Co-evolution of Members’ Attachment to the Team and Team Interpersonal Networks Chunke Su Chunke Su Noshir Contractor Noshir Contractor University of Illinois at University of Illinois at Urbana-Champaign Urbana-Champaign Katherine J. Klein Katherine J. Klein University of Maryland at University of Maryland at College Park College Park Dynamics of Networks and Behavior Satellite symposium, XXII International Sunbelt Social Network Conference, Portorož, Slovenia, May 11, 2004
Transcript
Co-evolution of Members’ Attachment to the Team and Team Interpersonal Networks
Chunke SuChunke Su
Noshir ContractorNoshir Contractor
University of Illinois at University of Illinois at Urbana-ChampaignUrbana-Champaign
Katherine J. KleinKatherine J. Klein
University of Maryland at University of Maryland at College ParkCollege Park
Dynamics of Networks and Behavior Satellite symposium, XXII International Sunbelt Social Network Conference, Portorož, Slovenia, May 11, 2004
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We want to extend special thanks to We want to extend special thanks to Christian Steglich from University of Christian Steglich from University of Groningen for his efforts helping us trouble Groningen for his efforts helping us trouble shoot problems and providing suggestions shoot problems and providing suggestions for data analyses and interpretation.for data analyses and interpretation.
Christian will use the data from this study Christian will use the data from this study for the SIENA demo this afternoonfor the SIENA demo this afternoon
Acknowledgements
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Research IssuesThis study examines the dynamic co-evolution of This study examines the dynamic co-evolution of individuals’ attachment to project teams (an individuals’ attachment to project teams (an attribute) and their friendship network attribute) and their friendship network relationships with other individuals in the team.relationships with other individuals in the team.
1.1. How does interpersonal friendship network How does interpersonal friendship network
evolve over time?evolve over time?2.2. How do team members’ feelings of attachment How do team members’ feelings of attachment
to the team influence their friendship network to the team influence their friendship network over time?over time?
3.3. How does team members’ friendship network How does team members’ friendship network influence their feelings of attachment to the influence their feelings of attachment to the team over time? team over time?
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WHY DO WE CREATE,
MAINTAIN, DISSOLVE, AND
RECONSTITUTE OUR NETWORK LINKS?
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Monge, P. R. & Contractor, N. S. (2003). Theories of Communication Networks. New York: Oxford University Press.
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Multi-theoretical Multilevel Model (MTML)
Theories of self-interestTheories of self-interest Theories of mutual Theories of mutual
interestinterest Theories of social and Theories of social and
resource exchangeresource exchange Theories of contagionTheories of contagion
Theories of balanceTheories of balance Theories of homophilyTheories of homophily Theories of proximityTheories of proximity Theories of uncertainty Theories of uncertainty
reductionreduction Theories of co-evolutionTheories 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 York:Oxford University Press.
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Model 1: Creating TiesEndogenous Influence of the Network
Social Exchange TheorySocial Exchange Theory: Individuals are : Individuals are more likely to reciprocate friendship ties more likely to reciprocate friendship ties with those who have created ties with them with those who have created ties with them at previous times.at previous times.
Balance TheoryBalance Theory: Individuals are more likely : Individuals are more likely to create ties with friends of their friends. to create ties with friends of their friends.
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Model 2: Maintaining & Dissolving Ties
Endogenous Influence of the Network Social Exchange TheorySocial Exchange Theory: Individuals are : Individuals are
more likely to more likely to maintainmaintain reciprocated reciprocated friendship ties with those who have friendship ties with those who have previously created ties with them.previously created ties with them.
Social Exchange TheorySocial Exchange Theory: Individuals are : Individuals are less likely to less likely to dissolvedissolve ties reciprocated ties reciprocated friendship ties with those who have friendship ties with those who have previously created ties with them.previously created ties with them.
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Model 3: Exogenous Attribute Influence
on the Network Homophily TheoryHomophily Theory: Individuals are more likely to : Individuals are more likely to
create friendship ties with those who have similar create friendship ties with those who have similar attachment to the team.attachment to the team.
Theory of Self-interestTheory of Self-interest: Individuals are less likely : Individuals are less likely to create ties with those who have high to create ties with those who have high attachment to the team since they feel well attachment to the team since they feel well connected to the team. connected to the team.
Theory of Self-interestTheory of Self-interest: Individuals with high team : Individuals with high team attachment are less likely to create ties since they attachment are less likely to create ties since they feel well connected.feel well connected.
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Model 4: Network Influence on Actor Attachment
Contagion TheoryContagion Theory: Individuals are more : Individuals are more likely to have similar attachment to those likely to have similar attachment to those members of team with who they have ties. members of team with who they have ties.
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Model 5: Co-evolution of
Network Evolution and Actor Attributes
Simultaneous assessment of Simultaneous assessment of Models 1 through 4Models 1 through 4
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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).
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Data collection Data were collected from 3 teams (N=12, 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 didn’t disclose gender info
Ethnicity: 31 Caucasian (89%)2 Asian (6%)1 European mix (3%)1 didn’t disclose ethnic info
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Attachment to the Team
Individual report of one’s attachment to the team (abbr. AT)Individual report of one’s attachment to the team (abbr. AT) Questions:Questions:
1. If given the chance, I would choose to leave my team and join another. 1. If given the chance, I would choose to leave my team and join another. (Reverse score)(Reverse score)
2. I get along well with the members of my team.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.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.4. I feel that I am really part of my team.5. I look forward to being with members of my team each day.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. 6. I find that I do not usually get along with the other members of my team.
Strongly disagree (1) to strongly agree (5)Strongly disagree (1) to strongly agree (5)
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Friendship Network
Friendship networks Friendship networks
““Is this person a good friend of yours, Is this person a good friend of yours, someone you socialize with during your free someone you socialize with during your free time?”time?”
Scales from Baldwin, Bedell, and Johnson (1997)Scales from Baldwin, Bedell, and Johnson (1997)
Analysis SIENA (Simulation Investigation for Empirical SIENA (Simulation Investigation for Empirical
Network Analysis): a computer program that Network Analysis): a computer program that carries out the statistical estimation of models for carries out the statistical estimation of models for longitudinal social networks according to the longitudinal social networks according to the dynamic actor-oriented model of Snijders and van dynamic actor-oriented model of Snijders and van Duijn (1997) and Snijders (2001).Duijn (1997) and Snijders (2001).
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Descriptive Statistics 1: Attachment to the team
Time 1Time 1 Time 2Time 2 Time 3Time 3
Team 1Team 1
(n=12)(n=12)
M=4.26M=4.26
SD=0.43SD=0.43
M=4.58M=4.58
SD=0.57SD=0.57
M=4.18M=4.18
SD=1.53SD=1.53
Team 2Team 2
(n=12)(n=12)
M=4.62M=4.62
SD=0.40SD=0.40
M=4.83M=4.83
SD=0.37SD=0.37
M=4.58M=4.58
SD=0.48SD=0.48
Team 3Team 3
(n=11)(n=11)
M=4.24M=4.24
SD=0.61SD=0.61
M=4.42M=4.42
SD=0.50SD=0.50
M=4.41M=4.41
SD=0.51SD=0.51
All TeamsAll Teams
(N=35)(N=35)
M=4.38M=4.38
SD=0.50SD=0.50
M=4.61M=4.61
SD=0.50SD=0.50
M=4.39M=4.39
SD=0.97SD=0.97
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Descriptive Statistics 2: Friendship Networks
Time 1Time 1 Time 2Time 2 Time 3Time 3
Team 1Team 1
(n=12)(n=12)
M=0.48M=0.48
SD=0.50SD=0.50
Sum=63Sum=63
M=0.82M=0.82
SD=0.39SD=0.39
Sum=108Sum=108
M=0.68M=0.68
SD=0.46SD=0.46
Sum=90Sum=90
Team 2Team 2
(n=12)(n=12)
M=0.45M=0.45
SD=0.50SD=0.50
Sum=59Sum=59
M=0.84M=0.84
SD=0.36SD=0.36
Sum=111Sum=111
M=0.83M=0.83
SD=0.38SD=0.38
Sum=91Sum=91
Team 3Team 3
(n=11)(n=11)
M=0.47M=0.47
SD=0.50SD=0.50
Sum=52Sum=52
M=0.61M=0.61
SD=0.49SD=0.49
Sum=81Sum=81
M=0.76M=0.76
SD=0.43SD=0.43
Sum=83Sum=83
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Network Visualization
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Outline of data analysis
Model 1: Endogenous Model 1: Endogenous network evolution - network evolution - objective functionobjective function
Model 2: Endogenous Model 2: Endogenous network evolution - network evolution - objective + objective + endowment functionendowment function
Model 3: Exogenous Model 3: Exogenous network evolution network evolution influenced by actor influenced by actor attributesattributes
Model 4: Actor Model 4: Actor attributes influenced attributes influenced by network evolutionby network evolution
Model 5: Co-evolution Model 5: Co-evolution of network and actor of network and actor attributesattributes
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Analysis Results: Model 1 – Endogenous Evolution of Network (Creating Ties)
Objective function
ParametersParameters EstimatesEstimates Standard Standard ErrorsErrors
Analysis Results: Model 1 – Endogenous Evolution of Network (Creating Ties)
Objective function
Utility (actor i's friendship network) Utility (actor i's friendship network) = -1.96 x (# of outgoing friendship ties of actor i) = -1.96 x (# of outgoing friendship ties of actor i) + 1.18 x (# of reciprocated 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 + 0.25 x (# of transitive friendship triplets in which actor i is
the focal actor) the focal actor) For actor i to establish a friendship tie, there is a cost of 1.96 For actor i to establish a friendship tie, there is a cost of 1.96
attached. attached. If the tie is reciprocated, there is also a benefit of 1.18, thus the If the tie is reciprocated, there is also a benefit of 1.18, thus the
net cost of a reciprocated tie is 0.78. net cost of a reciprocated tie is 0.78. If the friendship tie shortens a 2-path i>j>k to a direct tie i>k If the friendship tie shortens a 2-path i>j>k to a direct tie i>k
(i.e., when the triplet i,j,k is a transitive triplet), there is an (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 additional benefit of 0.25. Since there may be multiple such triplets, the net value of one particular friendship tie may triplets, the net value of one particular friendship tie may become positive.become positive.
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Analysis Results: Model 1 – Endogenous Evolution of Network (Creating Ties)
Objective function Team members tend Team members tend
NOT to be friends with NOT to be friends with other members over time.other members over time.
Team members tend to Team members tend to reciprocate friendship reciprocate friendship ties with other members ties with other members over time. over time. (social (social exchange)exchange)
Team members tend to Team members tend to be friends with their be friends with their friends’ friends over friends’ friends over time. time. (balance)(balance)
I J I JX
I J I J
I
K
J
I
K
J
Time 1 Time 2
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Analysis Results: Model 2 – Endogenous Evolution of Network (Maintaining and Dissolving Ties)
Objective + Endowment function
ParametersParameters EstimatesEstimates Standard Standard ErrorsErrors
Analysis Results: Model 3 –Exogenous Influence of Actor Attribute on Network Evolution
ParametersParameters EstimatesEstimates Standard Standard ErrorsErrors
Convergence Convergence
t-statisticst-statistics
Density (out-Density (out-degree)degree)
-0.94*-0.94* 0.260.26 -0.02-0.02
AT similarityAT similarity 0.59*0.59* 0.300.30 0.060.06
AT alterAT alter -0.41*-0.41* 0.120.12 0.030.03
AT egoAT ego -0.24-0.24 0.130.13 0.000.00
* 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) Utility (actor i's friendship network) = -0.94 x (# of outgoing friendship ties of actor i) = -0.94 x (# of outgoing friendship ties of actor i) + 0.59 x (# of actor i’s friendship ties with other actors who + 0.59 x (# of actor i’s friendship ties with other actors who
have similar levels of team attachment) have similar levels of team attachment) - 0.41 x (sum of attachment scores for actor i’s friends)- 0.41 x (sum of attachment scores for actor i’s friends)
For actor i to establish a friendship tie, there is a cost of 0.94 For actor i to establish a friendship tie, there is a cost of 0.94 attached. attached.
If the friendship tie is to someone who has an identical level 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 of team attachment, there is a benefit of 0.59, thus the net cost of establishing a friendship tie is reduced to 0.35. cost of establishing a friendship tie is reduced to 0.35.
However, if the tie is to someone who has a high level of 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, the cost increases. For a unit of increase in team attachment of the alter, the cost of establishing a team attachment of the alter, the cost of establishing a friendship tie from actor i to the alter increases by 0.41.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
Team members tend NOT Team members tend NOT to be friends with other to be friends with other members over time.members over time.
Over time, team members Over time, team members tend to be friends with tend to be friends with other members who have other members who have similar levels of team similar levels of team attachment as they do. attachment as they do. (homophily)(homophily)
Over time, team members Over time, team members tend to be friends with tend to be friends with other members who report other members who report to have low levels of team to have low levels of team attachment.attachment.
I J I JX
Time 1 Time 2
HAT HAT
LAT LAT
HAT HAT
LAT LAT
I HAT
J LAT
I HAT
J LAT
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Analysis Results: Model 4Influence of Network on Evolution of Actor Attributes
ParametersParameters EstimatesEstimates Standard Standard ErrorsErrors
Convergence Convergence
t-statisticst-statistics
Density (out-Density (out-degree)degree)
-0.49*-0.49* 0.080.08 0.050.05
Behavior AT Behavior AT tendency tendency (“intercept term” (“intercept term” – preference for – preference for attachment)attachment)
1.491.49 1.121.12 -0.09-0.09
Behavior AT Behavior AT similaritysimilarity
-1.07-1.07 1.181.18 -0.06-0.06
* Significant at 0.05 level
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Analysis Results: Model 5 – Coevolution of Network + Attributes
* Significant at 0.05 level
ParametersParameters EstimatesEstimates Standard Standard ErrorsErrors
AT similarityAT similarity 0.580.58 0.450.45 -0.09-0.09
AT alterAT alter -0.51*-0.51* 0.080.08 -0.03-0.03
Behavior AT Behavior AT tendencytendency
1.341.34 0.910.91 0.130.13
Behavior AT Behavior AT similaritysimilarity
-0.92-0.92 0.990.99 0.090.09
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Analysis Results: Model 5 – Co-evolution of Network + Actor Attributes
Utility (actor i's friendship network) Utility (actor i's friendship network) = -0.21 x (# of outgoing friendship ties of actor i) = -0.21 x (# of outgoing friendship ties of actor i) + 1.18 x (# of reciprocated 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 + 0.23 x (# of transitive friendship triplets in which actor i is
the focal actor) the focal actor)- 0.51 x (sum of attachment scores for actor i’s friends)- 0.51 x (sum of attachment scores for actor i’s friends)
If the friendship tie from actor i to the alter is reciprocated, If the friendship tie from actor i to the alter is reciprocated, there is a benefit of 1.18 from establishing such a tie. there is a benefit of 1.18 from establishing such a tie.
If the friendship tie shortens a 2-path i>j>k to a direct tie i>k If the friendship tie shortens a 2-path i>j>k to a direct tie i>k (i.e., when the triplet i,j,k is a transitive triplet), there is an (i.e., when the triplet i,j,k is a transitive triplet), there is an additional benefit of 0.23. additional benefit of 0.23.
However, if the tie is to someone who has a high level of 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, the cost increases. For a unit of increase in team attachment of the alter, the cost of establishing a team attachment of the alter, the cost of establishing a friendship tie from actor i to the alter increases by 0.51.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 Team members tend to reciprocate friendship reciprocate friendship ties with other members ties with other members over time. over time.
Team members tend to Team members tend to be friends with their be friends with their friends’ friends over friends’ friends over time.time.
Over time, team Over time, team members tend to be members tend to be friends with other friends with other members who report to members who report to have low levels of team have low levels of team attachment. attachment.
I
J
K
I
J
K
Time 1 Time 2
I HAT
J LAT
I HAT
J LAT
I J I J
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Theoretical & Analytical Issues I
Additional theoretical mechanisms: contagion by structural Additional theoretical mechanisms: contagion by structural equivalence (influence), theories of collective action equivalence (influence), theories of collective action (selection), cognitive theories (cognitive social structures).(selection), cognitive theories (cognitive social structures).
Sample size for “behavioral” attributes is N while size for Sample size for “behavioral” attributes is N while size for relations are N(N-1). Hence difference in power and relations are N(N-1). Hence difference in power and standard errors.standard errors.
Time scale for “behavioral” changes may be lower than for Time scale for “behavioral” changes may be lower than for network relations.network relations.
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Theoretical & Analytical Issues II
Additional analysis using 97 more teams and 2 more Additional analysis using 97 more teams and 2 more relations: advice and adversarial between project teams.relations: advice and adversarial between project teams.
Omnibus goodness of fit tests for adequacy of model and Omnibus goodness of fit tests for adequacy of model and comparison between models (comparison between models (Michael SchweinbergerMichael Schweinberger)) . .
Meta-analysis across multiple teams versus one large data Meta-analysis across multiple teams versus one large data set of multiple teams (set of multiple teams (Andrea Knecht and Chris Andrea Knecht and Chris Baerveldt).Baerveldt).
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More information on University of Illinois More information on University of Illinois network research, laboratory, book, doctoral network research, laboratory, book, doctoral fellowships, post-docs, research scientist: fellowships, post-docs, research scientist:
