# Do I Belong? Modeling Sense of Virtual Community Among Linux Kernel
Contributors

Bianca Trinkenreich
Daniel M. German  Northern Arizona University
Flagstaff, AZ, USA
<EMAIL_ADDRESS>University of Victoria
Victoria, Canada
<EMAIL_ADDRESS>Klaas-Jan Stol
Marco A. Gerosa  Lero, the SFI Research Centre for Software
University College Cork, Ireland
<EMAIL_ADDRESS>Northern Arizona University
Flagstaff, AZ, USA
<EMAIL_ADDRESS>Anita Sarma
Igor Steinmacher  Oregon State University
Portland, OR, USA
<EMAIL_ADDRESS>Northern Arizona University
Flagstaff, AZ, USA
<EMAIL_ADDRESS>
###### Abstract

The sense of belonging to a community is a basic human need that impacts an
individual’s behavior, long-term engagement, and job satisfaction, as revealed
by research in disciplines such as psychology, healthcare, and education.
Despite much research on how to retain developers in Open Source Software
(OSS) projects and other virtual, peer-production communities, there is a
paucity of research investigating what might contribute to a sense of
belonging in these communities. To that end, we develop a theoretical model
that seeks to understand the link between OSS developer motives and a Sense of
Virtual Community (SVC). We test the model with a dataset collected in the
Linux Kernel developer community (N=225), using structural equation modeling
techniques. Our results for this case study show that intrinsic motivations
(social or hedonic motives) are positively associated with a sense of virtual
community, but living in an authoritative country and being paid to contribute
can reduce the sense of virtual community. Based on these results, we offer
suggestions for open source projects to foster a sense of virtual community,
with a view to retaining contributors and improving projects’ sustainability.

###### Index Terms:

sense of virtual community, belonging, open source, software developers, human
factors, survey, PLS-SEM

##  I Introduction

The sustainability and long-term survival of Open Source Software (OSS)
projects depend not only on attracting but, more crucially, retaining
motivated developers [1]. The reasons behind a developer’s decision to stay or
leave an OSS project can depend on different intrinsic or extrinsic factors,
including an individual’s feelings of identity and belonging to the community
[2]. Hagerty et al. defined a sense of belonging as “the experience of
personal involvement in a system or environment so that persons feel
themselves to be an integral part of that system or environment” [3]. The need
to belong is a powerful, fundamental, and pervasive force that has multiple
strong effects on emotional patterns and cognitive processes across all
cultures and different types of people [4]. Maslow [5] positioned ‘belonging’
as a basic human need, and Hagerty et al. [6] posited that a sense of
belonging represents a unique mental health concept. A sense of belonging is
key to productivity, satisfaction, and engagement [4], and can help to avoid
attrition [7]. In Science, Technology, Engineering, and Mathematics (STEM), a
sense of belonging is strongly related to retention [8], especially for
underrepresented groups [9].

The sense of belonging that members have towards others within a certain group
is known as a sense of community [10]. The dimensions of a sense of community
include feelings of membership and attachment to a group [11], a feeling that
members matter to one another and to the group [12]. The concept of sense of
virtual community (SVC) was developed by observing that virtual communities
represent a new form of community, in which social relationships are
predominantly forged in cyberspace [13].

Understanding SVC in OSS is relevant as it can influence the vitality and
sustainability of a community [14, 15], and is linked to more satisfied,
involved, and committed contributors [16]. Individuals who develop a
psychological and relational contract with a community are supported by a
state of being involved, rather than external factors such as earning
something or climbing a career ladder and therefore tend to develop a deeper,
reciprocal relationship with that community [10].

Since sustainability is a key concern for OSS projects, we must understand SVC
in OSS communities. While several studies have investigated different
motivations to contribute to OSS [17, 18, 19, 20, 21, 1, 22], none have
modeled how these factors can help or hinder in creating a sense of virtual
community. Without a deeper understanding of how the different factors
interplay to create a sense of community, strategies that aim to promote
individual factors will likely be unsuccessful in creating a sustainable
community. Understanding how different factors work together or against each
other can help communities strategize how to retain their contributors.
Therefore, in this paper, we ask the following research question:

Research Question: How does a sense of virtual community develop in Open
Source Software projects?

We answer our research question by first developing a theoretical model of SVC
grounded in prior literature (Sec. III). We then evaluate our model through a
sample (N=225) of Linux Kernel project contributors, using partial least
squares structural equation modeling (PLS-SEM) (Sec. IV). The results of our
analysis provide empirical support for part of our model, showing that
hedonism (motivation that aims to maximize pleasure and fun and minimize pain
[23]) and social motives (motivation that aims to maximize joint gains and
others’ gains [24]) have a positive association with a sense of virtual
community, which can be weakened when contributors are being paid or are
surrounded by an authoritative culture, i.e., national culture with a high
index of power distance (Sec. V). We conclude the paper by discussing the
implications of our findings, and threats to validity (Sec. VI).

##  II Background

###  II-A Sense of Virtual Community

While numerous definitions of the term ‘community’ exist, a common theme is
that it involves human relationships based on some common characteristics
[25]. The classical McMillan and Chavis [12] definition of ‘Sense of
Community’ includes four characteristics: (1) feelings of membership
(belonging to, and identifying with, the community), (2) feelings of influence
(having an influence on, and being influenced by the community), (3)
integration and fulfillment of needs (being supported by others in the
community while also supporting them), and (4) shared emotional connection
(relationships, shared history, and a ‘spirit’ of the community). Virtual
communities typify a relatively new form of interaction whereby community
members share information and knowledge in the virtual space for mutual
learning, collaboration, or problem solving [13].

The development of OSS involves distributed problem solving within a virtual
community [26]. Virtual communities are a particularly important type of
virtual group because they are self-sustaining social systems in which members
engage and connect with each other, developing a Sense of Virtual Community
(SVC) [27]. The sense of community includes membership, identity, belonging,
and attachment to a group that primarily interacts through electronic
communication [11, 28, 29]. SVC has been tailored to virtual communities by
deriving from McMillan’s theory of sense of community [12]. The goal of
measuring SVC is to assess the “community-ness” of a virtual community [11].

Community managers can assess and promote SVC to fulfill a core set of
members’ needs [30], so they feel they belong to a unique group. Such
meaningful relationships are associated with increased satisfaction and
communication with the virtual community, trust [31], and social capital in
the project [32]. SVC has been shown to lead to an occupational commitment
[33], and ultimately can help retain contributors and further attract
potential newcomers [11, 34], who are critical to the sustainability of OSS
projects [35].

###  II-B Motivations to Contribute to Open Source Software

The software engineering literature suggests that, by managing developers’
motivation and satisfaction, a software organization can achieve higher
productivity levels and avoid turnover, budget overflows, and delivery delays
[36]. Motivations for joining Open Source has been the topic of considerable
research [17, 18, 19, 20, 21, 1, 22]; motivations can be extrinsic or
intrinsic. Extrinsic motivations are based on outside incentives that make
people change their actions due to an external intervention [37]. As many
companies, including Microsoft, Google, and IBM, hire or sponsor OSS
contributors [38], career ambition and payment have become common extrinsic
motivations [39]. However, intrinsic motivations also explain much of
contributors’ motivations [22], moving a person to act for fun or enjoy a
challenge, kinship, altruistic reasons, or ideology, rather than in response
to external pressures or rewards [40].

Previous research showed that several forces influence the decision of an OSS
contributor to join, remain, or leave an OSS project [41, 42, 43]. Despite the
extensive attention this topic has received, there are still no studies
investigating how OSS contributors driven by different motivations develop a
sense of virtual community. We argue that understanding how a sense of virtual
community develops in OSS involves understanding the relationship between
individual characteristics and motivations and the resulting community-related
feelings.

##  III Theory Development

Feelings of belonging in an online community can be influenced by several
individual characteristics and factors of the surrounding environment [44]. In
the education literature, researchers [45, 46] found associations between
students’ sense of belonging and a range of motivational variables.
Motivational factors can be regarded as expectations related to the
interaction with a virtual community (answering why users behave). Integration
and fulfillment of needs refer to the idea that common needs, goals, and
beliefs provide an integrative force for a cohesive community that can meet
collective and individual needs. Thus, meeting members’ needs is a primary
function of a strong community [12].

Individuals who develop a psychological relationship contract with a community
because it is focused on a state of being involved—rather than earning
something or getting somewhere—tend to develop a sense of community [10].
Previous research on online communities also showed that individuals who are
driven by social motives [47] tend to develop a sense of virtual community
[48, 28]. Based on the Fundamental Social Motives Inventory, we included both
kinship and altruism as social motives [47] and propose the following
hypothesis:

Hypothesis 1 (H1). Open Source contributors motivated by social reasons have a
higher sense of virtual community.

Most of the respondents in Gerosa et al.’s study (91%) agreed (or strongly
agreed) that they contribute to OSS for entertainment (fun) [22]. Hedonic
motivation is a type of motivation that aims to maximize pleasure and fun and
minimize pain. It is an umbrella term that includes hedonic expectancy,
perceived enjoyment, and playfulness [23]. Considering that expectations of
enjoyable experiences, feelings of amusement, and being mentally or
intellectually stimulated by interactions are associated with a sense of
virtual community [13, 15], and that changes in the perceived fulfillment of
their entertainment needs can determine the change of their sense of virtual
community [30], we propose the following hypothesis:

Hypothesis 2 (H2). Open Source contributors motivated by hedonic reasons have
a higher sense of virtual community.

It is known that some open source contributors have a strong ideological basis
for their actions [49], believing, for example, that source code should be
freely available. Recently, Gerosa et al.’s study showed that, however,
ideology is not a popular motivation—especially for young contributors [22].

Historically, the group-based morality of ‘fighting’ a shared dominant
opponent incites the sense of virtual community among contributors [50]. This
feeling was quite common in the 1990s, when big corporations characterized
Open Source as ‘communism’ [51] and Linux as a ‘cancer’ [52]. Besides
ideology, we include reciprocity in moral motives, as it represents the moral
desire of contributors who aim for social justice by giving back to the
community [53].

According to the Social Identity theory [54], sharing a moral vision is
positively associated with feelings of belonging. Moreover, a homogeneous
ideology throughout a religion was shown as being positively associated with a
sense of virtual community [55]. Hence, we posit that:

Hypothesis 3 (H3). Open Source contributors motivated by moral reasons have a
higher sense of virtual community.

Motivations may not always be strong enough to sustain an OSS contributor’s
participation [56]. Motivations may vary for different groups of people,
depending on contextual factors. This implies the existence of moderating
factors that change the relationship between motivations and a sense of
virtual community. Cognitive Evaluation Theory suggests that feelings of
autonomy are positively associated with intrinsic motivations and belonging,
while tangible rewards negatively affect intrinsic motivating factors [57].

We evaluated the role of a feeling of autonomy using the variable of power
distance from Hofstede’s framework of Country Culture [58] as a proxy; a lower
power distance would reflect in higher autonomy. We also evaluated the
exposition to tangible rewards using the variable is paid.

People in societies exhibiting a large degree of power distance tend to accept
a hierarchical order [59]. In high power distance cultures (where a high power
differential between individuals is accepted and considered normal),
information flows are usually constrained by hierarchy [58]. As an important
cultural value describing the acquiescent acceptance of authority, power
distance has received increasing attention in many domains [60, 61].

Prior research showed that, when surrounded by cultures with a high degree of
power distance, students reported a lower sense of belonging to their school
[62]. Therefore, in hierarchical cultures, leaders need control over the
information flow, and the desire to restrict autonomy and access to critical
information by lower-level team members could lead to significant
organizational barriers to sharing knowledge and working in a community [63].
Thus, we define the following moderation hypotheses:

Hypothesis 4a (H4a). Power distance moderates the association between Open
Source contributors’ social motives and their sense of virtual community.

Hypothesis 4b (H4b). Power distance moderates the association between Open
Source contributors’ hedonic motives and their sense of virtual community.

Hypothesis 4c (H4c). Power distance moderates the association between Open
Source contributors’ moral motives and their sense of virtual community.

The traditional notion that OSS developers are all volunteers is now long
outdated; many OSS contributors are currently paid, usually employed by a
company, to contribute [39, 64, 65]. Indeed, many Linux Kernel contributors
are paid to make their contributions, compensated by firms that have business
models relying on the Linux Kernel [66, 67, 68].

In contrast to traditional paid software development work, and despite its
benefits to OSS contributors, introducing financial incentives in OSS
communities create complex feelings among OSS developers [69]. For example,
developers on the Debian project expressed negative emotion because they felt
payment went against the project’s espoused values [70]. On the other side,
not receiving pay for their work to support their livelihoods can frustrate
OSS developers and affect their contributions [69].

Despite compensation, OSS contributors may be driven towards a project by both
simultaneous feelings of belonging (intrinsic) and payment (extrinsic) [1,
39]. Nevertheless, there is no research examining the complex impact of
receiving payment on intrinsic factors associated with SVC. As many OSS
developers are currently paid, we would expect that the behavior of those who
are paid and those who are not (volunteers) would diverge. Hence, we propose
the following three moderating hypotheses:

Hypothesis 5a (H5a). Being paid moderates the association between Open Source
contributors’ social motives and their sense of virtual community.

Hypothesis 5b (H5b). Being paid moderates the association between Open Source
contributors’ hedonic motives and their sense of virtual community.

Hypothesis 5c (H5c). Being paid moderates the association between Open Source
contributors’ moral motives and their sense of virtual community.

##  IV Research Design

Figure 1: Research Design and Phases for Results’ Analysis

The research design is summarized in Fig. 1. We conducted a survey among Linux
Kernel contributors to evaluate our theoretical model. We studied one specific
community to avoid confounding factors related to differences that each OSS
community can pose. Introduced in 1991, the Linux Kernel represents one of the
largest and most active OSS projects [71], boasting over ten million source
lines of code and more than 20,000 contributors from different countries and
cultural backgrounds, including volunteers and paid developers from more than
200 companies [72, 73]. Linux Kernel’s is impact is perceived in terms of
processes and infrastructure tools that emerged from the community [73]. While
the Linux Kernel Mailing List is known for its uncivil comments and toxic
discussions that tend to discourage people from joining the community [74],
community leaders aim to change the project’s image and increase the sense of
community among members. We closely collaborated with contributors and
maintainers of the Linux Foundation involved with Linux Kernel, who had a
crucial role in designing the data collection instrument and reaching out to
potential participants. They engaged in several meetings with the team and
reviewed the items of the questionnaires to provide their feedback, making
sure that the instrument was appropriate for the study goals. They also
distributed the survey to the Linux kernel community, playing an essential
role in recruiting the participants for this study.

We used Partial Least Squares–Structural Equation Modeling (PLS-SEM) to
analyze the relationships between motivations [75] and a sense of virtual
community. SEM is a second-generation multivariate data analysis method; a
recent survey (which also provides an introduction to the method) indicates
that PLS-SEM has been used to study a variety of phenomena in software
engineering [76]. SEM facilitates the simultaneous analysis of relationships
among constructs, each measured by one or more indicator variables. The main
advantage of SEM is being able to measure complex model relationships while
accounting for measurement error when using latent variables (e.g., Sense of
Virtual Community). PLS-SEM has previously been used in literature to evaluate
factors that impact the sense of belonging in other contexts [77, 78].

In the following, we discuss the measurement model (i.e., operationalization
of constructs), data collection, and analysis.

###  IV-A Measurement model

The theoretical model comprising the hypotheses is based on a number of
theoretical concepts; some of the concepts may be directly observed (e.g., ‘is
paid’), but others cannot (e.g., sense of virtual community)—these concepts
are represented as latent variables. A latent variable cannot be directly
measured or observed but instead is measured through a set of indicators or
manifest variables. For the latent variables in this study, we adapted
existing measurement instruments.

Sense of Virtual Community: We adapted items about feelings of a virtual
community from Blanchard’s [11] instrument of sense of virtual community to
better fit with the context of OSS contributions. In collaboration with a
group of Linux Kernel community managers, we analyzed the items proposed by
Blanchard et al. [33] and decided to use a subset of questions to compose a
shorter version of the instrument to cover the dimensions of SVC. The subset
was discussed synchronously by researchers and managers, and the items were
considered appropriate and meaningful to represent SVC to the Linux Kernel
contributors.

Intrinsic Motivations: We created items based on Gerosa et al. [22]’s
instrument, which was built upon previous studies of motivations in OSS [20,
19, 18]. Following the community managers’ request to make the questionnaire
as short as possible, we grouped the intrinsic motivation factors from Gerosa
et al.’s study [17] into three factors: 1. Social Motives (Kinship and
Altruism) [47]; 2. Hedonic Motives (Joy and Fun) [23]; and 3. Moral motives
(Ideology and Reciprocity) [53].

English Confidence: We reused four questions about the self-confidence of
fluency levels during interactions by speaking and writing in technical and
non-technical situations from a previous survey [79].

Power Distance: We asked in which country the respondent lived and used the
value per country proposed by Hofstede’s framework [58] as the Power Distance
dimension in the model.

For the demographic questions, we adapted questions from surveys used in OSS
communities to ask about tenure, self-identified gender, and compensation [80,
81]. Tenure was shown in 10-year slices in Table I for presentation purposes,
but was included as a continuous variable in our analysis. We provided a
dropdown list of years since 1991 (the year when the Linux Kernel was
launched) for respondents to inform the year they started contributing to the
project.

###  IV-B Data Collection and Analysis

We administered the online questionnaire using LimeSurvey, a leading Open
Source survey software, to survey Linux Kernel contributors. We explored their
motivations and their sense of virtual community. Our online appendix provides
the instrument and replication package [82].

####  IV-B1 Designing the instrument

The questions were discussed during 12 online meetings between October 2020
and February 2021 in a group of five researchers experienced in OSS and survey
studies and two members of the Linux community. The group discussed each of
the questions until reaching a consensus. The questionnaire provides informed
consent followed by closed questions about the importance of each motivation
factor as a reason to contribute to the Linux Kernel and questions about their
feelings about the Linux Kernel community. Finally, we added demographic
questions aiming to segment analysis and understand the phenomenon considering
the different dimensions of our participants, and an open question for
additional comments. Investigating the forces that push people with different
individual characteristics can help us better support a diverse community
[22]. The questions included gender identity, financial compensation, starting
the year at Linux Kernel, and country of residence.

####  IV-B2 Piloting the questionnaire

After designing the instrument, we piloted the questionnaire before
distributing it to the population of interest. In the first round, our
collaborators from the Linux Foundation recruited a group of Linux Kernel
maintainers, who answered the questionnaire and provided feedback. Although
the feedback was overall positive, maintainers suggested reverse-coding some
items for the SVC construct, i.e., items worded as negative statements (low
score indicates agreement). Inverse, negative, or reverse-coded items can be
defined as those having a directionality as opposed to the logic of the
construct being measured [83]. We agreed with the suggestion and inverted two
of the four items as this can help to mitigate acquiescence bias [84], which
can occur when participants tend to agree with statements without regard for
their actual content or due to laziness, indifference, or automatic
accommodation to a response pattern [85]. The item I feel at home in the group
was changed to I don’t feel at home in the group. We inverted and adapted the
question I feel that my contribution is valued to I want to contribute more
but I do not feel valued.

After the first pilot, we ran two more pilot sessions with two researchers who
are Open Source contributors. We used the think-aloud method [86] and recorded
their suggestions while answering the questions. We made minor changes to the
questionnaire and increased font size for better readability on different
devices.

####  IV-B3 Recruiting participants

The Linux Foundation contributors who collaborated in this study took the lead
in recruiting the participants from the Linux Kernel. They reached out to
maintainers and contributors using mailing lists from the Linux Kernel
community and interacted with maintainers to ask for engagement. Further, we
presented the study motivation during the first day of the Linux Plumbers
annual conference (https://lpc.events/event/11/), inviting participants to
answer the questionnaire. The survey was available between August 12 and
September 21, 2021.

####  IV-B4 Sample Analysis

We received 318 responses and carefully filtered the data to consider only
valid responses. Respondents who did not complete the whole questionnaire were
dropped (n=26). We also dropped the participants who answered “I’m not sure”
to any of the items included with the five-point Likert scale for Motivations
(n=16) and Sense of Virtual Community (n=51). In addition to the 5-point
Likert scale, we included a 6th alternative (“I’m not sure”) for participants
who either preferred not to, or did not know how to, answer the question (to
avoid forcing them), which is different from being neutral—based on the
dissonance between ignorance and indifference [87, 88]. Therefore, we
considered these responses as missing data. The efficacy of imputation methods
has not yet been validated when using FIMIX-PLS; Sarstedt et al. [89]
recommend removing all responses with missing values for any question before
segmenting data into clusters.

After applying these filters, we retained 225 valid responses from residents
of five different continents with a broad tenure distribution. The majority
identified as men (84.4%), from Europe (52.9%), and paid to contribute
(65.4%), matching previously reported distributions of OSS contributors [81].
Table I presents a summary of the demographics.

TABLE I: Demographics of the Linux Kernel respondents (n=225) Attribute | N | Percentage
---|---|---
Gender
Man | $190$ |  $84.4$$\mathrm{\char 37\relax}$
Woman | $21$ |  $9.4$%
Non-binary | $5$ |  $2.2$%
Prefer not to say | $8$ |  $3.6$%
Prefer to self describe | $1$ |  $0.4$%
Continent of Residence
Europe | $119$ |  $52.9$%
North America | $68$ |  $30.2$%
Asia | $32$ |  $14.2$%
South America | $6$ |  $2.7$%
Starting year at the Linux Kernel
2000 or earlier | $28$ |  $12.4$%
Between 2001 and 2010 | $77$ |  $34.2$%
Between 2011 and 2021 | $120$ |  $53.4$%
Current Compensation for the Linux Kernel contributions
Paid | $145$ |  $64.4$%
Unpaid (volunteer) | $80$ |  $35.6$%

To establish an appropriate sample size, we conducted a power analysis using
the free G*Power tool [90] (see online appendix for details). The maximum
number of predictors in our model is six (three motivations and three control
variables to SVC). This calculation indicated a minimum sample size of 62 and
our sample of 225 exceeded that number considerably.

We used the software package SmartPLS version 4 for the analyses. The analysis
procedures for PLS-SEM comprise two main steps, with tests and procedures in
each step. The first step is to evaluate the measurement model, which
empirically assesses the relationships between the constructs and indicators
(see Sec. V-A). The second step is to evaluate the theoretical (or structural)
model that represents the hypotheses (see Sec. V-B).

##  V Analysis and Results

In this section, we describe our results, which include the evaluation of the
measurement model (Sec. V-A), followed by the hypotheses evaluation in the
structural model (Sec. V-B), both computed through our survey data. We assess
the significance of our model by following the evaluation protocol proposed by
previous research [91, 76] to make results consistent with our claims. The
path weighting scheme was estimated using SmartPLS 4 [92].

Two tests are recommended to ensure that a dataset is suitable for factor
analysis [93, 94]. We first conducted Bartlett’s test of sphericity [93] on
all constructs. We found a p-value < .01 (p values less than .05 indicate that
factor analysis may be useful). Second, we calculated the Kaiser-Meyer-Olkin
(KMO) measure of sampling adequacy. Our result (.81) is well above the
recommended threshold of .60 [94].

###  V-A Evaluation of the Measurement Model

Some of the constructs in the theoretical model (see Fig. 2) are modeled as
latent variables, i.e., measured by more than one observed variable (i.e.,
item/question on the survey). The first step in evaluating a structural
equation model is to assess the soundness of the measurement of these latent
variables—this is referred to as evaluating the ‘measurement model’ [91]. We
present the assessment of several criteria.

####  V-A1 Convergent Validity

First, we assess whether the questions (indicators) that represent each latent
variable are understood by the respondents in the same way as they were
intended by the designers of the questions [95], i.e., we assess the
convergent validity of the measurement instrument. The assessment of
convergent validity relates to the degree to which a measure correlates
positively with alternative measures of the same construct. Our model contains
two latent variables, both of which are reflective (not formative), as
functions of the latent construct. Changes in the theoretical, latent
construct are reflected in changes in the indicator variables [91].

We used two metrics to assess convergent validity: the Average Variance
Extracted (AVE) and the loading of an indicator onto its construct (the outer
loading).

The AVE is equivalent to a construct’s communality [91], which is the
proportion of variance that is shared across indicators. A reflective
construct is assumed to reflect (or “cause”) any change in its indicators. The
AVE should be at least .50, indicating that it explains most of the variation
(i.e. 50% or more) in its indicators [91]. This variance is indicated by
taking the squared value of an indicator’s loading. As Table II shows, all AVE
values for both latent constructs in our model are above this threshold of
.50.

TABLE II: Internal Consistency Reliability |  Cronbach’s  |  CR | AVE
---|---|---|---
English Confidence | $.932$ | $.951$ | $.830$
Sense of Virtual Community | $.767$ | $.839$ | $.511$

A latent variable is measured by two or more indicators; indicators with
loading below .4 should be removed because this implies that a change in the
latent construct that it purportedly represents (or ‘reflects’) does not get
reflected in a sufficiently large change in the indicator [91]. Outer loading
of .7 is widely considered sufficient, and .6 is considered sufficient for
exploratory studies [91]. We followed an iterative process to evaluate the
outer loading of the latent constructs; the indicators of the construct
English Confidence all exceeded .7, but SVC had two indicators below .7. We
removed the SVC indicator which had a loading below .4 (svc6: a majority of
the developers and I want the same thing). After removing this indicator, the
AVE value of SVC (now with five indicators) increased from .44 to .51 and all
outer loadings were above .60.

Figure 2: Item loadings and path coefficients (p $<$ 0.05 indicated by a full
line). Non-significant links are indicated with a dashed line

####  V-A2 Internal Consistency Reliability

Second, we verified how well the different indicators are consistent with one
another and can reliably and consistently measure the constructs, i.e., we
assess the internal consistency reliability. A high degree of consistency
means that the indicators refer to the same construct. There are several tests
to measure internal consistency reliability. We performed both the Cronbach’s
and Composite Reliability tests; Cronbach’s frequently shows lower values,
whereas the Composite Reliability (CR) is a more liberal test, which sometimes
overestimates the values [91]. A desirable range of values for both Cronbach’s
and CR is between .7 and .9 [91]. Values below .6 suggest a lack of internal
consistency reliability, whereas values over .95 suggest that indicators are
too similar and thus not desirable. The Cronbach and CR values for both latent
variables fell in the range .75–.95; only the CR for English Confidence was
slightly over at .951. AVE values were both higher than .50.

####  V-A3 Discriminant Validity

Third, we verified whether each construct represents characteristics not
measured by other constructs, i.e., we assessed the discriminant validity of
the instrument (indicating the distinctiveness of the constructs). Our model
includes two latent variables (SVC and English Confidence). A primary means to
assess discriminant validity is to investigate the Heterotrait-monotrait
(HTMT) ratio of correlations, developed by Henseler et al. [96]. The
discriminant validity could be considered problematic if the HTMT ratio
exceeds .9 [96]; some scholars recommend a more conservative cut-off of .85
[91]. The HTMT ratio between the two latent constructs (SVC and English
Confidence) was .24. We also assessed the cross-loadings of indicators and the
Fornell-Larcker criterion. Items should only load onto their ‘native’
construct, the one they purportedly represent (Table III).

TABLE III: Cross loadings of the retained indicators on the constructs |  |  SVC |  Engl. Conf.
---|---|---|---
svc1 |  I don’t feel at home in the group |  .740 |  .191
svc2 |  I feel that I belong to the group |  .822 |  .231
svc3 |  If I have a problem, I know members in the group who I can ask for help |  .662 |  .063
svc4 |  I want to contribute more but I do not feel valued |  .583 |  .113
svc5 |  A majority of the developers in the group know me |  .722 |  .242
eng1 |  Participating in a non-technical discussion on the email list |  .180 |  .881
eng2 |  Performing Reviews |  .216 |  .925
eng3 |  Speaking with others (face to face) |  .226 |  .890
eng4 |  Participating in technical discussions on the email list |  .278 |  .939

For the sake of completeness, we report the Fornell-Larcker procedure in the
online appendix [82].

###  V-B Evaluation of the Theoretical Model

We now evaluate and discuss the theoretical model, which includes the
evaluation of the hypotheses.

####  V-B1 Assessing Collinearity

Our theoretical model has three different exogenous variables of intrinsic
motivations, the moderators ‘Compensation’ and ‘Power Distance,’ and the
control variables ‘English Confidence,’ ‘Gender,’ and ‘Tenure.’ We
hypothesized that the exogenous variables are associated with the endogenous
variable Sense of Virtual Community. To ensure that the three exogenous
constructs are independent, we calculate their collinearity using the Variance
Inflation Factor (VIF). A widely accepted cut-off value for the VIF is 5 [91],
and in our model, all VIF values are below 5.

####  V-B2 Path Coefficients and Significance

PLS does not make strong assumptions about the distribution (such as a Normal
distribution) of the data, so parametric tests of significance should not be
used. To evaluate whether path coefficients are statistically significant, PLS
packages employ a bootstrapping procedure. This involves drawing a large
number (usually five thousand) of random subsamples with replacement. The
replacement is needed to guarantee that all subsamples have the same number of
observations as the original data set. The PLS path model is estimated for
each subsample. From the resulting bootstrap distribution, a standard error
can be determined [91], which can subsequently be used to make statistical
inferences. The mean path coefficient determined by bootstrapping can differ
slightly from the path coefficient calculated directly from the sample; this
variability is captured in the standard error of the sampling distribution of
the mean.

Table IV shows the results for our hypotheses, including the mean of the
bootstrap distribution (B), the standard deviation (SD), the 95% confidence
interval, and the p-values.

The path coefficients in Fig. 2 and Table IV are interpreted as standardized
regression coefficients, indicating the direct effect of a variable on
another. Each hypothesis is represented by an arrow in the diagram in Fig. 2.
For example, the arrow pointing from Hedonic Motives to SVC represents H2.
Given its positive path coefficient (0.421), Hedonic Motives are positively
associated with SVC. The path coefficient is 0.421; this means that when the
score for “Hedonic” motives increases by one standard deviation unit, the
score for “Sense of Virtual Community” increases by 0.421 standard deviation
unit (the standard deviation is the amount of variation of a set of values).

Based on these results, we found support for Hypotheses H1 (p=.002), H2
(p=.000), H4a (p=.045), and H5b (p=.023). Hypothesis H3 was not supported, nor
were H4b, H4c, H5a, or H5b (all p values $>$ .2). The three control variables
all have significant associations with SVC: English confidence, gender, and
tenure (p < .05).

TABLE IV: Standarized path coefficients, standard deviations, confidence intervals, and p values | B | SD |  95% CI | p
---|---|---|---|---
H1 Social motives$\rightarrow$SVC | $.249$ | $.105$ |  (.04, .46) | $.002$
H2 Hedonic motives$\rightarrow$SVC | $.421$ | $.114$ |  (.19, .64) | $.000$
H3 Moral motives$\rightarrow$SVC | $-.140$ | $.112$ |  (-.36, .08) | $.215$
H4a Power distance × social motives $\rightarrow$ SVC | $-.152$ | $.076$ |  ($-.31$,$-.01$) | $.045$
H4b Power distance × hedonic motives $\rightarrow$SVC | $-.052$ | $.074$ |  ($-.18$, .11) | $.477$
H4c Power distance × moral motives$\rightarrow$SVC | $.042$ | $.069$ |  ($-.10$, .17) | $.539$
H5a is Paid × social motives$\rightarrow$SVC | $-.051$ | $.065$ |  ($-.32$, .20) | $.696$
H5b is Paid × hedonic motives$\rightarrow$SVC | $-.328$ | $.144$ |  ($-.62$, .05) | $.023$
H5c is Paid × moral motives$\rightarrow$SVC | $.115$ | $.137$ |  ($-.17$, .36) | $.404$
Gender minorities$\rightarrow$SVC | $-.493$ | $.170$ |  ($-.81$,$-.14$) | $.004$
English confidence$\rightarrow$SVC | $.134$ | $.006$ |  (.01,.25) | $.025$

####  V-B3 Coefficient of Determination

We assessed the relationship between constructs and the predictive
capabilities of the model. The R2 values of the endogenous variable in our
model (SVC) was 0.4, which is considered weak-moderate [91, 97].

We also inspected Stone-Geisser’s Q2 [98] value, which is a measure of
external validity, as an indicator of the model’s predictive relevance [91],
and can be obtained through a so-called blindfolding procedure (available
within the SmartPLS software). Blindfolding is a resampling technique that
omits certain data, predicts the omitted data points, then uses the prediction
error to cross-validate the model estimates [99]. Q2 values are calculated
only for the SVC, the reflective endogenous construct of our model, with a
value of .17. Values larger than 0 indicate the construct has predictive
relevance, while negative values show the model does not perform better than
the simple average of the endogenous variable would do.

The Standardized Root Mean Square Residual (SRMR) is a common fit measure that
is appropriate to detect misspecification of PLS-SEM models [76]. SRMR is the
square root of the sum of the squared differences between the model-implied
and the empirical correlation matrix, or the Euclidean distance between the
two matrices [100]. A value of 0 for SRMR would indicate a perfect fit, and a
cut-off value of 0.08 is considered adequate [101]. Our results suggest a good
fit of the empirical data in the theoretical model (SRMR = 0.06).

####  V-B4 Moderating Factors

We examined our data to determine if the impact of each intrinsic motivation
on a sense of virtual community would change when they are exposed to a high
Power Distance culture or when they are financially compensated to contribute.

Only significant results at 0.05 are reported, with confidence intervals
calculated through bootstrapping.

  * •

Power Distance Country Culture: Being surrounded by a high power distance
culture, in which leaders impose a high level of control and restrict the
information flow [58], has been reported to negatively affect the sense of
virtual community [63]. We did not find significant correlations between Power
Distance and SVC for hedonic or moral motivations. Still, we found it for
social motivations, which has a moderating effect on our model. Hence, we
found support for H4a but do not support H4b and H4c.

  * •

Compensation: Being paid to contribute reduces the sense of virtual community
of contributors driven by hedonic motivations but not by social motivations
and neither by moral motivations. Hence, we found support for H5b but rejected
H5a and H5c.

Fig. 3 presents an interaction diagram showing the simple slopes for the
relationship between the exogenous variable Social Motives and the endogenous
variable SVC. All three slopes are positive, indicating a positive
relationship; the top line (in green) is at +1 standard deviation of the
moderator, Power distance; the bottom slope (in red) is at $-1$ standard
deviation of the moderator. The middle slope (in blue) represents the
relationship at the mean level of Power distance. The figure shows that given
a higher level of Power distance, the relationship between social motives and
SVC is dampened (flatter), whereas with lower levels of Power distance, the
relationship is strengthened (steeper).

Figure 3: Power distance as a moderator of Social motives $\rightarrow{}$ SVC

####  V-B5 Control Variables

We also examined our data to determine if being part of gender minorities,
tenure, or English Confidence could strengthen or weaken the sense of virtual
community. We found that participants who identify as gender minorities tend
to have a lower sense of virtual community, while participants with higher
tenure and English Confidence reported a higher sense of virtual community.

###  V-C Cluster Analysis: Detecting Unobserved Heterogeneity

While moderators and context factors capture observed heterogeneity (see Sec.
V-B4), there may also be unobserved heterogeneity, or latent classes of
respondents, the presence of which could threaten the validity of results and
conclusions [89]. Latent classes of respondents refer to some groupings of
respondents on one or more criteria that were not measured. The hypothesis
results may differ for different groups.

We adopted Becker et al.’s approach [102], which jointly applies PLS-POS and
FIMIX algorithms to identify latent classes. In Step 1, we used the minimum
sample size for the maximum number of segments and ran FIMIX to find the
optimal number of segments. In Step 2, we ran PLS-POS to compute the
segmentation. In Step 3, we ran a multi-group analysis (PLS-MGA) and evaluated
whether the segments were distinguishable. In Step 4, we checked if the
resulting groups were plausible. We discuss the steps in more detail.

In Step 1, we assessed the maximum number of segments according to the minimum
sample size (see Sec. IV-B4). Dividing the sample size (225) by the minimum
sample size (62) yields a theoretical upper bound of three segments; each
segment should satisfy the minimum sample size. We ran FIMIX for one (meaning,
treating the original sample as a single segment), two, and three segments
[89]. The results were compared using several different retention criteria
(see Table V) [89]. For each criterion, the optimal solution is the number of
segments with the lowest value (in italics in Table V), except in terms of
criterion ‘EN,’ where higher values indicate a better separation of segments.
Sarstedt et al. [103] argue that researchers should start the fit analysis by
jointly considering the combination of modified Akaike’s Information Criterion
with factor 3 (AIC3) and Consistent AIC (CAIC) (Group 1 in Table V): when both
criteria suggest the same number of segments, this result is likely to be most
appropriate. As this is not the case here (AIC3 suggests 3 segments, CAIC
suggests 1 segment), a second evaluation considers whether modified Akaike’s
Information Criterion with factor 4 (AIC4) and Bayesian Information Criterion
(BIC) suggest the same number of segments (Group 2 in Table V). Again, this is
not the case as AIC4 suggests 3 segments, and BIC suggests 1 segment). The
third evaluation (Group 3) considers the joint analysis of Akaike’s
Information Criterion (AIC) and Minimum Description Length with factor 5
(MDL5); first, consider the number of segments indicated by the lowest values
of AIC (3 segments) and MDL5 (1 segment). The appropriate number of segments
should be lower than suggested by AIC (because it tends to overestimate) and
higher than the number of segments suggested by MDL5 (because it tends to
underestimate). Hence, this combination suggests that a 2-segment solution is
appropriate because 2 is lower than the 3 suggested by AIC and higher than the
1 suggested by MLD5. The value of EN is highest for the 2-segment solution.

TABLE V: Establishing adequate number of segments Group |  Criterion | 1-Segment | 2-Segment | 3-Segment
---|---|---|---|---
1 |  AIC3 | $574.153$ | $540.241$ | $517.508$
CAIC | $625.395$ | $646.141$ | $678.065$
2 |  AIC4 | $589.153$ | $571.241$ | $564.508$
BIC | $610.395$ | $615.141$ | $631.065$
|  AIC | $559.153$ | $509.241$ | $470.508$
3 |  MDL5 | $935.361$ | $1286.737$ | $1649.292$
4 |  EN | $0$ | $0.869$ | $0.821$

In Step 2, we evaluated the segment sizes of the 2-segment solution and
proportions of data to check whether groups were substantial or candidates for
exclusion. A segment is not substantial if its size is considerably lower in
proportion (e.g., a 2% segment size) or below the minimum sample size [102].
The 2-segment solution divided the dataset into groups with 158 (70.2%) and 67
(29.8%) observations; both considerable portions and larger than the minimum
sample size [102].

In Step 3, we ran a multi-group analysis (PLS-MGA) with parametric tests to
verify whether the segments were distinguishable [102], i.e., whether the
results were different for the two segments. We found significant differences
in hypotheses H4b-c, H5a-c, and on the control variables Tenure and English
Confidence (see Table VI), thus, we conclude these two segments represent two
different groups of respondents. Both groups presented R2, goodness-of-fit
(GoF), and SRMR [89] equal or more favorable than the original model. The
values of the path coefficients and the explained variance of the endogenous
variable SVC are shown in Table VI, which presents the results for the two
segments, as well as the original estimates (see column B in Table IV).

TABLE VI: Group Paths Coefficients: coeficients in bold are significant; lines in gray show significant difference between segments | 2-segment solution | Orig.
---|---|---
| Seg. 1 | Seg. 2 | All
| Hedonic | Social |
Sample size (N) | 158 | 67 | 225
Coefficient of determination (R2) | $.57$ | $.94$ | $.40$
H1 Social motives $\rightarrow$ SVC | $-.04$ | $.22$ | $.25$
H2 Hedonic motives$\rightarrow$SVC | $.31$ | $.06$ | $.42$
H3 Moral motives$\rightarrow$SVC | $-.03$ | $-.23$ | $-.14$
H4a Power distance × social mot.$\rightarrow$ SVC | $-.10$ | $-.24$ | $-.15$
H4b Power distance × hedonic mot.$\rightarrow$SVC | $-.07$ | $.14$ | $-.05$
H4c Power distance × moral motives$\rightarrow$SVC | $-.02$ | $.22$ | $.04$
H5a is Paid × social motives$\rightarrow$SVC | $.49$ | $-.61$ | $-.05$
H5b is Paid × hedonic motives$\rightarrow$SVC | $-.50$ | $.50$ | $-.33$
H5c is Paid × moral motives$\rightarrow$SVC | $-.15$ | $.32$ | $.12$
Gender minorities$\rightarrow$SVC | $-.70$ | $-.92$ | $-.49$
English confidence$\rightarrow$SVC | $-.15$ | $.88$ | $.13$
Tenure$\rightarrow$SVC | $.43$ | $-.05$ | $.28$

In Step 4, we examined that groups were “plausible” [102] by explaining the
different segments (highlighted in gray in Table VI) to label the segments.
This labeling is somewhat speculative and not definitive, not dissimilar to
the labeling of emergent factors in exploratory factor analysis. Given that
for Segment 1 only Hedonic motives are significant, we posit that this segment
represents Hedonists (B=.31); for Segment 2, we find that Social motives are
significant (B=.22), thus we label Segment 2 as Socially Motivated. We note
that moral motives were not significant in the original analysis (see column
‘Orig.’), but this did become significant with a negative coefficient
(B=$-0.23$) for Segment 2. For hedonists (Seg. 1), tenure (B=.43) is
positively associated with SVC. When social motives are associated with SVC
(Seg. 2), English Confidence positively affects SVC (B=.88). Both hedonists
(B=$-0.50$) and socially motivated (B=$-0.61$) contributors have the
association with SVC weakened when they are paid. Both groups showed that
being part of a gender minority is associated with less SVC.

##  VI Discussion

In this study, we developed a theoretical model grounded in psychology
literature to map the relationship between a Sense of Virtual Community and
intrinsic motivations in OSS. The theoretical model includes a number of
salient factors that have been shown to be important in belonging to an online
community in general but not yet within the OSS domain. Over the past two
decades, the nature of OSS communities (as a specific type of online
community) has changed; traditionally, OSS was male-dominated and primarily
volunteer-based, but being paid to contribute is now common, and increasingly
we observe the participation of what we refer to as “minorities” in the
broadest sense of the word, including women [104]. Our analysis highlights a
number of key findings and implications; as we discuss these quantitative
results, we bring exemplar quotes from the respondents’ responses to the final
open question of the survey to illustrate the discussion.

H1. Social motives $\rightarrow$ SVC: Social motives have a positive
association with SVC. The intrinsic social motivations of kinship and altruism
are positively associated with a sense of virtual community in OSS. This
finding was corroborated by one of our respondents in the final open question,
who associated SVC with social motivations: “I did not fit in, in a big way. I
was never able to create enough social capital to make networking effective,
no matter who I tried to connect with.” Another respondent mentioned “not
being able to relate to colleagues and named their perceived lack of SVC as “a
sense of otherness that never goes away.” However, the cluster analysis (Sec.
V-C) indicated Segment 1 (which we labeled ‘hedonic’) to be non-significant,
but Segment 2 (labeled ‘social’) is significant. We also found that for the
‘socially motivated’ English confidence is much more strongly related (B=.88
instead of .13) to SVC. This is intuitive because socially motivated people
seek interaction, and English is the primary language within the Linux Kernel
community.

H2. Hedonic Motives $\rightarrow$ SVC: Hedonic motives have a positive
association with a Sense of Virtual Community. OSS communities should seek to
prevent toxic and other types of undesirable behavior that might reduce
contributors’ enjoyment; communities could also consider setting more clear
community codes of conduct[105, 106, 74]. The cluster analysis showed that
when only hedonism (not social motives) is associated with SVC (Seg. 1),
Tenure is also associated with SVC. Hedonic-motivated contributors from our
sample are also the ones who have longer tenure associated with SVC. Those
contributors may have surpassed the initial barriers [107] and find enjoyment,
or as mentioned by another respondent: “It is therapeutic. When I feel bad
about myself, [..] it calms me down emotionally to do Kernel development when
I feel like that.”

H3. Moral Motives $\rightarrow$ SVC: The cluster analysis does not support H3.
While social motives are positively associated with SVC (Seg. 2), moral
motives are negatively associated with and reduce SVC. The first association
is expected and not surprising [47]. People motivated by kinship or because
they are happy to help others are keener to be part of the team and feel good
in a community [48, 28]. Interestingly, the SVC presented a negative
association with moral motivation. We argue that people motivated by
ideological reasons may contribute regardless of how they feel about belonging
there. They do it because they feel it is the right thing to do, either
because it is the most ethical choice, as advocated by the Free Software
Foundation (https://www.fsf.org/), or because they have a moral debt to the
software project that they use, so they pay back [53]. Future research can
investigate how strong the ties between these people and the community are and
what roles they play in building SVC for the rest of the community.

H4a/b. Power Distance moderates the relationship between (a) Social and (b)
Hedonic motives to SVC: Being surrounded by a culture with a high level of
power distance weakens SVC for socially motivated contributors (when we
consider all contributors). Still, if we consider Segment 1 (Hedonic) in the
cluster analysis, we observe that power distance also weakens the SVC
associated with hedonism. These results align with Cognitive Evaluation Theory
[57]; contributors driven by hedonic (Seg. 1) or social motives (Seg. 2) need
more autonomy (through less hierarchy—less Power Distance) to develop a Sense
of Virtual Community. When not exerted in toxic and harsh ways to discipline
community members, concerted control of communications can also ultimately
play a pro-social role in increasing the SVC by increasing cohesiveness,
commitment, and conformity [108].

H5a/b. Payment moderates the relationship between (a) Social and (b) Hedonic
motives to SVC: Being paid to contribute weakens the association with SVC for
hedonist contributors. The cluster analysis shows that being paid to
contribute also weakens the SVC associated with social motives. Paid
contributors, even those driven by hedonic or social motivations, showed a
lower Sense of Virtual Community to the Linux Kernel. This result aligns with
Cognitive Evaluation Theory [57] and might be explained by the conflicting
identities and divided loyalties that paid contributors have to both their
sponsoring firms and the Linux Kernel community [39]. We hypothesize that
these contributors would leave the community if there were no payment to
compensate for their participation.

Implications for OSS communities to retain contributors

SVC is associated with practices on exchanging support [33, 15], creating
identities and making identifications [33], producing mutual cognitive and
affective trust amongst members of a community [33], and establishing norms
and a “concertive (but not enforced) control” [108], in which members of the
community become responsible for directing their work and monitoring
themselves. OSS communities can provide not only online interest groups for
members, chat rooms, instant messaging, and discussion forums to encourage
community involvement [109] but also online tools with shared spaces for
contributors to work “together” on issues to be able to discuss and
collaborate on similar interests. Better interactions can strengthen
contributors’ Sense of Virtual Community, especially those seeking social
relationships. When the information being exchanged surpasses the technical
content and includes socio-emotional support, it shows personal relationships
among group members, and finally brings feelings of acceptance by members
[33]. OSS communities should foster exchanging support among members to bring
a positive impact on developing SVC [15]. The exchanging support includes
technical and social support and happens through comments in pull requests and
participation in mailing lists (by either reading or posting messages).
Communities can manage pull requests and mailing lists to guarantee that
members’ posts are not being missed [74] and that the communication adheres to
the code of conduct.

Implications for OSS communities to attract newcomers. Exchanging information
and providing support to other community members are practices associated with
positive feelings toward the community, and members’ stronger attachment to
the community [110]. Community members can encourage newcomers to become more
active and move beyond the stage of ‘lurker,’ enticing them to participate in
mailing lists [15] and to start making social connections to establish mutual
trust, be known by other contributors, and facilitate the development of their
Sense of Virtual Community. Conferences and meetups can help hedonic and
socially motivated contributors have fun and increase their social capital.

Implications for Research. This study suggests a positive link between Social
and Hedonic motivations and a Sense of Virtual Community. Further, the cluster
analysis has detected unobserved heterogeneity within our sample, suggesting
that there are different subgroups within the community for which different
motivations play a more prominent role. Future work could explore how the
challenges faced by contributors influence the development of a Sense of
Virtual Community and how a Sense of Virtual Community influences the
decisions to stay or leave a project. While we included three control
variables, future work can consider additional variables, for example,
demographic variables such as age.

Our study focuses on the Linux Kernel community, which is a limitation to the
generalizability of this study; we suggest that our findings provide a useful
starting point to conduct similar studies across other specific communities or
across OSS developers regardless of which community they partake in. When
considering other projects, we also suggest that different project governance
models might also play a role in SVC. This study has also demonstrated that
payment plays a role in SVC and that minorities and marginalized individuals
feel less part of the community.

Finally, our study has focused on the antecedents of a sense of virtual
community in OSS but not on the consequences of it, and this could be a
further area of focus in future work. Future work can investigate whether SVC
is related to contributor satisfaction and whether a reduced SVC leads to
contributors’ attrition, thus jeopardizing a community’s sustainability.

##  VII Limitations and Threats to Validity

Construct Validity. We adopted and tailored existing measurement instruments
for some constructs based on prior literature. Our analysis of the measurement
model confirmed that our constructs were internally consistent and scored
satisfactorily on convergent and discriminant validity tests. In this study we
have used respondents’ country of residence as a proxy for Power Distance as a
dimension of culture as defined by Hofstede [59]. While also used in other
studies [62], we acknowledge it is an approximation and not a perfect measure.
One potential issue is that  we do not know how long respondents have lived in
their current country of residence. Another potential issue is that
contributors’ culture from where they grew up may differ from their current
culture. This is why we report the metric as being surrounded by a specific
culture instead of having a specific culture. Measuring culture in a more
precise way is an important avenue for future work in general.

Internal Validity. Our hypotheses propose associations between different
constructs rather than causal relationships, as the present study is a cross-
sectional sample study [111]. We acknowledge the limitation that our
respondents comprise contributors who are more likely to have a sense of
virtual community as they dedicated their time to answering the questionnaire,
suggesting a response bias. While it is clear that contributors motivated by
some intrinsic-social reasons tend to experience a sense of virtual community
and that power distance and financial compensation can influence those
associations, a theoretical model such as ours cannot capture a complete and
exhaustive list of factors. Other factors can play a role and our results
represent a starting point for future studies.

External Validity. The Linux Kernel is a mature project that has attracted
contributors for its value over the years, and while studied frequently and
sometimes positioned as a ‘quintessential’ open source project, open source
projects can vary in many ways. The specific context of the Linux Kernel
project may therefore have impacted the results, which are therefore not
necessarily generalizable to other OSS projects. Nevertheless, theory-building
is a continuous and iterative process of proposing, testing, and modifying
theory [112], in which a single case study is a first step towards
constructing theories. In that sense, it is more valuable to interpret these
results as a starting point and seek theoretical generalizability rather than
statistical generalizability. Further, given the very important role that the
Linux Kernel project plays in the software industry, this project we argue
this is an appropriate starting point; further replication studies can
validate and extend our theoretical model.

Our survey was conducted online and anonymously, but the numbers are aligned
with the overall distribution of the Linux Kernel contributors. The Linux
Kernel includes contributions of more than 20,000 developers [73], and are
mostly paid to contribute [66, 68]. According to previous research, around 10%
of contributors to Linux Kernel identify themselves as women [80], and the
majority is from the USA, which is aligned with our sample. The responses were
sufficiently consistent to find full or partial empirical support for four
hypotheses.

##  VIII Conclusion

A Sense of Virtual Community (SVC) helps individuals feel valued in their
community, leading to more satisfied, involved, and committed contributors.
While research has identified different motivations and challenges for
contributors to OSS, it is unclear how a sense of community is created and
what factors impact it.

In this paper, we close this gap by developing a theoretical model for sense
of virtual community in OSS through a survey of Linux Kernel contributors. We
found evidence that a subset of intrinsic motivations (social and hedonic
motives) are positively associated with SVC; however, other extrinsic factors
such as the country’s culture and being paid to contribute can lessen SVC
among contributors. Additionally, those with higher English confidence feel a
higher sense of belonging in the community, and contributors who identify as
part of a gender minority (non-men), tend to feel less of a sense of virtual
community.

Our results also show heterogeneity in our respondents, suggesting that there
are different subgroups within the community for whom different motivations
play a more prominent role. This suggests that a “one size fits all” approach
would not work when designing interventions to create an inclusive, welcoming
community. Our SVC model can help researchers and community design
interventions by highlighting the different factors that interplay in creating
a sense of virtual community in OSS for different subgroups of contributors.

## Acknowledgments

We are indebted to Kate Stewart, Vice President of Dependable Embedded Systems
at the Linux Foundation, and Shuah Khan, maintainer and contributor of the
Linux Kernel, for their invaluable support and assistance in the survey design
and distribution. We much appreciate the extensive efforts and time they spent
in meetings and reviews, and their thoughtful input to the survey design, and
reaching out to the Linux Kernel community members. We are deeply grateful to
all respondents of this survey. The National Science Foundation partially
supports this work under Grant Numbers 1900903, 1901031, 2236198, 2235601, and
Science Foundation Ireland grants no. 13/RC/2094-P2 to Lero, the SFI Research
Centre for Software, and no. 15/SIRG/3293.

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