{Controls}}_{{it}}+{Peer}{{Controls}}_{{it}}+{{SO}}_{i}{+{Cl}_{i}+\varepsilon }_{{it}}$$

(2)

${Y}_{{it}}$ represents the academic performance outcome for student i in semester $t$. This general model specification is estimated separately for each of our three continuous dependent variables: (1) semester average score, (2) failed subject ratio, and (3) semester major ranking.

The term ${\beta }_{0}$ is the intercept. The coefficients ${\beta }_{1}$, ${\beta }_{2}$, ${\beta }_{3}$, and β₄ correspond to the standardized effects of the four primary independent variables for student i in semester $t$: Roommate commensality ($C1{{Comm}}_{{it}}$), Second-category commensality ($C2{{Comm}}_{{it}}$), Third-category commensality ($C3{{Comm}}_{{it}}$), and the Commensality diversity index (${\beta }_{4}{{PeerIndex}}_{{it}}$). In analyses focusing solely on roommate peers, the coefficients ${\beta }_{2}$, ${\beta }_{3}$ and ${\beta }_{4}$ are constrained to zero.

The model includes several sets of control variables.${{Controls}}_{{it}}$ is a vector of student-specific characteristics (e.g., standardized CEE scores, gender, etc.). ${Peer}{{Controls}}_{{it}}$ is a vector of peer group characteristics (e.g., peers’ average CEE scores, etc.). ${{SO}}_{i}$ and ${Cl}_{i}$ represent full sets of fixed effects (dummy variables) for student i’s province of origin and class, respectively, to control for unobserved time-invariant heterogeneity at these levels. Finally, ${\varepsilon }_{{it}}$ is the idiosyncratic error term.

When analyzing long-term effects (Eq. 3), the dependent variable ${Y}_{i2}$ is from the second semester, while all explanatory variables are from the first semester (e.g., $C1{{Comm}}_{{it}}$). The expression for the regression model is as Formula (3):

$${Y}_{i2}={\beta }_{0}+{\beta }_{1}C1{{Comm}}_{i1}+{\beta }_{2}C2{{Comm}}_{i1}+{\beta }_{3}C3{{Comm}}_{i1}+{\beta }_{4}{{PeerIndex}}_{i1}+{{Controls}}_{i1}+{Peer}{{Controls}}_{i1}+{{SO}}_{i}{+{Cl}_{i}+\varepsilon }_{i2}$$

(3)

Here, the dependent variable ${Y}_{i2}$ is from the second semester, while all independent and control variables are from the first semester. The other terms remain consistent with those described in Eq. (2).

When the dependent variable was a count variable, specifically the number of failed subjects, we applied the negative binomial regression model. This choice was informed by the nature of count data, which are non-negative integers and often exhibit overdispersion (variance exceeding the mean). Although both Poisson and negative binomial regression models are suitable for count data⁶⁷, the negative binomial model is more appropriate when overdispersion is present. In our dataset, the variance of the number of failed subjects significantly exceeded the mean, making the negative binomial regression the suitable choice.

Negative binomial regression

When the dependent variable is the number of failed subjects in the short-term, the negative binomial regression model is employed, as shown in Eq. (4).

$${\text{ln}}{(E[Y}_{{it}}])={\beta }_{0}+{\beta }_{1}C1{{Comm}}_{{it}}+{\beta }_{2}C2{{Comm}}_{it}+{\beta }_{3}C3{{Comm}}_{{it}}+{\beta }_{4}{{PeerIndex}}_{it}+{{Controls}}_{{it}}+{Peer}{{Controls}}_{{it}}+{{SO}}_{i}{+{Cl}_{i}+\varepsilon }_{{it}}$$

(4)

Where ${Y}_{{it}}$ is the number of failed subjects for student i in semester t, and ${E[Y}_{{it}}]$ is its conditional expectation. The model uses a standard log link function. All independent variables, controls, and dummy sets are defined as in Eq. (2) in the Methods section.

For the long-term analysis, where the dependent variable is the number of failed subjects, the model is presented in Eq. (5). Here again, the dependent variable is from the second semester, while explanatory variables are from the first.

$${\text{ln}}(E[Y_{i2}])={\beta}_{0}+{\beta}_{1}C1{{Comm}}_{i1}+{\beta }_{2}C2{{Comm}}_{i1}+{\beta }_{3}C3{{Comm}}_{i1}+{\beta }_{4}{{PeerIndex}}_{i1}+{{Controls}}_{i1}+{Peer}{{Controls}}_{i1}+{{SO}}_{i}{+{Cl}_{i}}+{\varepsilon }_{i2}$$

(5)