Co-evolution of Members

1
Co-evolution of Members Attachment to the Team
and Team Interpersonal Networks

• Chunke Su
• Noshir Contractor
• University of Illinois at Urbana-Champaign
• Katherine J. Klein
• University of Maryland at College Park

Dynamics of Networks and Behavior Satellite
symposium, XXII International Sunbelt Social
Network Conference, Portorož, Slovenia, May 11,
2004
2
Acknowledgements

• We want to extend special thanks to Christian
  Steglich from University of Groningen for his
  efforts helping us trouble shoot problems and
  providing suggestions for data analyses and
  interpretation.
• Christian will use the data from this study
  for the SIENA demo this afternoon

3
Research Issues

• This study examines the dynamic co-evolution of
  individuals attachment to project teams (an
  attribute) and their friendship network
  relationships with other individuals in the team.
• How does interpersonal friendship network evolve
  over time?
• How do team members feelings of attachment to
  the team influence their friendship network over
  time?
• How does team members friendship network
  influence their feelings of attachment to the
  team over time?

4
WHY DO WE CREATE, MAINTAIN, DISSOLVE, AND
RECONSTITUTE OUR NETWORK LINKS?
5
Monge, P. R. Contractor, N. S. (2003).
Theories of Communication Networks. New York
Oxford University Press.
6
Multi-theoretical Multilevel Model (MTML)

• Theories of self-interest
• Theories of mutual interest
• Theories of social and resource exchange
• Theories of contagion

• Theories of balance
• Theories of homophily
• Theories of proximity
• Theories of uncertainty reduction
• Theories of co-evolution

Sources Contractor, Wasserman, Faust (in
press). Academy of Management Review. Monge, P.
R. Contractor, N. S. (2003). Theories of
Communication Networks. New YorkOxford
University Press.
7
Model 1 Creating TiesEndogenous Influence of
the Network

• Social Exchange Theory Individuals are more
  likely to reciprocate friendship ties with those
  who have created ties with them at previous
  times.
• Balance Theory Individuals are more likely to
  create ties with friends of their friends.

8
Model 2 Maintaining Dissolving Ties
Endogenous Influence of the Network

• Social Exchange Theory Individuals are more
  likely to maintain reciprocated friendship ties
  with those who have previously created ties
  with them.
• Social Exchange Theory Individuals are less
  likely to dissolve ties reciprocated friendship
  ties with those who have previously created ties
  with them.

9
Model 3 Exogenous Attribute Influence on the
Network

• Homophily Theory Individuals are more likely to
  create friendship ties with those who have
  similar attachment to the team.
• Theory of Self-interest Individuals are less
  likely to create ties with those who have high
  attachment to the team since they feel well
  connected to the team.
• Theory of Self-interest Individuals with high
  team attachment are less likely to create ties
  since they feel well connected.

10
Model 4 Network Influence on Actor Attachment

• Contagion Theory Individuals are more likely to
  have similar attachment to those members of team
  with who they have ties.

11
Model 5 Co-evolution of Network Evolution and
Actor Attributes

• Simultaneous assessment of Models 1 through 4

12
Participants

• Longitudinal survey data were collected from a
  residential, team-based, 10-month long national
  service program (the National Civilian Community
  Corps, part of the U.S. federal government
  program, Americorps).
• Teams performed diverse service projects,
  typically varying in length from one to two
  months (e.g., tutoring elementary school
  children, mentoring homeless youth, coordinating
  after-school activities for teens).
• Team members received an educational grant and a
  modest stipend in return. Each team was led by a
  formally designated team leader, chosen by the
  program administrators not by team members to
  lead the team.
• Teams in the program ranged in size from 9 to 12.
  Members are predominantly female (68) and white
  (82). Team members ranged in age from 17 to 25
  (M 20.80 years, SD 1.93).

13
Data collection

• Data were collected from 3 teams (N12, 12, 11)
  at 3 points in time.
• T1 within the first two weeks following team
  formation
• T2 five months after team formation
• T3 ten months after team formation
• Demographic information
• Gender
• 21 female members (60)
• 13 male members (37)
• 1 didnt disclose gender info
• Ethnicity
• 31 Caucasian (89)
• 2 Asian (6)
• 1 European mix (3)
• 1 didnt disclose ethnic info

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Attachment to the Team

• Individual report of ones attachment to the team
  (abbr. AT)
• Questions
• 1. If given the chance, I would choose to leave
  my team and join another. (Reverse score)
• 2. I get along well with the members of my team.
• 3. I will readily defend the members of my team
  from criticism by outsiders.
• 4. I feel that I am really part of my team.
• 5. I look forward to being with members of my
  team each day.
• 6. I find that I do not usually get along with
  the other members of my team. (Reverse score)
• Measurement scales 5-point Likert scale
• Strongly disagree (1) to strongly agree (5)

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Friendship Network

• Friendship networks
• Is this person a good friend of yours, someone
  you socialize with during your free time?
• Scales from Baldwin, Bedell, and Johnson
  (1997)
• Measurement binary scale
• yes1 no0

16
Analysis

• SIENA (Simulation Investigation for Empirical
  Network Analysis) a computer program that
  carries out the statistical estimation of models
  for longitudinal social networks according to the
  dynamic actor-oriented model of Snijders and van
  Duijn (1997) and Snijders (2001).

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Descriptive Statistics 1 Attachment to the team
Time 1 Time 2 Time 3
Team 1 (n12) M4.26 SD0.43 M4.58 SD0.57 M4.18 SD1.53
Team 2 (n12) M4.62 SD0.40 M4.83 SD0.37 M4.58 SD0.48
Team 3 (n11) M4.24 SD0.61 M4.42 SD0.50 M4.41 SD0.51
All Teams (N35) M4.38 SD0.50 M4.61 SD0.50 M4.39 SD0.97
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Descriptive Statistics 2 Friendship Networks
Time 1 Time 2 Time 3
Team 1 (n12) M0.48 SD0.50 Sum63 M0.82 SD0.39 Sum108 M0.68 SD0.46 Sum90
Team 2 (n12) M0.45 SD0.50 Sum59 M0.84 SD0.36 Sum111 M0.83 SD0.38 Sum91
Team 3 (n11) M0.47 SD0.50 Sum52 M0.61 SD0.49 Sum81 M0.76 SD0.43 Sum83
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Network Visualization
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Outline of data analysis

• Model 1 Endogenous network evolution - objective
  function

• Model 2 Endogenous network evolution - objective
  endowment function

• Model 3 Exogenous network evolution influenced
  by actor attributes

• Model 5 Co-evolution of network and actor
  attributes

• Model 4 Actor attributes influenced by network
  evolution

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Analysis Results Model 1 Endogenous Evolution
of Network (Creating Ties) Objective function
Parameters Estimates Standard Errors Convergence t-statistics
Density (out-degree) -1.96 0.19 -0.09
Reciprocity 1.18 0.19 -0.09
Transitivity 0.25 0.13 -0.11
Significant at 0.05 level
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Analysis Results Model 1 Endogenous Evolution
of Network (Creating Ties) Objective function

• Utility (actor i's friendship network)
• -1.96 x ( of outgoing friendship ties of
  actor i)
• 1.18 x ( of reciprocated friendship ties of
  actor i)
• 0.25 x ( of transitive friendship triplets in
  which actor i is the focal actor)
• For actor i to establish a friendship tie, there
  is a cost of 1.96 attached.
• If the tie is reciprocated, there is also a
  benefit of 1.18, thus the net cost of a
  reciprocated tie is 0.78.
• If the friendship tie shortens a 2-path igtjgtk to
  a direct tie igtk (i.e., when the triplet i,j,k is
  a transitive triplet), there is an additional
  benefit of 0.25. Since there may be multiple such
  triplets, the net value of one particular
  friendship tie may become positive.

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Analysis Results Model 1 Endogenous Evolution
of Network (Creating Ties) Objective function

• Team members tend NOT to be friends with other
  members over time.
• Team members tend to reciprocate friendship ties
  with other members over time. (social exchange)
• Team members tend to be friends with their
  friends friends over time. (balance)

X
I
J
I
J
I
J
I
J
K
K
I
I
J
J
Time 1
Time 2
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Analysis Results Model 2 Endogenous Evolution
of Network (Maintaining and Dissolving Ties)
Objective Endowment function
Parameters Estimates Standard Errors Convergence t-statistics
Density (out-degree) -0.86 7.57 -0.04
Reciprocity 5.75 36.62 -0.27
Breaking reciprocated relation 8.17 35.29 -0.42
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Analysis Results Model 3 Exogenous Influence of
Actor Attribute on Network Evolution
Parameters Estimates Standard Errors Convergence t-statistics
Density (out-degree) -0.94 0.26 -0.02
AT similarity 0.59 0.30 0.06
AT alter -0.41 0.12 0.03
AT ego -0.24 0.13 0.00
Significant at 0.05 level
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Analysis Results Model 3 Exogenous Influence
of Actor Attribute on Network Evolution

• Utility (actor i's friendship network)
• -0.94 x ( of outgoing friendship ties of
  actor i)
• 0.59 x ( of actor is friendship ties with
  other actors who have similar levels of
  team attachment)
• - 0.41 x (sum of attachment scores for actor is
  friends)
• For actor i to establish a friendship tie, there
  is a cost of 0.94 attached.
• If the friendship tie is to someone who has an
  identical level of team attachment, there is a
  benefit of 0.59, thus the net cost of
  establishing a friendship tie is reduced to 0.35.
  
• However, if the tie is to someone who has a high
  level of team attachment, the cost increases. For
  a unit of increase in team attachment of the
  alter, the cost of establishing a friendship tie
  from actor i to the alter increases by 0.41.

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Analysis Results Model 3 Exogenous Influence
of Actor Attribute on Network Evolution
X

• Team members tend NOT to be friends with other
  members over time.
• Over time, team members tend to be friends with
  other members who have similar levels of team
  attachment as they do.
• (homophily)
• Over time, team members tend to be friends with
  other members who report to have low levels of
  team attachment.

I
J
I
J
HAT
HAT
HAT
HAT
LAT
LAT
LAT
LAT
I
HAT
I
HAT
J
LAT
J
LAT
Time 1
Time 2
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Analysis Results Model 4Influence of Network on
Evolution of Actor Attributes
Parameters Estimates Standard Errors Convergence t-statistics
Density (out-degree) -0.49 0.08 0.05
Behavior AT tendency (intercept term preference for attachment) 1.49 1.12 -0.09
Behavior AT similarity -1.07 1.18 -0.06
Significant at 0.05 level
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Analysis Results Model 5 Coevolution of
Network Attributes
Parameters Estimates Standard Errors Convergence t-statistics
Density (out-degree) -0.21 0.47 -0.09
Reciprocity 1.18 0.14 -0.10
Transitivity 0.23 0.10 -0.09
AT similarity 0.58 0.45 -0.09
AT alter -0.51 0.08 -0.03
Behavior AT tendency 1.34 0.91 0.13
Behavior AT similarity -0.92 0.99 0.09
Significant at 0.05 level
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Analysis Results Model 5 Co-evolution of
Network Actor Attributes

• Utility (actor i's friendship network)
• -0.21 x ( of outgoing friendship ties of
  actor i)
• 1.18 x ( of reciprocated friendship ties of
  actor i)
• 0.23 x ( of transitive friendship triplets in
  which actor i is the focal actor)
• - 0.51 x (sum of attachment scores for actor is
  friends)
• If the friendship tie from actor i to the alter
  is reciprocated, there is a benefit of 1.18 from
  establishing such a tie.
• If the friendship tie shortens a 2-path igtjgtk to
  a direct tie igtk (i.e., when the triplet i,j,k is
  a transitive triplet), there is an additional
  benefit of 0.23.
• However, if the tie is to someone who has a high
  level of team attachment, the cost increases. For
  a unit of increase in team attachment of the
  alter, the cost of establishing a friendship tie
  from actor i to the alter increases by 0.51.

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Analysis Results Model 5 Co-evolution of
Network Actor Attributes

• Team members tend to reciprocate friendship ties
  with other members over time.
• Team members tend to be friends with their
  friends friends over time.
• Over time, team members tend to be friends with
  other members who report to have low levels of
  team attachment.

I
J
I
J
J
J
I
I
K
K
I
HAT
I
HAT
J
LAT
J
LAT
Time 1
Time 2
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Theoretical Analytical Issues I

• Additional theoretical mechanisms contagion by
  structural equivalence (influence), theories of
  collective action (selection), cognitive theories
  (cognitive social structures).
• Sample size for behavioral attributes is N
  while size for relations are N(N-1). Hence
  difference in power and standard errors.
• Time scale for behavioral changes may be lower
  than for network relations.

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Theoretical Analytical Issues II

• Additional analysis using 97 more teams and 2
  more relations advice and adversarial between
  project teams.
• Omnibus goodness of fit tests for adequacy of
  model and comparison between models (Michael
  Schweinberger) .
• Meta-analysis across multiple teams versus one
  large data set of multiple teams (Andrea Knecht
  and Chris Baerveldt).

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• More information on University of Illinois
  network research, laboratory, book, doctoral
  fellowships, post-docs, research scientist
• nosh_at_uiuc.edu
• www.uiuc.edu/ph/www/nosh

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Thank you!