Dawn Foster, Guido Conaldi, Riccardo De Vita University of Greenwich Centre for Business Network Analysis http://www.gre.ac.uk/business/research/centres/cbna/home Presented at the Third European Conference on Social Networks (EUSN) Mainz, Germany on 27 September 2017 This study investigates collaboration in an open source software community using proximity theory as the theoretical lens with social network analysis and modeling of activities over time to predict collaboration. Actors in this study are part of the Linux kernel community where they collaborate on one or more sub-projects using mailing lists as the primary method of collaboration. Collaboration occurs in real-time between actors that contribute to multiple sub-projects, work for firms that pay them to contribute to the Linux kernel, and are working virtually from locations across the globe. This complex setting can be better understood by using several dimensions of proximity: organizational, cognitive, institutional, social, and geographical. Collaboration is analysed using data from source code contributions and mailing list participation. Open source software is developed in the open where anyone can view the source code and anyone with the knowledge to do so can contribute to the project. With no central group responsible for coordination of tasks, collaboration on the development of this software is emergent. Because people from around the world work on these projects together using online tools with publicly accessible interactions between people, it is a relevant setting for using social network analysis to understand and model network relationships.

1. Understanding Collaboration in Fluid
Organizations, a Proximity Approach
Presented at the Third European Conference on Social Networks (EUSN)
Mainz, Germany on 27 September 2017
Dawn Foster, Guido Conaldi, Riccardo De Vita
University of Greenwich
Centre for Business Network Analysis
http://www.gre.ac.uk/business/research/centres/cbna/home

2. Research Overview
How do participants who are employed by firms
collaborate within a fluid organization?
Proximity theory as a theoretical framework:
• to understand intraorganizational collaboration
• within fluid organizations
• using an open source software project, the
Linux kernel, as the empirical setting.
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3. Contributions
• Contribute to literature on fluid organizations by determining the
impact of firm affiliation on intraorganizational collaboration
between individuals in fluid organizations.
• Existing studies on open source mostly individual motivations.
• Firms can influence collaboration of employees.
• Demonstrate that proximity theory can be used to better
understand collaboration within fluid organizations.
• Boschma’s (2005) five dimensions should further our understanding.
• Most proximity studies are inter; fluid boundaries blur distinction.
As fluid organizations become more common,
understanding collaboration within them is increasingly important.
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4. Fluid Organizations
• In fluid organizations, the boundaries and structures allow fluid
movement within the organization as individuals collaborate to
coordinate activities (Ashkenas et al., 2002; Glance & Huberman,
1994).
• Some fluid organizations are based on global virtual work across
many time zones with people from different backgrounds (Nurmi
& Hinds, 2016) and may include individuals from different firms
and different types of institutions (O’Mahony & Bechky, 2008).
• Collaboration, especially within fluid organizations, crosses
dimensions of proximity, including cognitive, organizational,
social, institutional and geographical (Balland, 2012; Boschma,
2005; Cantner & Graf, 2006; Crescenzi, Nathan, & Rodríguez-
Pose, 2016; Knoben & Oerlemans, 2006).
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5. Proximity Theory
• Social proximity: relations between actors with trust coming from
friendship and experience (Boschma 2005).
• Institutional proximity: whether individuals are in a similar
institutional setting, like corporation, non-profit, university, non-
affiliated, etc. (Balland 2012; Crescenzi et al. 2013).
• Organizational proximity: relationship within and between
organizations (Boschma 2005).
• Cognitive proximity: similarity of frames of reference and knowledge
(Knoben & Oerlemans 2006).
• Geographic Proximity: physical, spatial distance between actors
(Boschma 2005). Online, geographical proximity is often irrelevant, but
some scholars have used time zones (O’Leary & Cummings, 2007).
5

6. Empirical Setting: Open Source
• Open source frequently studied as a fluid organization (e.g. Chen &
O’Mahony, 2009; O'Mahony & Bechky, 2008; Puranam et al., 2014).
• Contributions by individuals, not firms (O’Mahony, 2007), but firms
increasingly have employees contribute as a way to participate
(Jensen & Scacchi, 2007; Roberts et al., 2006).
• Linux Kernel*:
• < 8% of contributions by
unaffiliated software developers
• Neutral project, competing
companies participate
• 22 million lines of code
• 14,000 developers
• 1,300 organisations
6
Linux Kernel
Computer Hardware (CPU, memory, disk)
Linux Operating System (Red Hat, Ubuntu)
Applications (web browser, office)
SystemonlyUserfacing
* Corbet & Kroah-Hartman, 2016

7. Collaboration Network
• Network ties: Mailing Lists – ego replies to
alter
• Collaboration for code review, patch feedback,
bugs & discussions are on mailing lists before
source code is accepted into repository.
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8. Dataset
USB Mailing List (linux-usb)
• Dates: 2013-10-31 - 2015-10-31
• 60 day moving window
• Messages (Events): 8170 in 3492 threads
• Ties: Ego reply to a message from Alter
• Actors: 892 (Egos: 705, Alters: 712)
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9. Relational Event Models
• Mailing list data with a time stamps for each message provides
useful data for relational event models when used to explain
likelihood of collaboration between 2 developers given influence
of dimensions of proximity and other effects.
• Predicting events in an ordinal sequence is product of
multinomial likelihoods (Butts, 2008).
• Ordinal model estimated using Multinomial Conditional Logistic
Regression.
• Using clogit in R, which is based on coxph.
• Realized event compared to 10 randomly sampled possible
events (Opsahl & Hogan, 2011).
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10. Variable Operationalization• Proximity:
• Geographic: time zone similarity
• Organizational: both work for same firm
• Social: number of times dyad participated in same thread
• Cognitive: contribute to same source code subsystems
• Institutional: employed by same type of institution (corporate, non-profit, etc.)
• Dyadic-Level Covariates:
• Alter Maintainer: alter is in a leadership (maintainer) position
• Is Committer: one or both have made code contributions
• Network-Level Covariates:
• Transitive closure: num of x’s ego replied to where x has replied to alter
• Cyclic closure: num of x’s alter replied to where x has replied to ego
• Shared partnership in: same x replies to both ego and alter
• Shared partnership out: ego and alter reply to messages by same x
• Repeated events: number of times ego replied to messages by alter
• Recency effect: 1/n with n as # of people alter emailed before ego
• Participation shift: 1 if last person alter replied to was ego
10
xe a
e a
e a
a
1/3
1/2
1
xa e
xe a
xe a

11. coef exp(coef) se(coef)
inst prox -2.907e-02 9.713e-01 2.006e-02
geo prox 9.962e-03 1.010e+00 1.735e-02
org prox 4.426e-02 1.045e+00 1.693e-02 **
social prox 2.355e+01 1.683e+10 2.975e-01 ***
social prox (sq) -3.376e+01 2.173e-15 5.673e-01 ***
cog prox 5.038e-01 1.655e+00 3.573e-02 ***
cog prox (sq) -3.738e-01 6.881e-01 1.780e-02 ***
alter maintainer 4.508e-02 1.046e+00 1.399e-02 **
either commit 1.997e-01 1.221e+00 1.959e-02 ***
repeated events 1.567e-01 1.170e+00 5.378e-02 **
transitive clsr -2.414e-01 7.855e-01 8.931e-02 **
cyclic closure 6.610e-01 1.937e+00 9.203e-02 ***
shared part in -1.635e+00 1.949e-01 1.091e-01 ***
shared part out -1.292e+00 2.746e-01 9.954e-02 ***
recency effect 3.567e-01 1.429e+00 3.265e-02 ***
particip shift -2.676e-01 7.652e-01 2.996e-02 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05
Results
11
BIC 22269
BIC 27508
Proximity + Controls Full: Better than Proximity alone
Note: Bayesian information criterion (BIC) scores used to compare
maximum likelihood models - lower scores indicate better model fit.
coef exp(coef) se(coef)
inst prox 1.993e-02 1.020e+00 1.793e-02
geo prox 3.089e-02 1.031e+00 1.538e-02 *
org prox 1.264e-01 1.135e+00 1.499e-02 ***
social prox 1.545e+01 5.114e+06 1.916e-01 ***
social prox (sq) -2.682e+01 2.246e-12 5.114e-01 ***
cog prox -2.559e-01 7.742e-01 3.162e-02 ***
cog prox (sq) -1.134e-01 8.928e-01 1.469e-02 ***
alter maintainter 9.512e-02 1.100e+00 1.254e-02 ***
either commit 1.327e-01 1.142e+00 1.791e-02 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05

12. Results Summary
• The results indicate that cognitive, organizational,
and social proximity can be used to predict
collaboration, while institutional and geographic
proximity are not significant.
• Implication: Proximity is relevant and can be used to
explain collaboration in a fluid organization.
• Implication: Firms have at least some influence on
how employees collaborate within fluid organizations.
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13. Further Research
• Model the decision to send an original
message in addition to the replies (two-
step process).
• Multi-level approach using mailing lists as
levels to simultaneously model multiple
mailing lists as settings for collaboration.
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14. Thank You and Questions
Authors:
• Dawn M. Foster D.M.Foster@greenwich.ac.uk
@geekygirldawn on Twitter
• Guido Conaldi G.Conaldi@greenwich.ac.uk
• Riccardo De Vita R.DeVita@greenwich.ac.uk
University of Greenwich, Centre for Business Network Analysis
http://www.gre.ac.uk/business/research/centres/cbna
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