latexSupplementary references

# Disadvantaged students increase their academic performance through
collective intelligence exposure in emergency remote learning due to COVID 19.

Cristian Candia Data Science Institute, Facultad de Ingeniería, Universidad
del Desarrollo, Las Condes, 7610658, Chile.  Laboratorio de Investigación e
Innovación Educativa, IDECLAB, Dirección de Docencia, Universidad de
Concepción, Concepción, 4070383, Chile  Alejandra Maldonado-Trapp  Laboratorio
de Investigación e Innovación Educativa, IDECLAB, Dirección de Docencia,
Universidad de Concepción, Concepción, 4070383, Chile  Departamento de Física,
Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción,
Concepción, Chile  Karla Lobos  Laboratorio de Investigación e Innovación
Educativa, IDECLAB, Dirección de Docencia, Universidad de Concepción,
Concepción, 4070383, Chile  Fernando Peña  Laboratorio de Investigación e
Innovación Educativa, IDECLAB, Dirección de Docencia, Universidad de
Concepción, Concepción, 4070383, Chile  Carola Bruna  Laboratorio de
Investigación e Innovación Educativa, IDECLAB, Dirección de Docencia,
Universidad de Concepción, Concepción, 4070383, Chile  Departamento de
Bioquímica y Biología Molecular, Facultad de Ciencias Biológicas, Universidad
de Concepción, Concepción, Chile

###### Abstract

During the COVID-19 crisis, educational institutions worldwide shifted from
face-to-face instruction to emergency remote teaching (ERT) modalities. In
this forced and sudden transition, teachers and students did not have the
opportunity to acquire the knowledge or skills necessary for online learning
modalities implemented through a learning management system (LMS). Therefore,
undergraduate teachers tend to mainly use a LMS as an information repository
and rarely promote virtual interactions among students, thus limiting the
benefits of collective intelligence for students. We analyzed data on 7,528
undergraduate students and found that cooperative and consensus dynamics among
university students in discussion forums positively affect their final GPA,
with a steeper effect for students with low academic performance during high
school. These results hold above and beyond socioeconomic and other LMS
activity confounders. Furthermore, using natural language processing, we show
that first-year students with low academic performance during high school are
exposed to more content-intensive posts in discussion forums, leading to
significantly higher university GPAs than their low-performance peers in high
school. We expect these results to motivate higher education teachers
worldwide to promote cooperative and consensus dynamics among students using
tools such as forum discussions in their classes to reap the benefits of
social learning and collective intelligence.

## Main

We are constantly exposed to collective intelligence that, broadly speaking,
aims at the enrichment of individuals [Lévy, 1997]. Examples include
cooperating and reaching consensus in team tasks, searching for past
customers’ experiences, and accessing nonlocal and distributed knowledge on
Google or Wikipedia. Integrating information spread among a myriad of people
to make it available to the public upon a single query is a type of collective
intelligence that aims to improve individual outcomes [Lévy, 1997]. However,
little is known about the benefits of this type of collective intelligence in
educational experiences.

The recent COVID-19 crisis forced a transition from face-to-face classes to an
emergency remote teaching (ERT) modality with the assistance of the digital
technologies of a Learning Management System (LMS). In this pressing process,
teachers and students did not have the opportunity to acquire the knowledge or
skills to respond to the remote teaching modality. Therefore, teachers tend to
mainly use a LMS as an information repository and rarely promote virtual
interactions among students, thus limiting the benefits of collective
intelligence for students. In addition, students had to adopt new ways to
communicate and interact with each other for academic purposes, such as email,
chat rooms, and academic forums. Thus, the emergency remote learning modality
provides a setting to study the role of social interactions and users’
consensus in discussion forums as a source of collective intelligence for
improving individual academic performance.

In on-campus education, social interactions are mainly mediated by
collaboration and social abilities, which are highlighted as crucial
competencies for life and work in the twenty-first century [Pellegrino and
Hilton, 2003]. Therefore, they are a large part of current educational
endeavors [McFarland et al., 2014, Rohrbeck et al., 2003, Slavin, 2015,
Newman, 2002, Slavin et al., 2003, Slavin, 2011, Pulgar et al., 2019, Pulgar
et al., 2020]. At the group level, social relations between peers are pivotal
for social learning [Henrich, 2015, Gil-White and Henrich, 2001, Pentland,
2015, Johnson and Johnson, 1987, Roger and Johnson, 1994] and play a key role
in academic outcomes [Kassarnig et al., 2018, Blansky et al., 2013, Sacerdote,
2011, Davies, 2018, Biancani and McFarland, 2013, Pulgar et al., 2021, Candia
et al., 2019b]. At the individual level, students’ positions in their social
networks and their academic performance are significant and positively
correlated [Baldwin et al., 1997, Caprara et al., 2000, Mouw, 2006, Bruun and
Brewe, 2013, Gašević et al., 2013, Blansky et al., 2013, Ivaniushina and
Alexandrov, 2018, Stadtfeld et al., 2019, Kassarnig et al., 2018].

In contrast, in online education, social interactions and collaboration take a
different form and occur mainly through computer-mediated communication
[Traxler et al., 2018]. Hence, social interactions respond to different
demands linked to the features of digital technology. During emergency remote
teaching, students have reported consistently poor and unsatisfactory
interactions between peers and with the instructor [Almahasees et al., 2021,
Coman et al., 2020, Sepulveda-Escobar and Morrison, 2020, Mseleku, 2020, van
der Spoel et al., 2020], which may contribute to the perception that
synchronous activities are more effective [Nguyen et al., 2021, Aristovnik et
al., 2020]. Therefore, it is relevant to study whether and how collaborative
spaces provided by the LMS can contribute to the educational process.

Numerous studies conceptualize online participation using the frequency of
posts in discussion forums ([Romiszowski and Mason, 2004, Vonderwell and
Zachariah, 2005] and reading time [Hrastinski, 2009, Wise et al., 2013].
However, this approach is incomplete because the frequency of actions in
discussion forums ignores interactions between people and emergent collective
effects [Barabási, 2003]. A more comprehensive approach for understanding
participation and engagement lies in social network analysis [Garton et al.,
1997], where interactions are observed among students who jointly participate
in forums [Traxler et al., 2018]. Small-scale research literature has found
positive relationships between students’ participation in online courses and
academic success [Morris et al., 2005, Traxler et al., 2018, Dawson, 2008].
However, these results depend on students’ readiness to deal with online
demands [Kebritchi et al., 2017] and their academic orientations [Dawson,
2010].

Here, we conduct a large-scale study monitoring students’ interactions in
discussion forums at a large university in Chile. We use tools from social
network analysis to quantify students’ behavior in discussion forums and its
effects on academic performance. Our motivation is based on the participants’
ability to produce, read, reply to, and value content, generating an emergent
consensus on what information is valuable and what is not for their academic
contexts. Thus, we aim to explore the role of discussion forums as a source of
collective intelligence to improve individual academic performance.

### Online learning

The effectiveness of online education has been widely studied over the last
decades. An increasing number of institutions are adopting its principles,
particularly in higher education, because it facilitates access to a broader
audience of learners while reducing restrictions in access to information
[Panigrahi et al., 2018, Kebritchi et al., 2017]. Online education provides
learners with the flexibility and autonomy to engage with course content
according to their own pace and disposition. However, designing online courses
involves several challenges for successful implementation and adoption. In
addition to the lack of human interaction in learning as one of the
limitations of online learning [Graham, 2006], researchers have identified
variables linked with learners’ expectations and skills that mediate their
cognitive and social engagement in a course [Panigrahi et al., 2018, Kebritchi
et al., 2017] as well as curriculum design and teaching strategies [Nazir et
al., 2015, Hu and Hui, 2010]. Both elements are essential to foster students’
engagement and participation in online courses, a variable shown to be related
to academic success [Traxler et al., 2018, Morris et al., 2005, Pye et al.,
2015]. This section explores the different individual- and course-level
variables that contribute to students’ participation and success in online
courses.

Researchers have found that learners’ expectations, readiness, sense of
belonging, identity, self-efficacy, and participation are critical for
satisfaction and success in online courses [Kebritchi et al., 2017]. First,
having appropriate learning expectations might increase adaptability and
optimize learning opportunities [Li and Irby, 2008, Lyons, 2004, Alraimi et
al., 2015, Bhattacherjee, 2001]. Second, the flexibility and autonomy embedded
in online courses require students to have the ability to manage their own
time [Hill, 2002, Roper, 2007]. Within the readiness framework, scholars have
studied issues such as the level of technical skills for the use of computers
and the internet [Peng et al., 2006]. Extending the latter, Hung and
colleagues [Hung et al., 2010] suggested a five-dimensional model of readiness
that includes self-directed learning, motivation for learning, computer and
internet self-efficacy, online communication self-efficacy, and learner
control. Self-efficacy is defined as individuals’ judgment of their own
ability to perform different types of tasks [Bandura, 1986]. Consequently,
Information and Communications Technologies (ICT) self-efficacy is related to
learners’ confidence in utilizing computers and the internet and conveying
ideas via the available digital technologies. These subdimensions of readiness
stress the importance of autonomy and motivation toward learning as well as
the ability to deal with and manipulate ICTs and their forms of communication
to effectively navigate the advantages and challenges of online learning
[Kebritchi et al., 2017].

Furthermore, the lack of human connection in online courses might lead
learners to feel isolated from their classroom peers, thus affecting their
sense of identity and further academic expectations and learning [Koole,
2014]. Successful online courses encourage collective rather than
individualistic cultural norms as the former foster familiarity and trust
among members. This consequently facilitates a sense of belonging and the
intention to share knowledge [Zhao et al., 2010], thus improving the quality
of discussions [Shih and Huang, 2014]. Therefore, it is vital to encourage in
learners a sense of belonging within online learning environments, enabling
the further development of academic goals and purpose [Koole, 2014, Lapadat,
2007]. For instance, collaborative class participation in MOOCs (massive open
online courses) has been shown to foster further participation and reduce
desertion [Ferschke et al., 2015].

In connection with learners’ identity, participation in different online
learning formats is another fundamental phenomenon discussed in the
literature. Researchers recognize two forms of participation in online
courses: participation as interactions between peers and instructors via
written comments and responses [Romiszowski and Mason, 2004, Vonderwell and
Zachariah, 2005] and participation by reading these interactions more than
writing them [Hrastinski, 2009, Wise et al., 2013]. Within this line of
research, scholars have challenged the dichotomy between active participation
(i.e., writing in online courses) and passive participation (i.e., reading
online comments) given that the latter demands active engagement with and
reflection on the content [Kebritchi et al., 2017, Hrastinski, 2009]. A study
conducted by Wise and colleagues [Wise et al., 2013] found that approximately
three-quarters of students’ time is spent reading and observing written forms
of interactions in online courses. When measuring participation and its
effects on learning, researchers should focus on both forms of participation,
the frequency of written posts and the time spent observing and reading
written messages in online forums. A study conducted at the University of
Georgia found that time spent reading written messages, was a predictor of
final grades [Morris et al., 2005].

In addition to learners’ preparation to deal with online courses, their
experience is mediated by the curriculum design and course structure.
Researchers have reported a myriad of recommendations for increasing students’
participation and engagement in online courses. For instance, effective online
courses should be centered on students [Chametzky, 2014, Luyt, 2013] with
emphasis on collaboration [Niess and Gillow-Wiles, 2013, Gupta and Bostrom,
2013, Tsai, 2013]. Additionally, communication in online courses requires
guidelines for developing a climate of psychological safety for open
communication, which has been shown to foster students’ participation over
time [Zhao et al., 2010]. Such considerations directly contribute to learners’
sense of identity and belonging because students have the opportunity to work
in their zones of proximal development alongside others. These principles do
not differ from the social principles widely predicated in face-to-face
education, yet their adoption in online formats requires further consideration
of technical characteristics. Accordingly, the use of diverse digital
technologies might enable further motivation to engage in the cognitive and
social processes designed in online courses [Panigrahi et al., 2018]. The
research-based recommendations for developing content in an online course
include the integration of technology within a mix of collaborative and
reflective activities and with clear performance expectations and assessment
[Niess and Gillow-Wiles, 2013].

### Online learners’ participation

Learners’ participation in online learning environments has been studied
following quantitative (e.g., frequency of posts [Morris et al., 2005]) and
qualitative perspectives (e.g., content analysis [De Wever et al., 2006]).
More recently, researchers have turned to social network analysis (SNA) in an
attempt to comprehend such participation using relational measurements such as
students’ network centrality and their structural roles in the network
[Traxler et al., 2018, Garton et al., 1997].

For instance, Traxler and colleagues [Traxler et al., 2018] explored
participation networks in consecutive online learning courses, conceptualizing
network ties as joint interactions by posting on the same online forums; these
authors found significant correlations between network centrality and grades.
Because network centrality provides information on actors’ social integration
in the network, Dawson [Dawson, 2008] studied the relationship between network
centrality and reported levels of the sense of community in the context of
computer-mediated communication (CMC) and found positive correlations for
closeness and degree centrality and a negative correlation for betweenness and
sense of community. A subsequent study by Dawson showed network and
performance-level differences between high- and low-performing students in
online forums. In detail, high-performing students enjoyed more extensive
networks whose members had high average grades compared to their low-
performing counterparts [Dawson, 2010]. Additionally, and consistent with the
expert versus novice literature, the content analysis revealed that high-
performing networks were centered on conceptual content ideas, while in the
low-performing network, the questions and comments focused on fact-based
questions.

The above studies utilize SNA principles to conceptualize participation as
aggregated interaction with forum posts. This relational perspective enables
further examination of its connection with the academic success and
sociodemographic features of students. In this work, we take an additional
step in understanding the effects of online participation on academic success
by conducting a large-scale study of all undergraduate students in their first
and third years at a university in Chile. We map their coparticipant network
and content exposure in discussion forums to evaluate its impact on academic
performance.

## Results

#### Data

Are discussion forums a source of collective intelligence that improves
students’ academic performance? We investigated the role of network centrality
metrics in discussion forums, which capture forum and individual features
related to the amount and quality of the information to which students were
exposed, on the individual final GPA for all 7,528 students in their first
year (n=3,585) and third year (n=3,943) in a large Chilean university. We only
considered students who entered university via regular admission and enrolled
in daytime modality degree programs, mainly because alternative admission
methods respond to different students’ profiles and different institutional
dynamics. Finally, we filtered out all students whose final GPA in semester
1-2021 was under 4.0, the minimum pass mark in Chile, because they had
incomplete information in the university records. Thus, after the data
filtering process, we analyzed three groups of students.

Table 1: Data description for hierarchical models. Variable |  Type |  Description |  Note
---|---|---|---
Ave. GPA 2021-1 |  Dependent variable |  Corresponds to the final GPA of each student after the first class semester (July 2020). |  We run three models where we study first-year students, third-year students enrolled in 2018 (no failed subjects), and third-year students enrolled before 2018 (failed one or more subjects). Collected from the university records.
Sex |  Fixed effect |  Student’s sex registered by the university (female or male). |  Collected from the university records.
N. Credits |  Fixed effect |  Students’ total number of academic hours enrolled. |  The sum of the in-class time that each subject requires. Collected from the university records.
Forum Writings |  Fixed effect |  Total number of posts written by each student. |  All the written posts are collected for each student from the CANVAS LMS platform.
Forum Readings |  Fixed effect |  Total number of posts read by each students. |  All the read posts are collected for each student from the CANVAS LMS platform.
High School GPA |  Fixed effect |  Student’s average high school grade. |  Collected from the university records.
Age |  Fixed effect |  Student’s age in July 2020. |  Collected from the university records.
Enrolled Degree Program |  Random effect |  Each degree program has different structures and number of classes, among others. We control for this using random effects. |  Each degree program has its own intercept. Collected from the university records.
High School |  Random effect |  Students’ high school is a proxy for income and cultural capital. We control for this using random effects combined with commune |  Each high school from each commune has its own intercept. Collected from the university records.
Commune (geographical) |  Random effect |  Students’ origin commune is a proxy for income and cultural capital. We control for this using random effects combined with high school. |  Each high school from each commune has its own intercept. Collected from the university records.
Entrance Path |  Filtering variable |  Students can enter the university in several ways, such as sports scholarships, foreign admission, and highly vulnerable background, among others. We consider only enrolled students enrolled by the regular path, corresponding to more than $90\%$ of all students. |  Collected from the university records.
Cohort |  Filtering variable |  Students’ cohort. |  Used to filter out students taking classes from other cohorts. Collected from the university records.
Entrance year |  Filtering variable |  The year when students entered the university for the first time. |  Used to filter out students who were previously enrolled in other degree programs. Collected from the university records.

  * •

Group I: First-year students who entered the university for the first time in
2020 (n=3,585).

  * •

Group II: Third-year students who entered the university for the first time in
2018 (i.e., students who had not failed any subject) (n=2,296).

  * •

Group III: Third-year students who entered the university for the first time
before 2018 (i.e., students who had failed one or more subjects) (n=1,647).

We measured students’ academic performance–our dependent variable–as the
average GPA at the end of the first semester of 2020. We controlled for
several students’ confounders ranging from sociodemographic features to
individual online behavior (Table 1). Sociodemographic variables were gathered
from the university records, and online behavior variables were gathered from
the databases of the Learning Management System (LMS) adopted by the
University, CANVAS (for more details of CANVAS data extraction, see
supplementary methods S1.1).

#### Co-participation in discussion forums

To assess the role of discussion forums as a valuable source of information
for students, we extract and build three features from them at the student
level (see Supplementary Methods S1.1). i) The relational network (Fig. 1) at
the individual level, where students are connected if they participated
significantly in different discussion forums. Then, we computed different
network centrality measures (Table 2). ii) The number of read, written, and
liked posts at the forum and individual levels to validate our network
centrality measure and to control for LMS individual activity. iii) The text
content of each student’s post for further analysis using natural language
processing.

Figure 1: Graphic depiction of the relationship mapping in CANVAS classroom
forums. A) Bipartite relations. There are two groups of nodes individuals or
actors and threaded posts or events. Individuals can participate in different
threaded posts. Arrows indicate the actors that participate in each threaded
postB). Individuals relate to each other if they participate in the same
threaded post; for instance, actors A and B participate together in threaded
posts 1, 2, and 3. Therefore, they have participated in three different
discussion forums. Note that actor D only participates in threaded post 4, and
no one else participates there. Therefore, actor D has no connections. C) The
resulting network of read threaded posts for first-year students; colors
represent connected components. Note that the network also considers
instructors and teaching assistants because they are relevant actors in the
content diffusion process. See Figure S1 for writing posts and third-year
networks.

We elicit a network of co-participation for both first- and third-year
students (Fig. 1) to build a bipartite network that relates actors (students,
teachers, and teaching assistants) and events (LMS CANVAS threaded forums
posts) (Fig. 1A). Given that we are interested in individual participation, we
project the bipartite network on the actor dimension, linking individuals if
they participated (wrote or read) in the same threaded post (Fig. 1B). Hence,
we obtain an individual network for each written and read post (Fig. 1C) in
each year of academic training.

We note that the mapped coparticipant network using only written posts
captures the information of fewer students than reading posts, and the role of
discussion forums as a source of collective intelligence relies on students
consuming and being exposed to content created by others. Therefore, we choose
to work with the read posts co-participation network (for more details about
the network mapping and filtering process, see Methods, Supplementary Methods
S1.2 and Fig. S1).

#### Network centrality to quantify the exposure to collective intelligence

Figure 2: Node degree captures forums and individual features for first-year
students. R and S represent the Pearson and Spearman correlations,
respectively, and p is their associated p value. We replicate these results
for third-year students enrolled in 2018 (Group II, Fig. S5) and third-year
students enrolled before 2018 (Group 3, Fig. S6). For the regression models
see Table S1. Note that the models do not exhibit a considerable variance
inflation factor (Tables S2, S3, and S4))

The node degree captures both the features of both students and discussion
forums. We focused on the network node (student) degree because more relations
occur in important or relevant posts [Kleinberg, 1999], and the network degree
offers a simple measure that quantifies the activity level in discussion
forums (more reading and writing leads to a higher network degree). Moreover,
the node degree also accounts for posts’ importance because important posts
will be read, replied to and liked by more students, leading to a higher
network node degree. These two characteristics motivate the node degree as a
proxy for collective intelligence exposure [Lévy, 1997]. We validate this idea
by computing Pearson and Spearman correlations and running linear regression
models (see Table S1, and Figures 2, S5, and S6).

Figure 2 shows the Pearson (R) and Spearman (S) correlations and their
respective p values for the node degree and different forum features (average
of written/read/liked posts across all discussion forums in which students
participated), individual online behavior (the total number of
writings/readings/likes of each student in LMS Canvas), and individual
academic performance (high school GPA, application score to their degree
program, and university GPA at the end of their first semester in 2020). We
find positive and significant correlations for all these variables for first-
year students, suggesting that the node degree is a strong measure of exposure
to important posts, individual activity on discussion forums, and previous and
current academic performance. We find similar results for third-year students
from group II (Fig. S5) and group III (Fi. S6). Finally, we reinforce these
results using linear regression models to explain the node degree in each
analyzed group (Table S1). We find that the node degree variance explained in
each group is $68\%$ (Group I), $63\%$ (Group II), and $72\%$ (Group III). Our
results survive after controlling for sex, the number of inscribed credits
(proportional to the academic hours required by each class), students’ age,
fixed effects per degree program, high school, family income, the ranking of
the enrolled degree program, and the length (in semesters) of the enrolled
degree program. Considering all control variables, the explained variance
rises to $81\%$ (Group I), $87\%$ (Group II), and $85\%$ (Group III). We note
that the variance inflation factors are all at low and moderate levels (see
Tables S2, S3, and S4), indicating no multicollinearity problems.

We hypothesize that the effect of co-participation will be different for each
group given their particular features. For instance, first-year students
(group I) do not know each other; therefore, they do not have any other
communication channel but the university LMS. Third-year students enrolled in
2018 (group II) already knew each other for two years. They probably had
alternative communication channels; however, the discussion forum features
(creation, replying, reading, and valuation of posts) are attractive enough
for collective intelligence to emerge. Finally, third-year students enrolled
before 2018 (group III) could already know each other, although they may not
because they could belong to different previous cohorts. Nevertheless, their
self-regulation and autonomous engagement with the course content are probably
lower than those of group II given that these students have failed at least
one subject. Therefore, an effect of collective intelligence on academic
performance in this group is less likely.

#### Discussion forums as a source of collective intelligence

Figure 3: : Hierarchical regression models for the average GPA obtained by
three samples of students at the end of the first semester of 2020. The first
column refers to first-year students enrolled in 2020. The second column
refers to third-year students enrolled in 2018, i.e., students who have not
failed a subject. The third column refers to third-year students enrolled
before 2018, i.e., students taking overdue subjects. We show the standardized
regression coefficients (first row) to compare the effects between different
independent variables. The second row depicts the marginal effects on the
standardized number of students’ connections in the forum coexposure network
built from online class forum readings, quantified as the node degree (k). The
third row depicts the same marginal effects but for different high school
GPAs. (See Table S5 for more details; Fig. S8 for nonstandardized regression
models, and Fig. S9 for the diagonal plot of each model).

We bring our data to hierarchical models according to the following
specification:

$GPA_{i}=\beta_{0i[jl]}+\beta_{1i[jl]}K_{i}+\beta_{ni}X_{ni},$ (1)

where $GPA_{i}$, our dependent variable, is the final GPA for each student $i$
at the end of the first semester of 2020, immediately after the emergency
remote teaching modality started. The motivation to use hierarchical models is
that the final GPA has different levels and increases at different rates with
the node degree ($K_{i}$) depending on the student’s enrolled degree program j
and the student’s former high school $l$. Therefore, $\beta_{0i}[j]$
represents the random intercept for each enrolled degree program ($j$) and
each commune-high school combination (l), $K_{i}$ is the student $i$ node
degree, and $\beta_{1i}[jl]$ represents the random slope of node degree for
each degree program and each high school. We observe that the effect of node
degree varies with the knowledge area (academic department): social sciences
has the strongest effect and engineering has the weakest effect (Fig. S7).
Finally, $X_{ni}$ represents an n-dimensional coefficient vector for each of
the n control variables for each student $i$ (see Table 1 for a description of
the included control variables).

The results (Fig. 3 first row) show that the node degree, $K_{i}$, has a
significant and positive effect on students’ final GPA for first-year students
and third-year students enrolled in 2018 beyond and above controlling for the
number of read and written posts. Moreover, we observe a negative and
significant interaction term between the node degree and high school GPA for
the same groups. We note that the node degree effects are not significant for
third-year students enrolled before 2018. These results suggest that networked
participation has extra value in capturing students’ behavior of forum
participation (see Table S5 for the regression models, Fig. S8 for the model
without standardizing the node degree, and Fig. S9 for the diagonal plot of
the model that graphically shows a noticeable correspondence between the
predicted and observed final GPA).

Interpreting interaction coefficients for two continuous variables can be
challenging; hence, we plot the unconditional marginal effects of node degree
on final GPA (Fig.3 second row). We observe that students’ node degree has a
global positive effect on the final GPA even after considering the negative
interaction and including all the available control variables.

However, what does the negative effect of the interaction term mean? To
disentangle the relationship between high-school GPA and node degree, we plot
the marginal effects of the node degree on final GPA conditioned on high
school GPA. We observe for first-year students and third-year students
enrolled in 2018 that the positive effect of the node degree is steeper for
low high-school GPA students (red color, p value $<0.01$) compared to students
with a high high-school GPA (blue color). Note that for high high-school GPA
(blue line) first-year students, the effect is practically nonsignificant.
Finally, there is no significant effect between the node degree and final GPA
for third-year students enrolled before 2018 (Fig. 3 third column).

#### Robustness checks

As robustness checks, we run the model without the interaction term and obtain
strong positive effects for the node degree on final GPA for both first-year
students and third-year students enrolled in 2018 and no effect for third-year
students enrolled before 2018 (Fig. S10). Nevertheless, an ANOVA shows that
the interaction term between the node degree and high school GPA is
significant for improving the performance of the model (p value $<0.05$) for
both first-year students and third-year students enrolled in 2018 (Table S6).

To show that our results do not depend on the specific measure of prior
individual ability, we replicate our results using the national exam average
score (PSU score) for application to higher education (Fig. S12) instead of
high-school GPA. Our results suggest that the main finding is robust for a
different proxy of students’ ability.

We explore whether the results are an artifact of the chosen centrality
measure. We replicate our analysis by replacing the node degree with the
PageRank centrality (Table 2), obtaining the same results (Fig. S13). We also
explore two other qualitatively different network centrality measures, the
clustering coefficient and Burt’s constraint. Using the clustering
coefficient, we test whether access to information within highly connected
neighborhoods (high clustering coefficient, Table 2) has a role in the final
GPA. Figure S11 shows that co-participating in forum posts in close groups has
a negative, although small, effect on final GPA for first-year students and
for third-year students enrolled in 2018. For third-year students enrolled
before 2018, we do not observe a significant effect. We provide more evidence
on this point by replicating these results using Burt’s network constraint,
which quantifies access to redundant information (Table 2). We find no
significant effect of Burt’s constraint on final GPA (Fig. S14).

#### Content exposure in discussion forums

We have replicated our main findings using alternative measures of prior
individual ability (high school GPA and national examination score) and
network centrality measures (node degree and PageRank). Additionally, we found
divergent validity on different centrality measures, which quantifies access
to redundant information (cluster coefficient and Burt’s constraint
centrality). Now, we ask why the effect of node degree on final GPA is steeper
for disadvantaged (low high-school GPA) students.

Figure 4: First-year students who are exposed to posts with high content
intensity benefit most from discussion forums (see Table S7). The first column
shows the distribution of the individual average content exposure for high
(green) and low (orange) GPA students. The second column shows the
relationship between the individual node degree and average content exposure
for high (green) and low (orange) GPA students. The third column shows the
marginal effects for the main model adding an interaction term between the
node degree and average content exposure (see Tables S7, S8, and S9 for more
details). Low, medium, and high refer to the average content exposure.

Here, we address the fact that there is significant variability in the type of
texts written in each forum, ranging from subject-related content to social-
related texts. We use a neural network approach to quantify the content
intensity of each forum post text (see Methods Forum Posts Semantics). We
define content intensity as the cosine similarity between each written text
and the content that each department taught. For instance, we characterize the
computer science department with all the words (tokens) in the course names. A
random sample of the tokens for the Department of Computer Science is
“cybersecurity, computing, commerce, technologies, society, optimization,
algorithm, logic, introduction, structure”. Then, we compare the similarity
between these tokens and each text post written in a computer science course.
To create the intuition, we provide two text examples. The first is a text
post with high content intensity (cosine similarity of $0.89$):

> Defining what is Information Technology. Computer technology is related to
> how data are managed and handled; within an industry, it can be understood
> as all systems that store, process, transmit, convert, copy or receive
> electronic information. An example of what computer technology would not be
> is using rudimentary methods such as managing shifts through books, storing
> employee data on paper, etc.

An example of a post with low content intensity (cosine similarity of $0.58$)
is the following:

> Presentation of weekly themes. The thing is you have to be committed to
> adding value, not to contributing hours.

We observe that the first post is related to computer science content, and the
second one is more related to social aspects of the course (for more details,
see Method section Forum Posts Semantics).

Thus, we ask whether the steeper effect of the node degree network centrality
on final GPA for disadvantaged students depends on the type of forum post text
in which they participate, quantified as the content intensity. The first
column in Figure 4 shows the density of the individual average content
exposure, quantified as the average of content intensity among all the post
texts in which each student participates per high school GPA (green density
corresponds to high GPA and orange density to low GPA). The average content
exposure is similar for each cohort, $0.62\pm 0.08$ for first-year students
enrolled in 2020, 0.65±0.09 for third-year students enrolled in 2018, and
$0.61\pm 0.10$ for third-year students enrolled before 2018. The second column
in Figure 4 shows the relationship between the student node degree and the
average content exposure conditioned on high school GPA. We find a positive
relation for low high-school GPA students (orange line) and a negative
relation for high high-school GPA students (green). This effect is the
strongest in first-year students and is mild for third-year students enrolled
in 2018. We do not find a significant effect for third-year students enrolled
before 2018. Thus, our results suggest that low high-school GPA students whose
node degree in discussion forums is high interact in more content-intensive
forum text posts than low high-school GPA students. We test this idea,
replicating our main result and adding an interaction term between content
intensity and node degree (third column Figure 4). We find that first-year
students who are exposed to high content-intensity posts (high panel) show the
strongest relation between the node degree and final university GPA (for more
details, see Tables S7, S8, and S9).

## Discussion

The reality of emergency remote teaching can be particularly challenging for
first-year university students due to the impossibility of developing in-
person relationships of friendship and collaboration, which are pivotal to
accessing information and for emotional and academic support. Therefore,
access to a source of collective intelligence that enables cooperative and
consensus dynamics between students can enrich their learning experiences
[Lévy, 1997].

Discussion forums are driven by collective intelligence, which allows people
to write, read and value text posts, thus promoting cooperation and consensus
on which are valuable texts and which are not. The simplest metric that
captures discussion forums’ dynamics is the node degree, defined as the number
of significant students’ connections in the underlying co-participation
network. Indeed, the node degree is positively and significantly associated
with features from the discussion forums, individual online behavior, and
previous and current academic performance (Figures 2, S5, and S6 and Table
S1). These results validate the idea that the node degree is a good proxy of
exposure to collective intelligence. Our results show that a high node degree
is positively and significantly associated with higher university GPA in
first- and third-year students enrolled in 2018 (Fig. 3 and Table S5); these
effects survive even after controlling for several confounder variables
regarding individual online behavior and individual features. We replicate our
results by interchanging node degree with an alternative network centrality,
the PageRank (S13) and high school GPA by the score in the national exam for
university application (S12).

The positive effect of the node degree on final GPA is steeper for first-year
students with a low high-school GPA (Fig. 3) (or low university application
scores, Fig. S12). Presumably, these students entered higher education with
deficiencies in learning content and skills to meet the demands of
undergraduate courses. Thus, our results suggest that participation in
discussion forums can serve as a source of collective intelligence, and
exposure to content created on them helps disadvantaged first-year students to
a greater extent. We hypothesize that access to relevant information regarding
subject content leads to higher individual academic performance. Using natural
language processing tools, we quantify the content intensity of each text in
discussion forums, i.e., how related each text is to the content taught by the
reader’s academic department. We find that first-year students with low high-
school GPA are exposed, on average, to high content-intensive texts. When we
replicate our main analysis separated by low, medium, and high content-
intensity texts, we find positive and significant evidence for our hypothesis:
disadvantaged first-year students benefit the most from discussion forums
because they consume more content-intensive texts (Fig. 4 and Tables S7, S8,
and S9).

The forums and messages written by their peers regarding the course content
become alternative mechanisms to access information and build learning. It
could be argued that forums—unlike messages shared in face-to-face contexts
whose access is limited by particular social relationships in a given time and
require the acknowledgment of students’ particular ignorance on a certain
topic—facilitate access to information for all participants in the course in
an anonymous fashion, which has been studied as a relevant mechanism for
encouraging collaboration [Freeman and Bamford, 2004, Song et al., 2015,
Chester and Gwynne, 1998]. Consequently, from the perspective of Vygotsky’s
zone of proximal development (ZPD) [Vygotsky, 1978], the forums not only allow
the writing and discussion of the content to be learned but also expand the
limits of possible learning to those who enter the first year in a situation
of academic disadvantage. In this way, participation in discussion forums
reduces the differences in performance between students of different academic
conditions in the first year of university. This is also evidenced in third-
year students enrolled in 2018 (second column Fig. 3).

It is also interesting to recognize that first-year students who enter the
university with better school grades and national exam scores do not benefit
from participating in the forums (blue line in first column Fig. 3). In line
with this interpretation, students in such conditions may have skills,
competencies, and support networks to access relevant information for success
in higher education. This interpretation is also sustained by third-year
students with good high school performance. Another potential explanation is
that advantaged students trust others’ knowledge and contributions less
[Tschannen-Moran, 2001]. Thus, advantaged students may have reputation
incentives to write posts but no incentives to consume others’ content.

Finally, we found divergent validity in third-year students enrolled before
2018, i.e., those who took overdue subjects from the third year (Group III).
Greater participation in discussion forums does not benefit their academic
performance. This phenomenon could be explained by the fact that these
students are repeating subjects and may not need forums to build learning
since they may have previous experience in these contents and social networks
outside the subject to improve their performance. Another potential
explanation is that Group III could arguably be students with low self-
efficacy, self-regulation, motivation, and/or engagement; therefore, they
participate less in everything (which could also explain their failed
subjects). If they participated and engaged in discussion forums, they could
have spent considerable time in the forums as a means of access to the
content, but without apparent success.

Thus, our findings suggest that the collective intelligence embedded in
discussion forums can even level the field for disadvantaged students in a
remote learning modality. Figures 3 and 4 show that disadvantaged students
with the highest node degree can even increase their final university GPA to
the level of advantaged students. This consequence can be pivotal for
developing efficient new strategies for encouraging and facilitating learning
in disadvantaged and vulnerable students.

## Methods

### Mapping discussion forum’s co-participations

The bipartite approach is broadly used, for example, to model scientific
collaboration networks [Hou et al., 2008, Tomassini and Luthi, 2007], product
exports in economics [Hidalgo et al., 2007], relations between different
species in ecology [Dormann et al., 2009, Saavedra et al., 2009], relations
between diseases in medicine [Barabási et al., 2011], and the similarity of
degree programs in higher education [Candia et al., 2019a]. More recently,
some online education studies have used this approach to capture student
interactions on forums [Traxler et al., 2018]. Here, we adopt the same
approach.

To establish the effect of class forums’ interactions, we elicit a network of
co-participation for both first- and third-year students (Fig. 1). Individuals
can participate (read or write) in any threaded post in their registered
courses, defining a bipartite relation between individuals or actors
(students, teachers, and teaching assistants) and threaded posts or events
(Fig. 1A). It is possible to project bipartite relations in dimensions, actors
and events. We are interested in online human co-participation; hence, we link
individuals if they participate in the same threaded post (Fig. 1B).

The projected bipartite networks are built from thousands of readings or
writings on CANVAS discussion forums, with content ranging from conversations
related to subjects to topics related to social bonding and with different
levels of participation for different actors. Therefore, we can reasonably
argue that not all co-participation is equally significant. The most active
individuals may be connected by some central structure underlying the entire
network, which is the structure that we need to elicit. Thus, to unveil the
backbone of the co-participation network, we filter out all the links that can
be explained by a null model. To this aim, we compute the $\phi$ correlations
between actors, and then we compute a t test for correlation significance
using a p value of $0.05$. Finally, we discard all negative correlations and
nonsignificant correlations, and we remove all loose nodes (Fig. 1C and Fig.
S1; for more details about the filtering process, see Supplementary method
S1.2).

### Centrality metrics

To explore and understand the forums’ navigation patterns associated with
academic success, we calculate different and alternative network centrality
metrics from the co-participation network (Table 2), including node degree,
PageRank, local clustering, and Burt’s constraint. We use these student-level
centrality metrics in our regression models to study the relationship between
students’ forum co-participation and their final GPA in the first semester of
2020.

We focus on the network node degree (Table 2) as our main centrality metric
that captures behavioral information from students interacting in discussion
forums. To state the robustness of our findings, we use PageRank centrality,
which also accounts for the centrality of the network neighbors of each given
student, i.e., a connection with a central student in the co-participation
network is weighted more than a connection with a noncentral student. The
clustering coefficient and Burt’s constraint are used to explore the effect of
accessing redundant information in discussion forums.

Table 2: Network metrics and their definitions. $w_{ij}$ is the number of links between students $i$ and $j$, and N is the total number of students. Notation |  Definition
---|---
$G(V_{i},E)$ |  Network G is the backbone of the forum posts’ network. V represents the vertex (students, i) and E is the edges.
$k(V_{i})=\frac{1}{N}\sum_{j\neq i}w_{ji}$ |  Node degree is a centrality metric that quantifies the number of connections that a student has in the forum co-exposure network.
$P(V_{i})=\frac{1-d}{N}+d\sum_{j=1}^{n}\frac{w_{ij}P_{j}}{\sum_{k=1}^{n}w_{kj}}$ |  PageRank is a centrality metric that quantifies the number of connections and the importance of those connections for each student in the forum co-exposure network; d represents a dumping factor. The inventors of Page-Rank [Page et al., 1999] recommend to set it as $d=0.85$.
$C_{i}={\frac{|\\{e_{{jk}}:v_{j},v_{k}\in N_{i},e_{{jk}}\in E\\}|}{k_{i}(k_{i}-1)}}$ |  The clustering coefficient is defined as the proportion of the number of links between the neighbors of vertex $i$ divided by the number of links that could possibly exist between them. The more neighbors are connected between them, the higher the clustering is, leading to a higher probability to access redundant information.
$C^{\prime}_{i}=\sum_{j}w_{ij}[1-\sum_{q}\frac{w_{iq}}{\sum_{j_{i\neq j}}w_{ij}}w_{jq}],q\neq i,j$ |  Burt’s constraint for an undirected network is a centrality metric that quantifies the access to structural holes in the forum co-exposure network. The higher Burt’s constraint is, the higher the probability of accessing redundant information.

### Regression models

To evaluate the impact of co-participation in discussion forums on the
students’ GPA obtained at the end of the first semester of 2020, we apply all
our data to regression models. Considering that each degree program works
differently and has different characteristics and that different high school
contexts have different effects on university outcomes, we opt to use mixed
(or hierarchical) regression models [Gelman and Hill, 2006]. Hierarchical
regressions allow us to model the variance of the estimators induced by each
group, defined by students’ degree programs and secondary school.

The analysis is conducted at the student level. Therefore, the dependent
variable is the GPA across all the courses registered by each student at the
end of the first semester of 2020. After testing different specifications, the
proposed models consider as significant control variables the fixed effects of
gender, age, the number of credits enrolled, and the high school GPA (or the
weighted score in the national exam, PSU). The models also include random
effects in the intercepts (each of the categories in each group has an
independent intercept) for the degree program and the student’s secondary
school (Table 1).

Finally, we run the analysis for all students in the daytime mode who were
enrolled through the regular admission path. We note that the analysis covers
all students with an average grade greater than or equal to 4.0 (the minimum
passing grade in Chile), and we discard all students who dropped out of their
degree programs within the first semester of 2020 because it is impossible to
compute a reliable average GPA for analysis. Thus, the final number of
analyzed students is $2,648$ first-year students, $1,467$ third-year students
enrolled for the first time at the university in 2018 (no-failed subjects),
and $638$ third-year students enrolled for the first time at the university
before 2018 (with at least one failed subject).

### Forum posts semantics

We use Word2Vec [Mikolov et al., 2013a, Mikolov et al., 2013b], a word
embedding technique that enables us to represent words in a vector space–or
semantic space–where the semantic relations between words are represented by
the vectors’ directions. We use a pretrained semantic space [Cardellino, 2019]
built from a corpus of more than 2 billion Spanish tokens (words, combinations
of words, and chunks of words).

Thus, we characterize and represent each university’s academic department in a
semantic space. Each token is represented as a vector in the semantic space.
In particular, the difference between two vectors’ directions indicates the
semantic dissimilarity of the words and is quantified as the cosine similarity
between vectors ranging, theoretically, between $-1$ and $1$. In other words,
parallel vectors (minimum direction difference) indicate maximum similarity
(cosine similarity equal to $1$), and orthogonal vectors (maximum direction
difference) indicate minimum similarity (cosine similarity equal to $0$).

We consider all the words that describe the names of the courses taught by
each academic department. We filter out all the stop words, and then we
lemmatize all the words. The resulting groups of words are considered a proxy
for the subjects’ content that characterizes each academic department. Then,
using the vectorial sum, we build a semantic representation for each academic
department in the semantic space.

Next, we represent each post in the semantic space summing each post’s word
vectorially. Thus, we can estimate how close (in terms of content) each post
is to its corresponding academic department (the academic department where the
subject is being taught) in the semantic space. We compute the cosine
similarity between both vectors (discussion forum post and department), which
results in a content intensity measure for each written text in online
discussion forums [Garten et al., 2018].

Finally, we compute a student’s average content exposure by averaging the
content intensity of each post that a certain student read.

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## Acknowledgments

The research reported in this publication was supported by Unidad de
Fortalecimiento Institucional of the Ministerio de Educación Chile, project
InES 2018 UCO1808 Laboratorio de Innovación educativa basada en investigación
para el fortalecimiento de los aprendizajes de ciencias básicas en la
Universidad de Concepción. This research was partially supported by FONDEF
ID19I10413. C.C. thanks Javier Pulgar for his thorough and insightful comments
and suggestions.

## Author contributions statement

The authors confirm contribution to the paper as follows: study conception and
design: C. C, and K.L.; data extraction and data cleaning: F.P. and C.C.;
model creation and data analysis: C.C.; interpretation of results: C. C, A. M
and C.B.; original draft preparation: C. C and A. M; manuscript review and
editing: C. C, A. M and C.B.; project administration: K.L.; research
supervision: C.B.

## Competing interests

The authors declare no competing interests.

## Supplementary material

##  S1 Supplementary methods

###  S1.1 Data Gathering

We gathered data on students from Canvas LMS, adopted by the whole university.
We focused on the Canvas Data Portal service, which through its API, canvas-
data-cli, provides the data associated with student’s activity on the
platform, in an orderly and structured way. In the study we use the requests
records, which provides information at the level of the specific action
performed by the user together with its date-time. These records are commonly
called log records.

The data cleaning process of the log records involved remove duplicates and
records without associated user or action. Then, using regular expressions, we
performed the processing of the log’s url (url encompasses information on the
location of the action with the following structure:
/courses/10/discussion/280. This url refers to an action in the course ’10’
and the forum discussion ’280’). We also processed the web_application_action
field that encompasses if the action is ’read’ or ’write’.

After cleaning and processing the log records, we use the tables the
course_dim, user_dim and dicussion_entry_dim of Canvas Data Portal in order to
obtain the course (subject) ID associated to each action, the user ID who
performs the action, and the text message associated with each action (reading
or writing).

The table dicussion_entry_dim contains the identifier of each message,
identifier of the forum to which it belongs, the user ID who writes the text
message, and an indicator if the user replies to a colleague or replies in the
forum root. On the other hand, the table discussion_topic_dim reports who
created the forum, the forum topic, and the creation time, containing the
associated course to which they belong.

The text posts were cleaned of html tags. Thus, we discarded comments that
were only images, empty posts, posts that were only pure html tags. Besides,
discussion forums without any comments were not considered.

For the semantic analysis of text posts, the messages were tokenized and
lemmatized. We discarded very short messages, posts with pure emojis, text in
non-spanish language, or messages without tokens contained in the word
embedding model (Word2Vec).

Using the user_dim and pseudonym_dim tables we obtained the institutional
identifier of the student, which was essential for joining behavioral data on
the Canvas LMS with institutional records.

The institutional records of each students are extracted from BI tool used by
the University, as well as the names of the faculties, departments and
subjects (where we did a manual curation), among many others.

Finally, the dataset used in this article encompass both behavioral data from
Canvas LMS and institutional records.

###  S1.2 Network filtering process

We use all the data from CANVAS of all the individuals (students, student
assistants and teachers) who wrote or read a post in the forums associated
with all the courses associated with any first or third year curriculum.

For each individual, the data set comprises a list of all the forums where
they participated passively or actively, either reading or writing a text.
From here, a list of pairs of co-participation (joint reads and / or writes)
of individuals is generated for each forum, that is, we associate individuals
if they both participate in the same forum. After obtaining a list for each
forum, we construct a matrix of co-participations, $M$, that counts the times
that each pair of people participate in the same forum, $M_{ij}$, that is, if
individual 1 and individual 2 participated 4 times in forum A and 3 times in
forum B, the entry of the matrix associated with both individuals is defined
as $M_{12}=4+3=7$. Furthermore, we define $M_{i}=\sum_{j}M_{ij}$ as the total
number of shares of each individual. Next, a projection of a mode is created
by linking all the actors that were connected to the same event node (Figure
1). A student who posts multiple times in a thread will have links of greater
weight to the other participants of the thread in the actor’s screening. Add
up the weights of multiple links between two people (from posting in multiple
common threads).

The procedure described is known as the bipartite network model, recurrently
used to model situations in which both people (“actors”) and some set of
shared activities (“events”) are of interest. This approach has been used, for
example, to model scientific collaboration networks [Hou et al., 2008,
Tomassini and Luthi, 2007], where scientists (actors) and articles (events)
are the two types of nodes. Also, this approach has been used in economics
[Hidalgo et al., 2007], ecology [Dormann et al., 2009, Saavedra et al., 2009],
and education [Candia et al., 2019a]. More recently, some online education
studies have used it to capture student interactions on forums [Traxler et
al., 2018]. The bipartite analysis is developed in two stages. First, the
network is created with two types of nodes (individuals and forums). The
bipartisan approach gives us a loud and strongly interconnected picture of
forum conversations. The social network generated from the bipartite
methodology has more links and more connections than typical networks based on
class surveys. So, given that these networks build from thousands of readings
and posts, with content ranging from conversations related to courses to
topics related to social bonding, it seems reasonable that not all
interactions are equally important. The most active individuals may be
connected by some central structure underlying the entire “noisy” network, and
it is these kinds of structures that we need to reveal. Therefore, the
following steps are performed:

  * •

Calculate the $\phi$ correlations between pairs of individuals as
$\phi_{ij}=\frac{M_{ij}Z-M_{i}M_{j}}{\sqrt{M_{j}M_{i}(Z-M_{i})(Z-M_{j})}}$

  * •

Discard all links with negative correlations. Negative correlations represent
people that co-participate in forums in a lower proportion than expected at
random.

  * •

Calculate the $t$ statistic to evaluate whether the correlations are
significantly different from zero with a significance threshold of p-value
$<0.05$ as $t_{ij}=\phi_{ij}\frac{\sqrt{D-2}}{\sqrt{1-\phi_{ij}^{2}}}$.

  * •

All loose nodes are discarded.

We map four participation networks based on the type of participation (reading
or writing) and the courses enrolled (first or third year) (Figure 3). We note
that of the 6,433 students who are enrolled in first-year courses, the network
contains information on 4,901 students and capturing information on 117
assistant students and 208 teachers. In comparison, the network of co-
participation (writing) for first-year students contains information on only
1050 students, 34 assistant students, and 104 teachers. On the other hand, the
network of third-year courses, out of 4543 students enrolled in third-year
courses, captures information from 3705 students, 129 assistants, and 175
teachers in reading-type participation and 944 students, 28 assistants 90
teachers in participation writing type.

Figure S1: Participation networks in online forums. A) Reading-type
participation network among students enrolled in first-year courses. B)
Reading-type participation network among students enrolled in third-year
courses. C) Network of writing-type participation among students enrolled in
first-year courses. D) Network of writing-type participation among students
enrolled in third-year courses. Colors represent connected components, that
is, people who have at least one path through other people connecting them
within the network.

###  S1.3 Filtered network correlations

Figure S2: Correlation plot for the average GPA obtained by first-year
students at the end of the first semester of 2020 and different network
centralities. The diagonal shows the variable histogram, the top triangle
shows the Pearson correlation and their significance, and the bottom triangle
shows the scatter plot between two variables.

Figure S3: Correlation plot for the average GPA obtained by third-year
students (enrolled in 2018) at the end of the first semester of 2020 and
different network centralities. The diagonal shows the variable histogram, the
top triangle shows the Pearson correlation and their significance, and the
bottom triangle shows the scatter plot between two variables.

Figure S4: Correlation plot for the average GPA obtained by third-year
students (enrolled before 2018) at the end of the first semester of 2020 and
different network centralities. The diagonal shows the variable histogram, the
top triangle shows the Pearson correlation and their significance, and the
bottom triangle shows the scatter plot between two variables.

##  S2 Supplementary results and robustness checks

###  S2.1 Degree centrality captures forum and individual’s features

Figure S5: Node degree captures forums and individual’s features for third-
year students enrolled in 2018. $R$ and $S$ represent Pearson and Spearman
correlation respectively and $p$ is their associated p-value. For the
regression models see Table S5. Note that models do not exhibit a considerable
variance inflation factor (Table S3)

Figure S6: Node degree captures forums and individual’s features for third-
year students enrolled before 2018. $R$ and $S$ represent Pearson and Spearman
correlation respectively and $p$ is their associated p-value. For the
regression models see Table S1. Note that models do not exhibit a considerable
variance inflation factor (Table S4)

Table S1: Linear regression models for node degree. | Dependent variable:
---|---
| Node degree
| Group 1 | Group 2 | Group 3
| (1) | (2) | (3) | (4) | (5) | (6)
Forum’s Ave. Writings (z-score) |  6.206∗∗∗ |  9.900∗∗∗ |  4.034∗∗∗ |  $-$0.726 |  $-$0.188 |  8.975∗∗∗
| (0.709) | (0.946) | (1.115) | (1.578) | (1.276) | (1.833)
Squared Forum’s Ave. Writings (z-score) |  $-$2.701∗∗∗ |  $-$1.976∗∗∗ |  $-$1.999∗∗∗ |  $-$0.158 |  $-$0.266 |  $-$0.956∗∗∗
| (0.206) | (0.207) | (0.347) | (0.359) | (0.231) | (0.264)
Forum’s Ave. Readings (z-score) |  8.634∗∗∗ |  6.175∗∗∗ |  18.793∗∗∗ |  8.423∗∗∗ |  17.534∗∗∗ |  7.675∗∗∗
| (0.745) | (0.956) | (1.364) | (1.752) | (1.319) | (1.920)
Squared Forum’s Ave. Readings (z-score) |  $-$0.625∗∗∗ |  $-$0.715∗∗∗ |  $-$1.441∗∗∗ |  $-$0.425∗∗∗ |  $-$1.842∗∗∗ |  $-$0.776∗∗∗
| (0.185) | (0.191) | (0.125) | (0.133) | (0.199) | (0.232)
Forum’s Ave. Likes (z-score) |  8.793∗∗∗ |  3.692∗∗∗ |  $-$0.924∗ |  1.014∗ |  1.782∗∗∗ | 0.885
| (0.454) | (0.670) | (0.543) | (0.519) | (0.538) | (0.591)
Student’s Ave. Writings (z-score) |  $-$6.187∗∗∗ | 0.077 |  $-$7.765∗∗∗ | 1.035 |  $-$4.175∗∗∗ | 0.178
| (0.534) | (0.523) | (0.803) | (0.656) | (0.841) | (0.864)
Student’s Ave. Readings (z-score) |  37.786∗∗∗ |  42.958∗∗∗ |  35.859∗∗∗ |  32.964∗∗∗ |  25.387∗∗∗ |  24.933∗∗∗
| (0.907) | (0.963) | (1.187) | (1.047) | (1.197) | (1.342)
Squared Student’s Ave. Readings (z-score) |  $-$4.032∗∗∗ |  $-$4.101∗∗∗ |  $-$3.897∗∗∗ |  $-$3.422∗∗∗ |  $-$1.953∗∗∗ |  $-$1.789∗∗∗
| (0.124) | (0.119) | (0.171) | (0.140) | (0.127) | (0.134)
Student’s Ave. Likes (z-score) | 0.297 |  $-$0.105 |  $-$0.412 |  $-$0.407 | 0.211 |  $-$0.760
| (0.376) | (0.322) | (0.481) | (0.374) | (0.476) | (0.469)
High School GPA (z-score) |  4.014∗∗∗ | 0.201 |  5.261∗∗∗ | 0.393 |  2.820∗∗∗ | 0.241
| (0.411) | (0.473) | (0.540) | (0.481) | (0.621) | (0.789)
Sex [M] |  $-$0.287 |  $-$0.151 |  $-$0.506 |  $-$0.315 |  $-$1.236 |  $-$1.053
| (0.789) | (0.708) | (1.004) | (0.736) | (1.173) | (1.219)
N. Credits (z-score) | 0.493 | 0.353 |  $-$1.846∗∗∗ | 0.562 |  $-$0.977 | 0.865
| (0.433) | (0.447) | (0.492) | (0.478) | (0.609) | (0.770)
Age (z-score) | 0.076 |  $-$0.128 | 0.144 | 0.236 | 0.445 |  $-$0.273
| (0.379) | (0.330) | (0.518) | (0.359) | (0.623) | (0.611)
Constant |  45.591∗∗∗ |  54.080∗∗∗ |  38.481∗∗∗ |  44.005∗∗∗ |  20.374∗∗∗ |  23.672∗∗
| (0.565) | (6.367) | (0.669) | (5.622) | (0.835) | (9.860)
Degree program f. e. | No | Yes | No | Yes | No | Yes
High school f.e. | No | Yes | No | Yes | No | Yes
Family income quintil f.e. | No | Yes | No | Yes | No | Yes
Preference ranking | No | Yes | No | Yes | No | Yes
Degree program length | No | Yes | No | Yes | No | Yes
Observations | 3,249 | 3,249 | 1,697 | 1,697 | 844 | 844
R2 | 0.685 | 0.805 | 0.635 | 0.872 | 0.732 | 0.847
Adjusted R2 | 0.684 | 0.788 | 0.632 | 0.852 | 0.727 | 0.805
Residual Std. Error | 20.729 (df = 3235) | 16.992 (df = 2984) | 19.336 (df = 1683) | 12.253 (df = 1473) | 16.302 (df = 830) | 13.791 (df = 661)
F Statistic |  541.413∗∗∗ (df = 13; 3235) |  46.615∗∗∗ (df = 264; 2984) |  225.289∗∗∗ (df = 13; 1683) |  44.897∗∗∗ (df = 223; 1473) |  174.073∗∗∗ (df = 13; 830) |  20.113∗∗∗ (df = 182; 661)
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S2: Variance inflation factor for Group 1’s node degree model | GVIF | Df | GVIF$\hat{\mkern 6.0mu}$(1/(2*Df))
---|---|---|---
scale(mean_add_entry) | $9.836$ | $1$ | $3.136$
I(scale(mean_add_entry)$\hat{\mkern 6.0mu}$2) | $3.421$ | $1$ | $1.850$
scale(mean_read_entry) | $10.098$ | $1$ | $3.178$
I(scale(mean_read_entry)$\hat{\mkern 6.0mu}$2) | $4.131$ | $1$ | $2.033$
scale(mean_rate_entry) | $5.432$ | $1$ | $2.331$
scale(n_write_f) | $3.282$ | $1$ | $1.812$
scale(mark_entry_read) | $11.094$ | $1$ | $3.331$
I(scale(mark_entry_read)$\hat{\mkern 6.0mu}$2) | $5.362$ | $1$ | $2.316$
scale(rate_entry) | $1.284$ | $1$ | $1.133$
scale(Prom..Notas) | $2.544$ | $1$ | $1.595$
Género | $1.405$ | $1$ | $1.185$
scale(sum_Créditos) | $2.110$ | $1$ | $1.453$
scale(Age) | $1.224$ | $1$ | $1.106$
Quintil | $1.357$ | $3$ | $1.052$
Preferencia | $2.407$ | $9$ | $1.050$
Colegio.Comuna | $338.664$ | $172$ | $1.017$
Carrera | $151,524.200$ | $67$ | $1.093$
Table S3: Variance inflation factor for Group 2’s node degree model | GVIF | Df | GVIF$\hat{\mkern 6.0mu}$(1/(2*Df))
---|---|---|---
scale(mean_add_entry) | $29.256$ | $1$ | $5.409$
I(scale(mean_add_entry)$\hat{\mkern 6.0mu}$2) | $15.017$ | $1$ | $3.875$
scale(mean_read_entry) | $41.939$ | $1$ | $6.476$
I(scale(mean_read_entry)$\hat{\mkern 6.0mu}$2) | $22.682$ | $1$ | $4.763$
scale(mean_rate_entry) | $3.681$ | $1$ | $1.918$
scale(n_write_f) | $6.203$ | $1$ | $2.490$
scale(mark_entry_read) | $15.208$ | $1$ | $3.900$
I(scale(mark_entry_read)$\hat{\mkern 6.0mu}$2) | $8.064$ | $1$ | $2.840$
scale(rate_entry) | $2.084$ | $1$ | $1.444$
scale(Prom..Notas) | $2.326$ | $1$ | $1.525$
Género | $1.479$ | $1$ | $1.216$
scale(sum_Créditos) | $2.475$ | $1$ | $1.573$
scale(Age) | $1.291$ | $1$ | $1.136$
Quintil | $1.596$ | $3$ | $1.081$
Preferencia | $6.645$ | $8$ | $1.126$
Colegio.Comuna | $8,718.344$ | $140$ | $1.033$
Carrera | $3,523,250.000$ | $59$ | $1.136$
Table S4: Variance inflation factor for Group 3’s node degree model | GVIF | Df | GVIF$\hat{\mkern 6.0mu}$(1/(2*Df))
---|---|---|---
scale(mean_add_entry) | $20.314$ | $1$ | $4.507$
I(scale(mean_add_entry)$\hat{\mkern 6.0mu}$2) | $8.578$ | $1$ | $2.929$
scale(mean_read_entry) | $23.055$ | $1$ | $4.802$
I(scale(mean_read_entry)$\hat{\mkern 6.0mu}$2) | $9.705$ | $1$ | $3.115$
scale(mean_rate_entry) | $2.560$ | $1$ | $1.600$
scale(n_write_f) | $5.913$ | $1$ | $2.432$
scale(mark_entry_read) | $13.661$ | $1$ | $3.696$
I(scale(mark_entry_read)$\hat{\mkern 6.0mu}$2) | $7.672$ | $1$ | $2.770$
scale(rate_entry) | $1.851$ | $1$ | $1.360$
scale(Prom..Notas) | $2.705$ | $1$ | $1.645$
Género | $1.628$ | $1$ | $1.276$
scale(sum_Créditos) | $2.375$ | $1$ | $1.541$
scale(Age) | $1.469$ | $1$ | $1.212$
Quintil | $4.458$ | $5$ | $1.161$
factor(Preferencia) | $5.841$ | $8$ | $1.117$
Colegio.Comuna | $191,814.900$ | $96$ | $1.065$
Carrera | $7,561,474.000$ | $60$ | $1.141$

###  S2.2 Main model table

Table S5: Main hierarchical regression models represented in main Figure 3. | Dependent variable:
---|---
| Average GPA 1-2020
| First-year students | Third-year students | Third-year students
| (enrolled in 2020) | (enrolled in 2018) | (enrolled before 2018)
| (1) | (2) | (3)
Sex [M] |  $-$0.005 |  $-$0.117∗∗∗ |  $-$0.103∗∗∗
| (0.015) | (0.017) | (0.023)
N. Credits (z-score) |  $-$0.049∗∗∗ |  0.029∗∗∗ |  0.068∗∗∗
| (0.009) | (0.011) | (0.012)
Forum Writing (z-score) |  0.094∗∗∗ |  0.075∗∗∗ | 0.035
| (0.011) | (0.017) | (0.023)
Forum Reading (z-score) |  0.026∗ | 0.020 |  0.072∗∗
| (0.014) | (0.021) | (0.028)
Node Degree (z-score) |  0.081∗∗∗ |  0.133∗∗∗ |  $-$0.018
| (0.014) | (0.024) | (0.029)
High School GPA (z-score) |  0.102∗∗∗ |  0.119∗∗∗ |  0.081∗∗∗
| (0.009) | (0.011) | (0.015)
Age (z-score) | 0.004 | 0.005 |  $-$0.023∗∗
| (0.007) | (0.008) | (0.011)
Node Degree (z-score) x High School GPA (z-score) |  $-$0.034∗∗∗ |  $-$0.024∗∗ | 0.005
| (0.009) | (0.011) | (0.015)
Constant |  5.787∗∗∗ |  5.868∗∗∗ |  5.579∗∗∗
| (0.037) | (0.043) | (0.044)
Random slope for node degree in each degree program | Yes | Yes | Yes
Degree program random intercept | Yes | Yes | Yes
High school random intercept | Yes | Yes | Yes
Commune random intercept | Yes | Yes | Yes
Observations | 3,585 | 2,296 | 1,647
Log Likelihood |  $-$1,771.267 |  $-$990.039 |  $-$947.311
Akaike Inf. Crit. | 3,572.534 | 2,010.079 | 1,924.622
Bayesian Inf. Crit. | 3,665.302 | 2,096.163 | 2,005.722
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

###  S2.3 Main model random slopes

Figure S7: Hierarchical regression node degree random slope for different
knowledge areas. The dependent variable is the average GPA obtained by first-
year students at the end of the first semester of 2020. Colors represent
different high school GPAs.

###  S2.4 Main model non-standardized coefficients

Figure S8: Hierarchical regression models for the average GPA obtained by
three samples of students at the end of the first semester of 2020. The first
column refers to first-year students enrolled in 2020. The second column
refers to third-year students enrolled in 2018, i.e., students who do not have
any failed subject. The third column refers to third-year students enrolled
before 2018, i.e., students taking overdue subjects. The first row shows the
regression coefficients. The second row depicts the marginal effects on node
degree (k), and the third row depicts the same marginal effects for different
high school GPAs.

###  S2.5 Main model predicted vs actual average GPA

Figure S9: Predicted vs actual plot for the average GPA obtained by students
at the end of the first semester of 2020. A) First-year students entering
university for the first time. B) Third-year students who do not have any
failed subject. C) Third-year students taking overdue subjects. The red line
represents the perfect fit.

###  S2.6 The effect of node degree on undergrad GPA without the interaction
term

Figure S10: Hierarchical regression models for the average GPA obtained by three samples of students at the end of the first semester of 2020 not including the interaction term between node degree and high school GPA. The first column refers to first-year students enrolled in 2020. The second column refers to third-year students enrolled in 2018, i.e., students who do not have any failed subject. The third column refers to third-year students enrolled before 2018, i.e., students taking overdue subjects. We show the standardized regression coefficients (first row) to compare the effects between different independent variables. The second row depicts the marginal effects on the standardized number of students’ connections in the information co-exposure network built from online class forums readings, quantified as the node degree (k) for different high school GPAs (colors). Table S6: ANOVA testing the improvement at including the interaction term between node degree and high school GPA for each student sample (model 1, model 2, and model 3). The tested models are depicted in Fig. 3 (with interaction) and Fig.S10 (without interaction). For samples 1 and 2 the interaction term improves the models’ performance. | Df | AIC | BIC | logLik | deviance | Chisq | Chi Df | Pr(>Chisq)
---|---|---|---|---|---|---|---|---
model 1 no-interaction | $14$ | $3,584.574$ | $3,671.157$ |  -$1,778.287$ | $3,556.574$ |  |  |
model 1 interaction | $15$ | $3,572.534$ | $3,665.302$ |  -$1,771.267$ | $3,542.534$ | $14.039$ | $1$ | $0.0002$
model 2 no-interaction | $14$ | $2,013.215$ | $2,093.560$ |  -$992.608$ | $1,985.215$ |  |  |
model 2 interaction | $15$ | $2,010.079$ | $2,096.163$ |  -$990.039$ | $1,980.079$ | $5.136$ | $1$ | $0.023$
model 3 no-interaction | $14$ | $1,922.736$ | $1,998.430$ |  -$947.368$ | $1,894.736$ |  |  |
model 3 interaction | $15$ | $1,924.622$ | $2,005.722$ |  -$947.311$ | $1,894.622$ | $0.114$ | $1$ | $0.736$

###  S2.7 Clustering coefficient and university GPA

Figure S11: Hierarchical regression models for the average GPA obtained by
three samples of students at the end of the first semester of 2020. The first
column refers to first-year students enrolled in 2020. The second column
refers to third-year students enrolled in 2018, i.e., students who do not have
any failed subject. The third column refers to third-year students enrolled
before 2018, i.e., students taking overdue subjects. We show the standardized
regression coefficients (first row) to compare the effects between different
independent variables. The second row depicts the marginal effects on the
standardized student’s clustering coefficient (C) in the forum co-exposure
network built from online class forums readings for different high school GPAs
(colors), which quantifies the potential access to redundant information. (See
Fig.S14 for Burt’s network constraint that shows similar results).

###  S2.8 Node degree and national exam (PSU Score)

Figure S12: Marginal effects for the average GPA obtained by students at the
end of the first semester of 2020. A) First-year students entering university
for the first time. B) Third-year students who do not have any failed subject.
C) Third-year students taking overdue subjects. Colors represent high school
GPA.

###  S2.9 Main model using PageRank

Figure S13: Hierarchical regression models for the average GPA obtained by
three samples of students at the end of the first semester of 2020. The first
column refers to first-year students enrolled in 2020. The second column
refers to third-year students enrolled in 2018, i.e., students who do not have
any failed subject. The third column refers to third-year students enrolled
before 2018, i.e., students taking overdue subjects. We show the standardized
regression coefficients (first row) to compare the effects between different
independent variables. The second row depicts the marginal effects on the
standardized number of students’ connections in the information co-exposure
network built from online class forums readings, quantified as the PageRanl
(P). The third row depicts the same marginal effects but for different high
school GPAs. (See Fig.S8 for non-standardized regression models, TableS5 for
more details of non-standardized models, and Fig.S9 for the diagonal plot of
each model).

###  S2.10 Burt’s network constraint

Figure S14: Hierarchical regression models for the average GPA obtained by
three samples of students at the end of the first semester of 2020. The first
column refers to first-year students enrolled in 2020. The second column
refers to third-year students enrolled in 2018, i.e., students who do not have
any failed subject. The third column refers to third-year students enrolled
before 2018, i.e., students taking overdue subjects. We show the standardized
regression coefficients (first row) to compare the effects between different
independent variables. The second row depicts the marginal effects on the
standardized Burt’s constraint coefficient (C’) in the forum co-exposure
network built from online class forums readings for different high school GPAs
(colors), which quantifies the potential access to redundant information.

###  S2.11 Regression models with content exposure

Table S7: Hierarchical regression model adding content exposure for first-year students enrolled in 2020. | Dependent variable:
---|---
| Average GPA 1-2020
| Main model | Main model and content | Main model | Main model and content
|  |  | (no forum controls) | (no forum controls)
| (1) | (2) | (3) | (4)
Sex [M] |  $-$0.005 |  $-$0.010 |  $-$0.011 |  $-$0.017
| (0.015) | (0.015) | (0.015) | (0.015)
N. Credits (z-score) |  $-$0.049∗∗∗ |  $-$0.064∗∗∗ |  $-$0.048∗∗∗ |  $-$0.061∗∗∗
| (0.009) | (0.010) | (0.009) | (0.010)
Forum Writing (z-score) |  0.094∗∗∗ |  0.090∗∗∗ |  |
| (0.011) | (0.011) |  |
Forum Reading (z-score) |  0.026∗ |  0.028∗∗ |  |
| (0.014) | (0.014) |  |
Node Degree (z-score) |  0.081∗∗∗ |  0.096∗∗∗ |  0.131∗∗∗ |  0.143∗∗∗
| (0.014) | (0.025) | (0.014) | (0.025)
Content Exposure [Low] |  |  $-$0.082∗∗ |  |  $-$0.091∗∗
|  | (0.036) |  | (0.037)
Content Exposure [Medium] |  |  $-$0.082∗∗∗ |  |  $-$0.083∗∗∗
|  | (0.028) |  | (0.028)
High School GPA (z-score) |  0.102∗∗∗ |  0.103∗∗∗ |  0.111∗∗∗ |  0.111∗∗∗
| (0.009) | (0.010) | (0.010) | (0.010)
Age (z-score) | 0.004 | 0.003 | 0.006 | 0.004
| (0.007) | (0.007) | (0.007) | (0.007)
Node Degree (z-score) x Content Exposure [Low] |  |  $-$0.049∗ |  |  $-$0.063∗∗
|  | (0.028) |  | (0.028)
Node Degree (z-score) x Content Exposure [Medium] |  | 0.004 |  | 0.012
|  | (0.027) |  | (0.027)
Node Degree (z-score) x High School GPA (z-score) |  $-$0.034∗∗∗ |  $-$0.025∗∗∗ |  $-$0.030∗∗∗ |  $-$0.021∗∗
| (0.009) | (0.009) | (0.009) | (0.009)
Constant |  5.787∗∗∗ |  5.852∗∗∗ |  5.790∗∗∗ |  5.861∗∗∗
| (0.037) | (0.042) | (0.038) | (0.042)
Random slope for node degree in each degree program | Yes | Yes | Yes | Yes
Degree program random intercept | Yes | Yes | Yes | Yes
High school random intercept | Yes | Yes | Yes | Yes
Commune random intercept | Yes | Yes | Yes | Yes
Observations | 3,585 | 3,248 | 3,585 | 3,248
Log Likelihood |  $-$1,771.267 |  $-$1,580.114 |  $-$1,818.845 |  $-$1,619.718
Akaike Inf. Crit. | 3,572.534 | 3,198.227 | 3,663.691 | 3,273.436
Bayesian Inf. Crit. | 3,665.302 | 3,313.858 | 3,744.090 | 3,376.894
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S8: Hierarchical regression model adding content exposure for third-year students enrolled in 2018 | Dependent variable:
---|---
| Average GPA 1-2020
| Main model | Main model and content | Main model | Main model and content
|  |  | (no forum controls) | (no forum controls)
| (1) | (2) | (3) | (4)
Sex [M] |  $-$0.117∗∗∗ |  $-$0.091∗∗∗ |  $-$0.122∗∗∗ |  $-$0.098∗∗∗
| (0.017) | (0.019) | (0.017) | (0.019)
N. Credits (z-score) |  0.029∗∗∗ |  $-$0.007 |  0.031∗∗∗ |  $-$0.004
| (0.011) | (0.012) | (0.011) | (0.012)
Forum Writing (z-score) |  0.075∗∗∗ |  0.075∗∗∗ |  |
| (0.017) | (0.016) |  |
Forum Reading (z-score) | 0.020 |  0.033∗ |  |
| (0.021) | (0.020) |  |
Node Degree (z-score) |  0.133∗∗∗ |  0.084∗∗ |  0.175∗∗∗ |  0.157∗∗∗
| (0.024) | (0.038) | (0.021) | (0.037)
Content Exposure [Low] |  |  $-$0.004 |  |  $-$0.016
|  | (0.037) |  | (0.037)
Content Exposure [Medium] |  | 0.006 |  |  $-$0.001
|  | (0.030) |  | (0.031)
High School GPA (z-score) |  0.119∗∗∗ |  0.121∗∗∗ |  0.121∗∗∗ |  0.121∗∗∗
| (0.011) | (0.012) | (0.011) | (0.012)
Age (z-score) | 0.005 |  $-$0.002 | 0.004 |  $-$0.003
| (0.008) | (0.009) | (0.008) | (0.009)
Node Degree (z-score) x Content Exposure [Low] |  | 0.044 |  | 0.023
|  | (0.039) |  | (0.039)
Node Degree (z-score) x Content Exposure [Medium] |  |  $-$0.013 |  |  $-$0.035
|  | (0.033) |  | (0.033)
Node Degree (z-score) x High School GPA (z-score) |  $-$0.024∗∗ |  $-$0.023∗ |  $-$0.025∗∗ |  $-$0.023∗
| (0.011) | (0.012) | (0.011) | (0.012)
Constant |  5.868∗∗∗ |  5.879∗∗∗ |  5.874∗∗∗ |  5.892∗∗∗
| (0.043) | (0.051) | (0.044) | (0.052)
Random slope for node degree in each degree program | Yes | Yes | Yes | Yes
Degree program random intercept | Yes | Yes | Yes | Yes
High school random intercept | Yes | Yes | Yes | Yes
Commune random intercept | Yes | Yes | Yes | Yes
Observations | 2,296 | 1,697 | 2,296 | 1,697
Log Likelihood |  $-$990.039 |  $-$644.503 |  $-$1,005.517 |  $-$658.443
Akaike Inf. Crit. | 2,010.079 | 1,327.006 | 2,037.034 | 1,350.885
Bayesian Inf. Crit. | 2,096.163 | 1,430.302 | 2,111.640 | 1,443.308
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S9: Hierarchical regression model adding content exposure for third-year students enrolled before 2018. | Dependent variable:
---|---
| Average GPA 1-2020
| Main model | Main model and content | Main model | Main model and content
|  |  | (no forum controls) | (no forum controls)
| (1) | (2) | (3) | (4)
Sex [M] |  $-$0.103∗∗∗ |  $-$0.061∗ |  $-$0.108∗∗∗ |  $-$0.070∗∗
| (0.023) | (0.031) | (0.023) | (0.032)
N. Credits (z-score) |  0.068∗∗∗ |  0.082∗∗∗ |  0.069∗∗∗ |  0.084∗∗∗
| (0.012) | (0.019) | (0.012) | (0.019)
Forum Writing (z-score) | 0.036 |  0.037∗ |  |
| (0.023) | (0.022) |  |
Forum Reading (z-score) |  0.072∗∗ |  0.062∗∗ |  |
| (0.029) | (0.027) |  |
Node Degree (z-score) |  $-$0.019 | 0.033 | 0.042 |  0.099∗∗∗
| (0.030) | (0.040) | (0.028) | (0.038)
Content Exposure [Low] |  |  $-$0.122∗∗ |  |  $-$0.128∗∗
|  | (0.053) |  | (0.054)
Content Exposure [Medium] |  |  $-$0.060 |  |  $-$0.067
|  | (0.045) |  | (0.046)
High School GPA (z-score) |  0.081∗∗∗ |  0.080∗∗∗ |  0.083∗∗∗ |  0.081∗∗∗
| (0.015) | (0.020) | (0.015) | (0.020)
Age (z-score) |  $-$0.023∗∗ |  $-$0.030∗∗ |  $-$0.025∗∗ |  $-$0.033∗∗
| (0.011) | (0.015) | (0.011) | (0.015)
Node Degree (z-score) x Content Exposure [Low] |  |  $-$0.005 |  |  $-$0.017
|  | (0.048) |  | (0.049)
Node Degree (z-score) x Content Exposure [Medium] |  |  $-$0.032 |  |  $-$0.050
|  | (0.038) |  | (0.039)
Node Degree (z-score) x High School GPA (z-score) | 0.005 | 0.003 | 0.006 | 0.004
| (0.015) | (0.017) | (0.015) | (0.017)
Constant |  5.578∗∗∗ |  5.575∗∗∗ |  5.582∗∗∗ |  5.587∗∗∗
| (0.045) | (0.061) | (0.045) | (0.061)
Random slope for node degree in each degree program | Yes | Yes | Yes | Yes
Degree program random intercept | Yes | Yes | Yes | Yes
High school random intercept | Yes | Yes | Yes | Yes
Commune random intercept | Yes | Yes | Yes | Yes
Observations | 1,647 | 831 | 1,647 | 831
Log Likelihood |  $-$974.610 |  $-$480.193 |  $-$980.271 |  $-$485.264
Akaike Inf. Crit. | 1,979.220 | 998.387 | 1,986.543 | 1,004.527
Bayesian Inf. Crit. | 2,060.321 | 1,088.117 | 2,056.830 | 1,084.812
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01