The development of peer networks and academic performance in learning communities in higher education

In learning communities, students share their knowledge which might contribute to academic performance. This study disentangles peer selection from influence processes in modelling first-year students ’ academic performance after the transition to university. Longitudinal peer network data were obtained from 95 bachelor students at two time points in a social sciences study programme with eight learning communities. Using co-evolution modelling in RSiena, we found that students help each other more often when they are already friends and students who help each other academically are more likely to become friends. The higher a student performs, the more often the student is selected as a friend or as an academic helper and the more often this higher-performing student initiates friendship and academic help relationships. Although learning communities are often implemented to enhance academic performance, we did not find evidence that peer relationships in learning communities influence academic performance.


Introduction
Small group teaching, such as in learning communities (LCs), is increasingly implemented as an institutional answer to facilitate students in the transition from secondary education to university and to improve the overall first-year students' academic performance.Rooted in the principles of social constructivism (Vygotsky, 1978), LCs are implemented with the expectation that they contribute to academic performance based on the social mechanisms that take place in the LCs.Learning is considered as a socially situated process and optimized when students construct their knowledge actively together (Nie & Lau, 2010;O'Donnell, 2006;Smith et al., 2004).LCs consist of formally implemented small peer groups with a focus on active and collaborative peer learning.The rationale behind LCs is that through ongoing peer interaction in a relatively stable small group, students develop academic support relationships.LCs create a safe learning environment during the first semester and facilitate students to build a new support network after the transition to university (Brouwer & Jansen, 2019;Brouwer, Jansen, Flache, & Hofman, 2016).
Peer relationships within these small groups are highly important for a successful transition.A transition to university distinguishes four phases (Nicholson, 1990): preparation, encounter, adaptation, and stabilisation phase.The preparation phase takes place prior to the start at university and is beyond the scope of this study.Translating the other phases of Nicholson's transition model to the university context, the encounter and adaptation stage capture the first semester, in which students become acquainted with the university environment, build a new peer network and learn how to study.At the end of the academic year, the phase model suggests that students reach the stabilisation stage.This is the phase in which students achieve a status quo when they feel adjusted to university life (De Clercq et al., 2018;Nicholson, 1990).They know who they are, they have created their networks, and they have developed study habits.They sustain in applying their obtained learning skills and knowledge.In each of these phases, the role of peers in terms of friendships and help-seeking relationships might change during the semester (Tao et al., 2000).
By viewing learning as being socially constructed (Vygotsky, 1978), Vygotsky argues that the embedded relationships among students who participate in such a practice constitute important resources, such as knowledge, information, and support.According to social capital theory (Coleman, 1990), these resources can facilitate individual students to achieve their goals.Research into LCs provided evidence of their ability to achieve academic goals, i.e., academic performance (Butler & Dawkins, 2008;Hill & Woodward, 2013;Hotchkiss et al., 2006;Stassen, 2003).Although these insights are fruitful, these studies did not investigate how peer dynamics contribute to academic success, termed as performance (GPA), in LCs.For the learning process and academic performance, it seems important that social (i.e., friendship) and academic goals strengthen each other (Christie et al., 2004).To investigate these types of processes social network approaches are most suitable.
Yet only a few studies in higher education investigated small group processes by using a social network approach (Brouwer & Engels, 2021;Brouwer, Flache, Jansen, Hofman, & Steglich, 2018;Hommes et al., 2012;Katz, Lazer, Arrow, & Contractor, 2004;Smith, 2015;Thomas, 2000).The link between social networks and performance is predominantly investigated in secondary education (Fortuin et al., 2016;Gremmen et al., 2017;Kretschmer et al., 2018;Laninga-Wijnen et al., 2019;Rambaran et al., 2017;Shin & Ryan, 2014;Van Rijsewijk et al., 2018;Wang et al., 2018).In higher education, studies about social networks and performance are mainly based on individual self-perceived social integration rather than on longitudinally measured social networks (see for a recent review Mishra, 2020).To get more insight into selection and influence processes that underlie the link between social networks and academic performance, it is necessary to investigate longitudinally measures of complete networks with the appropriate tools (i.e., stochastic actor-oriented modelling (SAOM); Snijders, 2001;Snijders et al., 2010).Selection refers to initially connecting to somebody else, whereas influence refers to changes in attitudes or behaviour evoked by the connections (Steglich et al., 2010;Veenstra & Steglich, 2012).This type of analysis is needed because otherwise it remains unclear whether an association between peer relations and academic performance is due to influence from peers on a students' academic performance, or due to a student selecting peers as relations based on similarity in academic performance.
Previous work, based on social network models of selection processes, revealed that performance plays a role in the selection of friendship and/or study-related helpers among university students.It has been shown, in particular, that students who perform well are more likely to establish friendships with their fellow students (Brouwer et al., 2018;Dokuka, Valeeva, & Yudkevich, 2020;Lomi et al., 2011).Furthermore, friendships are crucial for students to become study-related helpers, which implies that study-related peer support emerges from friendships (Brouwer & Engels, 2021;Stadtfeld, Vörös, Elmer, Boda, & Raabe, 2019).This seems, however, one of the main reasons for performance network segregation (Brouwer et al., 2018) when students select similar performing friends who help each other with study-related questions.
The question arises whether friendship and help-seeking networks will contribute to academic performance?The literature about university students is mostly about selection effects and not about influence.Only a few studies have addressed this influence-question, maybe because of the challenges that arise in the collection and analysis of complete social network data.For example, Lomi et al. (2011) did find a significant influence effect among students in a very selective MBA programme.Dokuka et al. (2020) showed in a sample of economic students in Russia that friends became more similar over time in terms of performance (although the standard error was relatively high).The Russian context may differ from our study context in the Netherlands and other OECD countries.Dokuka et al. (2020) explained that the grades in Russian are visible on a website, which also can influence the selection of peers.In the study context in the Netherlands, students are only informed about the grades of their peers when they are informed by them.This may have a different impact on the role of the grades in the peer selection processes.Therefore, it is useful to replicate studies in different countries (including OECD countries) across the globe to get more insight into these peer selection and influence mechanisms after the transition from secondary education to university.
We contribute to this literature by investigating longitudinal peer network data and the relatedness to performance in LCs in a social sciences programme after the transition from secondary education to university and how the peer network dynamics influence performance over time.Moving beyond Brouwer et al. (2018) who investigated merely a peer selection process, the current study not only unravels social influence from the relational selection of peers, but it also investigates the impact of relational changes on performance over time in the higher education context where students are assigned to LCs.To our knowledge, this study is one of the few studies that investigate the co-evolution of peer networks and academic performance in LCs in higher education.Insight into these processes could be used to enhance the learning experience and performance in LCs by giving explicit attention to friendship and help relations.

Theoretical background
Influence and selection are generalized terms to account for distinct processes linking network relations to individual behaviour (Robins, 2015).In the current context, selection captures how students' performance affects whether they select others for friendship or help-seeking relations.Influence captures how friendship or help-seeking relations affect students' performance.Multiple underlying mechanisms may account for tendencies falling under either the selection or influence umbrella.Homophily (a tendency to preferentially select similar others) and propinquity (a tendency to preferentially select nearby others) are, for example, general underlying reasons for selection, explaining why certain students become friends.Based on these mechanisms, similar and geographically nearby students are more likely to form a friendship than dissimilar and distant students (e.g., Steglich et al., 2010).Influence, in turn, posits that friendship and help-seeking relations are conduits for imitation, contagion, assimilation, and social control processes (e.g., Friedkin, 1998) among students.For example, friendship relations provide channels through which students can monitor, imitate others, or learn from them to behave in a certain way.

Selection and influence in friendship networks in LCs
Peer relationships have an impact on student's development over time.In a peer network, not only the personal characteristics (e.g., behaviour, attitudes) change over time, but simultaneously also the relationships (i.e., with whom one is tied).This is called the co-evolution process (Steglich et al., 2010;Veenstra & Steglich, 2012).In LCs, friendships develop as the result of daily interaction and spatial proximity (Katz et al., 2004;Van Duijn et al., 2003).Friends facilitate social integration, which is important for a successful adaptation to the new learning environment after the transition to university (Buote et al., 2007;Noyens et al., 2019;Wilcox et al., 2005).Regarding the selection network process, becoming friends is likely when students are similar in their personal characteristics and performance level.This is the aforementioned homophily effect (Brouwer et al., 2018;Flashman, 2012;Lomi, Snijders, Steglich, & Torló, 2011;McPherson, Smith-Lovin, & Cook, 2001).Regarding influence mechanisms, the social cognitive theory (Bandura, 1977) posits that the individual, environment, and behaviour interact and that behaviour is the result of the perception of significant others.In the same vein, students in LCs might imitate behaviour from their peers when they interact frequently with each other during one full semester.Students may observe, for example, the study behaviour of their peers and copy this behaviour, which might be expressed in their grades.Friends might become more or less similar over time due to influence processes (Friedkin, 1998).

Selection and influence in help-seeking peer networks within LCs
Help-seeking from peers is a strategy of self-regulation that contributes to learning and academic performance (Ryan et al., 2001).When students spend parts of each day within their LC together, they establish help relationships to support each other in meeting the academic requirements (Nebus, 2006;Smith, 2015;Tomás-Miquel et al., 2015).Based on the original help-seeking model by Le Gall (1981), Aleven et al. (2003) identified different steps within the help-seeking process.After becoming aware that you need help and decide to seek help, you need to select a potential helper, use strategies to ask for help, and finally, evaluate whether the help was supportive.Students might hesitate to seek help from their peers when they are afraid that they will be perceived as less competent.This concern about incompetence might also be a reason that students refuse to request help from someone from the "outgroup", i.e., beyond the LC (cf., Wakefield et al., 2014).Therefore, they may feel more convenient to request help from peers within their LC because of the "low cost" to seek help (Borgatti & Cross, 2003).
When students decide to select a peer as a potential helper, they need a competent helper who is willing to help (Ryan et al., 2001).Derived from the organizational literature, the focal actor must appreciate what the other knows and that the help is timely provided (Borgatti & Cross, 2003).As previous network research showed (Brouwer et al., 2018), help is often requested from friends who are generally willing to provide timely help and know what the other knows (i.e., relational knowledge).Regarding the influence of peers on performance, Lomi et al. (2011) showed that students in an MBA-programme assimilate to the average grades of their helpers and friends.Based on homophily, it is likely that students become friends when they are similar in terms of performance (McPherson et al., 2001).Therefore, friends might not always be the best helpers in the sense that they will not contribute optimally to the performance of their peers, because they may have the same understanding of the material.It remains a question, however, how help-seeking within LCs, whether or not by friends, influences students' performance over time.

The current study
This study aims to investigate to what extent and how LCs contribute to peer relationship formation over time, i.e., friendship and helpseeking, and how this is interrelated with learning outcomes expressed in individual average grades (GPA).We address the following research questions: (1) What is the role of grades and being a member of the same LC in students' selection process of friends and help-seeking?To what extent are socially connected students in a study programme with LCs influenced by each other's grades?Thus, we try to unravel influence from selection in a curriculum where LCs are embedded in the programme.Therefore, we investigate the development of friendships and help-seeking relationships over time and the impact on academic performance in a study programme where students are assigned to LCs (i.e., fixed small collaborative groups).This study is a follow up from previous studies with selection models with static co-variates (e.g., grades; Brouwer et al., 2018), whereas in selection and influence models the co-variates co-evolve simultaneously with changes in the networks (Snijders et al., 2010;Veenstra & Steglich, 2012).
The current study is innovative in three ways: First, by disentangling peer selection from influence processes in modelling first-year students' academic performance after the transition from secondary education to university.Second, thus far, most studies concerning peer selection and influence processes were conducted in a secondary education context (Fortuin et al., 2016;Gremmen et al., 2017;2019;Kretschmer et al., 2018;Laninga-Wijnen et al., 2019;Rambaran et al., 2017;Shin & Ryan, 2014;Wang et al., 2018).The developmental stage of adolescents differs from that of university students.Only a few investigated influence effects among university students, but in a different educational system (Dokuka et al., 2020;Lomi et al., 2011).We examine the interplay of social relations and academic grades in a context with LCs in an OECD country (the Netherlands).Third, the rationale behind LCs is that peer relationships influence students' academic performance.To our knowledge, this has never been investigated with stochastic actor-based modelling and co-evolution data.In addition, we do not only study friendship networks but also help-seeking networks, which is quite important in academic settings wherein students have to ask timely for academic peer support to succeed (Aleven et al., 2003).

Sample and educational context
Participants were 95 first-year Dutch bachelor's degree students (58 female; 37 male) from one study program in the social sciences field.The mean age was 19.5 years old (SD = 1.6).They were enrolled in one of the eight LCs containing on average 12 students.In the current university and research context, the academic year is divided into four seven-week blocks.This means that each semester consists of two blocks.Students were assigned to their learning community by the educational office at the start of the academic year.The group composition remained the same during the first semester.Fellow learning community students followed together all the courses (i.e., lectures, practicals) of the firstyear bachelor study programme during the first semester.Students had on average 13 formal contact hours every week, but could also meet for informal extracurricular activities (i.e., group work, assignments).The LC was organized around a core course about academic skills, critical reflection, study skills, and professionalization.In the second semester, students met their LC members once a week during the core course, but for other courses, the group composition may differ from the fixed group composition of the LC (Brouwer et al., 2018).

Procedure
Using the Qualtrics programme, the survey data about personal characteristics and social network data were collected online during class at the end of the first and at the end of the second semester in the academic year 2013-2014.The completion time of the survey was 20-30 min.In advance, the instructor and the researcher explained the aims, the procedure of the study and that participation was voluntarily (though they were rewarded with credit points), and about data storage according to ethical guidelines.The ethics committee of the degree programme approved our research concerning small group teaching.After our request, all students gave their informed consent and consent for using their centrally administered personal details and study results (i.e., grades and credit points).The response rate was high (88; 93%); only three students did not participate and four students dropped out of the programme and were excluded from the study.As a rule of thumb, an 80% response rate can provide reliable results with SAOM (Ripley et al., 2020).
For the two network questions applied in the current study, students could nominate all fellow students from the faculty of social sciences.When students entered their student number, the complete roster of their peers in the LC became visible.Each student could enter a maximum of ten 1 other names of peers from the faculty of social sciences in addition to names that automatically appeared as a consequence of sharing a learning communitywhen they answered the question: "With whom of the first-year students of the Faculty of Social Sciences (besides the students from your LC) did you have regular contact with (e. g. activities, talking) in the past three weeks?The students were supported with this free recall method, because when they entered only a part of a name, names appeared automatically and they could select then their peers for the network questions about friendship and help-seeking (see Brouwer et al., 2018).

Friendship
Students nominated whom from their fellow students in the faculty is a friend or a possible friend.They answered this per selected person on a 5-point Likert scale with 1 = "best friend"; 2 = "friend"; 3 = "friendly relationship"; 4 = "neutral, not much in common"; 5 = "only known from face or name"; 6 = "not known at all" (Van de Bunt, 1999).For the analysis, we dichotomized the categories from "best friend'' to "friendly relationship" into 1 = "friend" and the other categories into 0 = "not a friend" to measure a friendship or a possible friendship relationship.

Help-seeking
Students nominated whom from their fellow students in the faculty they would ask for academic advice or support when they did not understand the study material.They answered on a five-point Likert scale from "strongly disagree" to "strongly agree".They had an additional option to indicate that they do not know this fellow student.We dichotomized the categories "strongly agree" and "agree" into 1 = "help relationship", and the other categories into 0 = "no help relationship".

Academic performance
We derived academic performance measures of the first and the second semester from the central administration.We calculated academic performance as a grade point average (GPA): the grade times the obtained European Credit points per course were summed over all courses in a semester and then divided by the European Credit points that could have been obtained in the programme during that semester.In the social networks literature, academic performance is often operationalized by measuring GPA (e.g., Dokuka et al., 2020;Palacios et al., 2019;Rambaran et al., 2017;Stadtfeld et al., 2019) and is seen as a potential outcome of learning.Even if average grades do not measure the actual learning process, variation between individuals in these grades and monitoring grades over time can be used to answer our main question: Whether peer relations affect learning outcomes?If a better performing student can influence a lower-performing student via a peer relation, then this should show up in an improvement of the grades of the lower-performing student (influence effect) compared to lower-performing students who do not have such a peer relation.Therefore, we used GPA as a measure for learning outcomes.The Dutch grading scale ranges from 1 (very poor) to 10 (outstanding) with 6-7 (satisfactory).Students pass a course only with a grade of a 6 or higher, otherwise they fail.RSiena requires ordinal data for the dependent variable and therefore, we rounded the grades from 1 to 9.

Statistical analysis
To disentangle influence from selection in friendship and academic help-seeking relationships and performance, we employed SAOMs (Snijders et al., 2010;Steglich et al., 2010), using the RSiena software (Simulation Investigation for Empirical Network Analysis) package in R, package version 1.1.284(Ripley et al., 2020).This package is suitable for analysing the co-evolution of social networks (i.e., friendships, help-seeking) and behaviour (i.e., performance).To identify selection effects, it is necessary to know who is not selected among all the available students in the network (see Veenstra & Steglich, 2012).Therefore, testing selection and influence in the developing relationships asks for longitudinal network data of complete (whole) networks within a socially meaningful group boundary, such as a degree programme.More conventional statistical tools are not appropriate, because network data violate the assumption of independent observations.We specified two models for the co-evolution of one social network (i.e., friendship or help-seeking) and one behaviour variable (performance), as follows.For each of the dependent variables, we include a rate parameter, which models how often students change one of their relationships (the relation now being understood as either friendship or help-seeking), or their performance.We first sketch the specification of the relationship-change model.Since relationships change not only as the result of students' performances, we include several so-called structural network effects as controls in our models.This helps to prevent biases in effect estimation of selection and influence.
Several common structural network effects are included in our models.Outdegree (a.k.a.density) refers to the baseline tendency of students to have relationships.Reciprocity is the tendency to reciprocate received nominations from other network members.Transitivity captures the tendency to form groups in which all members are connected.More specifically, a student tends to have a direct relationship with those students to whom the student also has an indirect relationship (i.e., friends of friends will become friends, and helpers of helpers will become helpers).We also include an interaction term of reciprocity and transitivity (Transitive reciprocated triplets) capturing whether reciprocity is more or less likely in transitive groups.Indegree-popularity captures the tendency that a student will receive additional relationship nominations when already receiving many, whereas Outdegree-activity captures the tendency that a student who already has many relationships will nominate even more.Indegree-activity means that one is more likely to nominate others when one is already nominated.Generally, the estimates comprise log-odds.When the effect is positive then students are likely to pursue such a network state.For example, a positive effect of reciprocity indicates that students tend to reciprocate a relation.Moreover, for instance, a negative parameter of transitive triplets stresses that students tend to avoid embeddedness in a triad.
Regarding the selection models, we include the following effects of other variables on the network.These are so-called exogenous network effects, which refer to the effects of relations in another network (e.g.friendship) have on the formation of relations in the focal network (e.g.help-seeking).In our study, students might seek help (Help-seeking) from their friends, or befriend (Friendships) their helpers.Furthermore, we include ego and alter effects.Ego (a.k.a.sender) effects express the extent to which students with a given characteristic nominate more fellow students.Alter (a.k.a.receiver) effects capture the extent to which students with a given characteristic are more often nominated by others.Similarity effects (a.k.a.homophily, i.e., Same gender, Same LC) express that similar students are more likely to have relationships with one another if they are similar in this regard.Membership of the same LC is included in the model.For performance, such similarity between students is expressed in the interaction effect between the two students' performance levels (Performance ego × Performance alter).The more the 1 The choice for a maximum of ten additional nominations allows us to convincingly model the structure of the network, while not burdening the participants too much via extensive time investments to possibly nominate all potential friends.The choice for a maximum of ten is not too distant from similar maxima chosen in three important studies in the social network literature.Knecht et al. (2010) rely on a maximum of twelve, Valente et al. (2005) rely on max five nominations, and Stadtfeld et al. (2019) rely on limited nominations ranging from five to twenty, depending on the network item.Post-analysis revealed that only a few students nominated 9 peers as friends and 8 as friends.Nobody nominated ten others in the free-recall of peers outside their LCs.This suggests that the maximum of 10 did not systematically bias our network data.
performance level of ego is positively associated with the performance level of alter, the more likely they are to have a relationship.Again, a positive estimate of exogenous network effects indicates, for example, whether students tend to form friendships or seek help from similar achieving-others.
Regarding the influence models, we now sketch the model of performance change.It includes standard effects of the linear and quadratic shape of the performance distribution (i.e., Linear shape; Quadratic shape) modelling.The overall trend (towards the upper vs. the lower end of the performance scale) and overall dispersion (i.e., a negative quadratic shape effect implies regression to the mean, whereas a positive effect refers to polarization in performance).Effects of degree on performance express whether students with many relationships have higher performance levels.We tested different effects for help-seeking than for friendships based on different expectations for the impact of helpseeking and friendship relationships on performance, with a tendency for reciprocity for the latter.For help-seeking, we differentiate students who seek a lot of help (Outdegree performance) and those approached for help very often (Indegree performance), while for friendship, we count 'real friendships' (i.e., reciprocated nominations) assessing effects of these deeper relationships (Nebus, 2006) on performance (Reciprocal degree performance).Next, we include an effect of the average performance of friends or helpers on their performance, limited to mutually-nominated friendships.Finally, in both models, we include gender, assessing whether women (=1) obtain higher grades than men.Additional SAOMs, in which we tested similar effects for friendships and help-seeking networks, did not converge to a satisfactory degree.We refer to the Supplementary Material for more information on additional estimated effects and goodness-of-fit tests.
Following Ripley et al. (2020), we do a post-hoc analysis modelling how performance affects selecting academic helpers and friends over time.Based on the log-odds derived from the combination of estimated ego-, alter-, and ego*alter-effects, these tables indicate whether low performers prefer high-or similar-performers and whether high-performers prefer similar performance.

Network descriptive statistics
At the start of the academic year, 63.9% of the participants indicated that they knew another fellow student from the faculty prior to their studies.Most of them knew the fellow student from secondary education (36.4%) or coming from the same city or village (19.3%), or sport (8.0%).Of the 95 first-year students in this study, 51.8% joined the introductory camp at the start of the academic year.Density is the proportion of the possible directed relationships that form actual relations (Wasserman & Faust, 1994).The density of the friendship and help-seeking network is higher within the LCs than beyond the LCs, i.e., within their study programme (see Table 1).Within LCs, the density decreases from the first semester to the second semester, students' relationships are more mutual than beyond their LCs in both networks during the first semester, and the most mutual relationships are present in the friendship network.Within LCs (with on average 12 participants), students have on average three friends in the first semester and two friends in the second semester, whereas they select on average three peers as a helper in the first semester and only one peer as a helper in the second semester.Beyond their LC, they have on average three friends across both semesters, whereas two to three peers are selected as academic helpers.It seems that students connect more to peers beyond their learning community after the first semester.The Jaccard Similarity Index has a value of more than 0.30.This implies sufficient stability between the consecutive waves and therefore, reliable estimates of the statistical parameters can be expected (see Ripley et al., 2020;Snijders, 2001;Snijders et al., 2010).

Performance level
Academic performance is the weighted grade point average in the first semester (M = 5.97; Mdn = 6.76;SD = 1.96) and the second semester (M = 4.99; Mdn = 6.44;SD = 2.88).Fig. 1 shows the distribution of the GPA of semester 1 and semester 2. Grades between 7 and 8 are most frequently awarded.The Geary's C network autocorrelation coefficient was calculated as an indication for the degree of spatial autocorrelation of performance of individuals who are connected in each of the networks (see Steglich et al., 2010).The values of Geary's C can vary between 0 and 2. A value lower than 1 is referring to a positive network autocorrelation implying that directly connected students are closer to each other in terms of academic performance.A value of 1 indicates that there is no autocorrelation.A value higher than 1 means that students in the networks diverge more in terms of performance.In both networks, Geary's C varied between 0.60 and 0.91.The autocorrelation is slightly decreasing over time (i.e., getting closer to 1) in the friendship and help-seeking networks.Over time, students become less close in terms of performance.Moran's I can vary from − 1 to +1.When the measure is  close to 0, there is no correlation between the network and the behaviour (i.e., performance).Moran's I is decreasing from T1 to T2 in both networks and becomes closer to 0, which implies that students are less associated with each other in both networks in terms of their performance level.Tentatively, we can conclude that grades have less impact on friendship formation and help-seeking relationships from the first semester to the second semester.

Results of the co-evolution models 2
Table 2 shows the results of the co-evolution models for respectively friendship and help-seeking network, and performance.The results are expressed in estimates and standard errors and can be interpreted as logodds for an existing relationship or increasing performance (see Ripley et al., 2020).A result is significant when the estimate divided by the standard error is in absolute terms similar or larger than two.
Regarding the endogenous structural effects, the effect for outdegree is negative implying that students selected less than half of the fellow students in their study programme as friends and helpers.In both networks, students tend to have mutual relationships (reciprocity positive effect) and tend to form a cluster of relationships (positive transitive triplets).A negative parameter for transitive reciprocated triplets, which is often the case, expresses that reciprocity is less strong within groups than between groups (i.e., transitivity is modelling informal group formation).Intuitively, this can be explained such that between groups relationships should be stronger than within groups to keep the relationship intact even though it bridges different groups, because reciprocal relationships are usually stronger than are non-reciprocal relationships (see Block, 2015).A significant positive parameter for outdegree-activity in the friendship network means that it is likely that students connect to additional others when they already have nominated many others as friends.In both networks, we find a significant negative effect for indegree-activity.Findings stress that it is less likely that students connect to others when they are nominated by many others, net of the effects of other network processes, in particular of reciprocity.

Selection of friends and help seekers
Regarding the selection of friends, when students ask each other for academic help, they are likely to become friends (positive effect friendships).The higher a student performs, the more often the student seems to be nominated as a friend (positive effect performance alter) and the more often a student initiates friendship relationships among their fellow students (positive effect performance ego), although both effects are slightly stronger for help-seeking.We do not find evidence for a performance similarity effect.It seems that students neither become friends with each other when they obtain similar grades, nor become friends with fellow students from their learning community over time.Regarding the controlling effect of gender, a negative gender alter effect for friendships means that women are less often nominated than men as friends and a negative gender ego effect means that women also initiate friendship relationships less often.The positive same gender effect means that it is more likely that students of the same gender become friends.
Regarding the selection of help-seekers, students are more likely to ask friends for academic help (positive effect help-seeking).The results also suggest that students ask more often help from higher-achieving fellow students (positive effect performance alter) and that higher-achieving students initiate more often help-seeking relationships (positive effect performance ego).It seems that similar-performance level does not contribute to explaining that students ask each other for help, net of the other homophily effects included in the model.Further, over time, students do not ask their fellow students from their learning community for academic help more often.We find a negative gender alter effect which means that odds are lower for women compared to men to be approached for help.The positive same gender effect points to the tendency of students of the same gender to ask similar others for help.

Influence of help seekers and friendship on performance
The rate change of performance indicates how often students change in their performance level over time.The linear and quadratic shape effects are not significant which implies that we do not find evidence for a certain tendency in the changes in the overall mean (trend) and dispersion of performance.
We do not find evidence for students' performance to depend on the average grades of their mutual friends.Furthermore, it seems that students with more reciprocated friendship relationships do not differ in terms of their grades from those with less reciprocated friendships.We do not find evidence for an indegree performance and outdegree performance effect in the help-seeking networks.Grades seemed not to be influenced by being nominated more often or by nominating other peers more often.We do neither find evidence for an average performance alter effect suggesting that the average grades of fellow students (alter) do not affect the focal students' grades (ego).In both networks, we controlled for gender but it does not seem that women compared to men are more likely to be influenced in their grades.

Post-hoc analysis
To elaborate further on the research question of how help-seeking relationships and friends are related to individual grades, we performed a post-hoc analysis.The post-hoc analysis reveals the overall patterns of friendship and help-seeking selection based on performance.Figs. 2 and 3 show the probability that a student with performance level X (different grey or coloured lines) selects a student (i.e., helpers or friends) with performance level Y.For example, the post-hoc analysis indicates whether a random student with a high-performance score is more likely to seek help from or befriend a random other student with either a low or high-performance score.In this way, we provide an alternative way to indicate whether and how friendship and helpseeking selection and performance are interrelated.These probabilities were calculated under the (counterfactual) assumption that students have two options only: either to select the candidate friend or helper in question or not to select him/her.This is counterfactual in the sense that parameter estimates were not obtained for such binary choices but under the assumption of multinomial choice from all available students.Fig. 2 shows that almost all students prefer to have higher-achieving friends, except for the very low performers, who seem to prefer to select similarly low-achieving friends or may not dare to ask higher-achieving peers.Again, higher-performers are more likely to select friends than lower-performers (i.e., to nominate their peers as friends), and the higher performers discriminate more between higher-and lowerperformers.Fig. 3 shows that lower as well as higher-achieving students prefer asking help from higher-achieving students (all lines increase from left to right).The slopes of the higher-achieving students are steeper than of the lower-achieving students suggesting that the higherperformers do not only initiate more help-seeking relation (binary probabilities are higher) but discriminate more between lower-and higher-achieving students.The post-hoc analysis revealed overall that, ceteris paribus, students with performance levels of 7, 8, or 9 are more likely to select similar high achievers as friends or for help compared to students with lower performance levels.Performance is thus an important factor for friendship and help-seeking selection, discriminating between students high and low on performance.
actor oriented model presented in Table 2. Generally, additional models did not improve the goodness-of-fit on key network auxiliary statistics.In cases that the fit improved, model convergence worsened.That is why we present the current set of parameters.We kindly refer the reader to the Supplementary Material for more information on goodness-of-fit tests.We provide a detailed description of the tests, also when readers are largely unfamiliar with RSiena.

Performance alter
The higher the fellow student performs, it is more likely that a student (ego) connect to this fellow students (alter).
0.17 c (0.06) 0.31 c (0.11) Performance ego The higher the focal student (ego) performs, it is more likely that this student has outgoing connections (initiating connections).
0.45 c (0.13) 0.80 c (0.33) Performance ego × performance alter (instead of performance similarity; mathematically similar to average performance alter) It is more likely that connections exist between two students with similar performance levels (homophily effect).Note.Ego = sender; student who initiate relationships; alter = receiver; fellow student selected by others.a This explanation holds for positive effects.
b Graphical representation of the network configurations.Grey arrows represent a connection and a black is the connection that will likely appear.c p ≤ .05;unrounded parameter estimate/(SE) ≥ 2; both models are estimated with 5000 iterations; overall maximum convergence ratio = 0.18.

Discussion
Friendship and help-seeking relationships among students provide important resources, such as knowledge, information, and support.The novelty of our study is that we unravel social influence from the selection of peers in friendship and help seeking networks, while simultaneously investigating the impact of relational changes on academic performance in the higher education context where students are assigned to LCs.The current study provides insights into what extent and how students connect to each other when they establish friendship and help seeking relationships in a study context with LCs and how these relationships contribute to individual academic performance over time.Our study advances the debate whether LCs can facilitate relationship formation among students and whether such processes enhance overall performance.Our results highlight that after the transition from secondary education to university LCs provide a safe environment in which students can easily connect to each other.LCs facilitate the creation of friendship and help-seeking relationships.
Our study corroborates prior work but also points to key differences.In a study in which learning environments are compared, Brouwer, Jansen, Severiens, and Meeuwisse (2019) showed that LCs contributed to students' belongingness, whereas Problem-Based Learning contributed more to academic achievement through formal peer interaction.
We do find similar effectiveness of LCs on friendship or help-seeking selection in terms of increased peer connections in LCs.Consistent with Lomi et al. (2011), students are more likely to ask friends for academic support and in turn, when they seek academic help from each other, it is more likely that they become friends.In contrast with previous work (Brouwer & Engels, 2021;Brouwer et al., 2018), selection based on individual grades obtained across the first year showed that higher-achieving students are more popular (incoming nominations) in both networks, but the effect is stronger in the help-seeking network than in the friendship network.Higher-achieving students are also more active (outgoing nominations) in both networks and again the effect is stronger in the help-seeking network than in the friendship network.The post-hoc analyses showed that almost all students prefer to have higher-achieving students as academic helpers.Following previous work (Bianchi et al., 2020;Brouwer et al., 2018), this suggests that the network tends to segregate between individuals with different levels of resources, here expressed in terms of their academic performance.While students do not actively seek out to relate to similar-achieving peers according to our results, this points to the possibility that the mutual preference of higher-achieving students for selecting each other as peers can also generate an assortment of friendship and network relations by similar performance levels as a by-product.
The transition to university is an exciting and challenging time.Especially higher-achieving students are active in the friendship and help-seeking network which implies that these students are active in establishing new supportive networks as freshmen.The lower-achieving students seem to have more difficulties building their social capital when starting a study (Coleman, 1990).The LCs are here small groups of students who attend lectures together during the first semester.To create more diversity in the friendship and help-seeking networks, it seems that more needs to be done than just forming small groups.For example, Palacios et al. (2019) pointed out in their study about the composition of classrooms that ability groups can impact peer relationship formation.Boda, Elmer, Vörös, and Stadtfeld (2020) showed that network interventions in higher education have a short-term effect on relationship formation.Future research should provide more insights into how small groups, such as LCs, should be created to enhance the diversity of capabilities in the networks.This may also provide the lower-achieving students with the opportunity to learn from higher-achieving students.The co-occurrence of friendship and help-seeking relationship formation means that the diversity might extend to different relationships.In line with Aleven et al. (2003), it seems important that, in particular, lower-achieving students learn when and how to ask for support on time.
LCs are often implemented to improve the overall academic performance, but our findings shed new light on the effectiveness of LCs on achievement.Our results suggest that students select the higherachieving student for friendship and academic support, but the individual (average) grades seem not to be influenced by the help-seeking and friendship relations.In the literature, GPA is widely used as an indication for academic performance and learning (e.g., Dokuka et al., 2020;Palacios et al., 2019;Rambaran et al., 2017;Stadtfeld et al., 2019).An explanation, however, for not finding influence effects of peer relationships on grades in our study is that the individual differences in terms of GPA are very limited (little variance).In the current study, students obtained mainly a grade between 6 and 7 and the Goodness of Fit-test (see Supplementary Material) showed that this was not fully in line with what the stochastic actor-based model predicted.In practice, the range of grades from 1 (very poor) to 10 (excellent) is not used fully, but restricted from grade 4 to grade 8. Continuing the debate about grading in small groups in higher education, we argue that it might be better to measure students' potential in learning with standardized tests to get an indication of how students' learning outcomes develop over time, but also pay attention to the assessment of other skills, such as collaboration (Brouwer & Jansen, 2019).This might not only give more variance in academic performance over time and, therefore, more insight into the capacities of students, but is also more representative for what students learn in academia.Additionally, for further research, we recommend measuring progress with the obtained credits and including this in the model as an indicator for study progress (pass or fail), in addition to GPA as an indicator for the level of academic performance.This will provide more insights into selection and influence effects within the peer networks in terms of the progress of students, and whether LCs can contribute to succeeding in higher education via peer support.
Surprisingly, contrasting the literature on homophily and proximity (e.g., McPherson et al., 2001;Rivera et al., 2010), we did not find evidence that students are more likely to establish friendships or seek help from peers within their learning community over time.This might be explained by the frequency of meetings in their learning community that decreased from the first semester to the second semester.The descriptive results showed that students establish more friendships and help-seeking relationships outside their learning community during the second semester.Based on the proximity mechanism (Rivera et al., 2010), it seems useful to meet more frequently also during the second semester to remain connected with your peers of the LC.These proximity effects of LCs should be investigated more in future research.
Another question for further research is under which conditions peer relationships in LCs enhance the intended positive effects on academic performance.Poldin et al. (2016) found that students' performance increases when they study with a more able peer but not when the relationship entails solely social activities, rather than study-related activities.Further qualitative research should focus on the specific activities fellow students undertake instead of merely investigating friendship and academic help-seeking relationships.Moreover, not only performance plays a role in peer network formation.Small group teaching, such as LCs, are often implemented within university curricula to enhance student engagement (Zhao & Kuh, 2004;Zepke & Leach, 2010).Student engagement consists of three dimensions: cognitive (e.g., knowledge), behavioural (e.g., study behaviour), and affective engagement (e.g., emotions; Fredricks et al., 2004).It would be interesting to include these three dimensions of engagement in the SOAMs, to see the selection and influence effects of the different dimensions of engagement within peer networks.
The findings should be considered by taking into account some limitations of the study.First, the study is conducted in a single and small study programme.Therefore, future research should replicate this study in other cohorts and settings with similar forms of small-scale teaching.Second, to investigate selection and influence mechanisms, the network boundary was limited to the peer network in the same faculty and did not include other help sources, such as instructors, or friendships from outside the university.Previous works showed that first-year students ask for support from faculty and peers (Brouwer & Engels, 2021;Brouwer et al., 2016;Mishra, 2020).To get a more complete picture of friendship and help-seeking networks of first-year students, ego network data should be combined with the complete network data (e.g., Crossley et al., 2015).Van Waes et al. (2018) showed the added value of ego networks in teachers' professional networks.Third, the higher-achieving students are most active and popular in both networks.Spitzmuller and Van Dyne (2013) showed students might have different reasons for connecting to their peers, in particular, helping others.However, this study does not provide insight into the reasons why students connect to others.Again qualitative research, for example, interviews, need to be performed to get a nuanced picture of why students connect to each other for friendship and help-seeking, and also why they do not connect to their peers.This would also provide more insight into the steps university students take in the help-seeking process (Aleven et al., 2003).
LCs are increasingly implemented to facilitate students in the transition from secondary education to university and to improve academic performance.Our findings reveal that when a cohort of students is divided into small groups, such as LCs, this facilitates students in their relationship formation (i.e., friendship, help-seeking) immediately after the transition from secondary education to university.We do not find evidence that merely LCs contribute to academic performance.Especially higher-achieving students are more popular and active in the friendship and help-seeking network, leaving their lower-achieving counterparts astray.Positive effects of LCs could enhance performance when attention is paid to the educational design, which emphasizes, for instance, collaboration among students with different performance levels.The findings suggest that interventions need to be performed rather than only creating small student groups.
It is more likely that a student (ego) nominates a fellow students (alter) when this student is female (female = 1 (striated in configuration); male = 0

Fig. 2 .Fig. 3 .
Fig. 2. Counterfactual binary probabilities of ego-alter selection effects of friendships.Line colours indicate the selecting students' performance level, while the x-axis indicates the selected students' performance level.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1
Descriptive network statistics.

Table 2
Results of the co-evolution help-seeking and friendship models.