Impact of Academic Interaction Networks on Grades & Jobs: Evidence from Four-year University Trajectories

Student interactions play a critical role in education. Interactions and collaborative partner-ships formed within universities can have a profound impact on academic and job-related performance. However, little is known about the mechanisms using which these networks develop inside the classroom, generate network effects, and impact academic and employment outcomes. We analyze 1.5 million de-identiﬁed in-class interactions, grades, and job outcomes for 6,355 undergraduates through a four-year education program to show that students with larger networks exhibit better academic and employment outcomes, and that high-performing students beneﬁt from stronger network effects, as compared to their mid- and low-performing students. Our results also suggest the existence of a network premium - mid-performers with larger networks can achieve higher average salaries than high-performers with smaller networks. We adapted a stochastic actor-oriented model (SAOM) to model the underlying mechanisms of course selection, network formation, and peer inﬂuence among students. Our research sheds light on the importance of interaction networks as drivers of academic and employment performance, as well as the different mechanisms through which high- and low-performing students beneﬁt from them. As education shifts to online, educators and policymakers should invest in the design of digital interactions and communities (e.g.forums) which can generate and sustain healthy networks among students.

attending the same course, 234,265 course enrollment records and grades, and first job placements for an entire cohort of 6,355 undergraduate students from the National University of Singapore (NUS) spanning a four-year tenure. Our data on activity and interactions thus provides a proxy of the interactions between students (See Table 1 in the SI Appendix for detailed data descriptions and Section 1 for additional information on data context). We first use a set of panel regression analyses to examine the relationship between interaction network size, academic outcomes and first job placements. Next, we deploy a 3-stage variant of the stochastic actor-oriented model (SAOM) to jointly estimate the underlying processes of course selection, and overall network effects 1 . In this study, we provide empirical evidence to help guide policies on new teaching modes that can help develop and nurture productive student networks.
Details on the network and performance effects used in this study have been illustrated in the supplementary materials.

Results
Model-free analyses. Students actively interact and form connections with other students over the course of a four-year university program. Their academic and employment outcomes are affected by their level of network embeddedness. To model differences in degree centrality, we categorized students with more than 10 links (75 th percentile) per term as the High Degree group and those with fewer than 2 links (25 th percentile) as the Low Degree group. All other students were categorized as the Middle Degree group. For academic performance, we categorized students with a Cumulative Average Point (CAP), the cumulative academic performance of the student, of 4-5 points into the High CAP group, and those with a CAP lower than 3 point into the Low CAP group. All other students were categorized as the Middle CAP group. In conjunction, interactions serve a dual role of benefiting academic performance and job search. While high-performing students can use their network as a premium to boost success in the job market, mid-and low-performing students can use their networks to compensate for the lack of other type of resources (e.g., academic abilities). Despite variance in the probability of securing jobs, we do not observe such large variances in the magnitude of starting salary across the degree centrality groups as shown in Figure 1/Panel C. However, the differences in starting salary across different levels of degree centrality are statistically significant overall (p =0.001), in the High CAP group (p =0.05) and in the Low CAP group (p =0.02), but not in the Middle CAP group (p =0.16). We estimated a set of regression models quantifying these relationships among degree centrality, CAP, employment status and starting salary while controlling for gender, nationality, faculty and entrance scores. The estimation results are provided in the supplemental material, Table 3. The results of these regression analyses are consistent with our descriptive summaries from Figure 1 and suggest that degree centrality is correlated with employment status upon graduation. In addition, we observed some individual differences in employment related outcomes among the students. Females in our sample were more likely to secure a job, but with a lower starting salary, as compared to their male counterparts. Entrance exam scores were positively linked to overall CAP, but negatively linked to their employment status, as well as starting salaries.
Our model-free analyses provide evidence of the importance of interaction networks and academic performance on employment outcomes. Next, we model the underlying mechanisms through which networks affect academic performance and employment. Networks can affect employment outcomes directly or through the mediating role of academic performance. Similarly, academic performance might also affect employment outcomes through the mediating role of networks. We performed a set of mediation analyses using Baron and Kenny's approach to test these competing hypotheses (See Tables 4-7 in the supplemental material for estimation results). Our analyses show that both interaction networks and academic performance partially mediate the impact of each other on employment outcomes.
Tracking the evolution of interaction networks and academic performance. We further investigate the dynamics and underlying mechanisms by focusing on a subset of representative students from the business school. Figure 2 illustrates the dynamics of term-wise academic performance, the evolution of homophily, and the clustering of the interaction networks. The students' interaction network and academic performance co-evolve by affecting each other. While past work has attempted to disentangle network formation and behavior change (20,21), our empirical analysis is further complicated by the presence of course selection decisions that affect both network formation as well as course outcomes. In the present study, we extended a SAOM framework with a simple sample-selection stage (21,20,22) to develop a three-stage co-evolution model that characterizes the multiplexity of course selection, inter-action network formation, and academic performance. The conceptual framework is shown in Figure 3. The objective functions and detailed model specification are briefly described in the Methods section, and detailed summaries are provided in Section 3 as part of the supplementary materials. We present estimation results using a MCMC-based method of moments estimator.
Considering the computational costs of estimating the SAOM model, we estimated the threestage SAOM model on the sample of business school students (N =683). We provide similar estimates for students from other schools in the supplementary material (Table 10). We further used this model to analyze the heterogeneous effects of network formation and peer influence among students of varying academic abilities.
Linking peer-effects in interactions network to academic performance. In Table 1, we present estimates of the peer effect specified in our three stage model. The homophily estimate in Table 1 (a) is significantly positive (5.64, p <0.001), indicating that, on average, students are likely to build connections with peers who have similar academic performance. The peer influence estimate in Table 1  To evaluate the effectiveness of our proposed model, we compare the model fitness of our three-stage SAOM model against a baseline model that only considers the co-evolution of interaction network and performance changes, without accounting for course selection decisions from Stage (i). The results in Table 1 show that our proposed model outperforms the baseline model on two aspects. First, the focal parameters of interests from our three-stage SAOM model are significant and consistent, i.e., homophily (5.64, p <0.001) and peer influence (5.79, p <0.001), whereas the estimates from the baseline model are insignificant, i.e., homophily (9.85, p=0.13) and peer influence (5.78, p=0.40). This is unlikely given the abundance of past work demonstrating the presence of network effects in student networks. Second, we conducted a goodness of fit (GOF) test to assess how well our proposed model specification fits the empirical data. The GOF is measured by computing the differences between the observed values of network measures and the simulated statistics for the same measures at the end of each period (23). To reduce the risk of over-fitting, we used auxiliary statistics based on network measures which were not explicitly fitted in our model estimation. In Table 1, we report the difference in model fit using the Mahalanobis distance (MHD) (24), and show that the three-stage SAOM model (MHD=301.57) has a substantially better model fit than the baseline two-stage model (MHD=21384.20). We further incorporated a latent space model proposed by (25) to check the sensitivity of our proposed three-stage model to any latent homophily related concerns, as described in the supplementary material, Section 7 and Table 13. To further examine the prevalence of heterogeneity in overall network effects, we conducted a subgroup analysis based on differences in academic performance levels. The results in Table 1 show that the estimate for homophily effect is significant and positive (

Discussion
We investigated the impact of interaction networks on academic performance and job placements. Using de-identified and longitudinal data from a four-year university program, we modeled the complexity of student in-class interactions through the three stages of course selection, network formation, and peer influence. First, we found that student interactions have an impact on academic performance and job market outcomes. The results highlight the important role of social collaborations in driving both academic performance and job placements. Moreover, the significant variance in job placement outcomes across network centrality levels suggests that for many students, their social embeddedness serve to offer a job market premium, and help partially offset academic performance.
To further unravel the underlying mechanisms, we deployed a three-stage SAOM framework to model the multiplexity of course selection, network dynamics, and academic performance over the course of a four-year academic program. We found that the overall network effects have a significant and positive role in student academic performance and future course selection decisions, after controlling for selection decisions at both course and individual levels.
Moreover, we found significant heterogeneous effects across different academic ability groups.
Compared to mid-performing students, high-performing students are more likely to connect to similar high-performing students, while low-performing students are less likely to connect to similar low-performing students. The positive impact of peer influence among high-performing students is stronger than that among both mid-performers and low-performers. However, our study does not capture the modes and channels of communication between students such as information sharing, collaboration or cooperative work.
ki (X t , G t ,M , V ) + ǫ (1) To measure the heterogeneous effects across students with differing academic ability, we included two additional dummy variables to represent whether a student ranked higher than the 75 th percentile of students in each term (High GPA), or ranked below the 25 th percentile  Table 2.
ki (X t , G t ,M , V, High GP A, Low GP A) ki (X t , G t ,M , V, High GP A, Low GP A) + ǫ  Figure 1: The associations between student academic performance, degree centrality and job placements. (A) Network degree explains the CAP scores. The boxplots represent the CAP scores of all students, students in the High Degree group, students in the Middle Degree and in the Low Degree group. The asterisk in the Panel A indicate there exists a significant difference between all students, High Degree students and Low Degree students. (B) The average overall employment rates across CAP groups and degree groups. The boxplots show the values of mean − 2sd, mean − sd, mean, mean + sd, and mean + 2sd, respectively. (C) The average amount of annual salary across CAP groups and different degree groups. The boxplots illustrate the values of minimum, first quartile, median, third quartile and maximum of students' annual salary. We also tested the difference of students' mean employment status and starting salary within each CAP group using a Kruskal-Wallis test T from 1 to 8 indicates eight semesters and the colors of bars in each T denotes the three GPA groups: green denotes high GPA (4-5) group, yellow denotes the middle GPA (3-3.99) group and red denotes the low GPA (<3) group. The length of bars indicates the number of students in that particular group. Similarly, the color and width of flows indicate the number of students transferred from the source group to the target group. For instance, the green colored flow indicates the mobility of students from a high performer group (i.e. source group) to other groups (i.e. target groups). (B) The proportion of same group neighborhoods over 8 terms is illustrated through the trends of homophily in the three academic groups. Here, the homophily is measured by the number of the same GPA group neighbors divided by the number of total neighbors. The homophily levels for the high, middle, low performing academic groups, and overall are shown in green, yellow, red, and black, respectively. (C) Dynamic processes of social network evolution and academic performance change. Nodes represent students and ties between nodes indicate the interpersonal interactions. The co-evolving processes of social interactions and academic performance suggests that there might be endogenous effects in assessing overall network effects during a four-year university education. Figure 3: Decision making process spanning course selection, student collaborations, and academic performance. In stage (1), we model course selection in period t as a function of preference similarity with linked students, performance in period t-1, and other covariates such as gender and nationality. In stages (2) and (3), we model the interpersonal network and academic performance changes jointly. To estimate peer influence, we control for two types of homophily effects: course-level homophily from stage (1), and individual-level homophily, stemming from attribute similarity and performance similarity.