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 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 Christian will use the data from this study for the SIENA demo this afternoon Acknowledgements

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. 1. How does interpersonal friendship network evolve over time? 2. How do team members’ feelings of attachment to the team influence their friendship network over time? 3. 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) n Theories of self-interest n Theories of mutual interest n Theories of social and resource exchange n Theories of contagion n Theories of balance n Theories of homophily n Theories of proximity n Theories of uncertainty reduction n 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 York:Oxford University Press.

7 Model 1: Creating Ties Endogenous 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. 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. 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 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. 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. 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 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. 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. 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 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 = years, SD = 1.93).

13 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

14 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. (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 Measurement scales: 5-point Likert scale Strongly disagree (1) to strongly agree (5)

15 Friendship Network Friendship networks 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 Measurement: binary scale yes=1 no=0

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). 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).

17 Descriptive Statistics 1: Attachment to the team Time 1 Time 2 Time 3 Team 1 (n=12)M=4.26SD=0.43M=4.58SD=0.57M=4.18SD=1.53 Team 2 (n=12)M=4.62SD=0.40M=4.83SD=0.37M=4.58SD=0.48 Team 3 (n=11)M=4.24SD=0.61M=4.42SD=0.50M=4.41SD=0.51 All Teams (N=35)M=4.38SD=0.50M=4.61SD=0.50M=4.39SD=0.97

18 Descriptive Statistics 2: Friendship Networks Time 1 Time 2 Time 3 Team 1 (n=12)M=0.48SD=0.50Sum=63M=0.82SD=0.39Sum=108M=0.68SD=0.46Sum=90 Team 2 (n=12)M=0.45SD=0.50Sum=59M=0.84SD=0.36Sum=111M=0.83SD=0.38Sum=91 Team 3 (n=11)M=0.47SD=0.50Sum=52M=0.61SD=0.49Sum=81M=0.76SD=0.43Sum=83

19 Network Visualization

20 Outline of data analysis Model 1: Endogenous network evolution - objective function 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 3: Exogenous network evolution influenced by actor attributes Model 4: Actor attributes influenced by network evolution Model 4: Actor attributes influenced by network evolution Model 5: Co-evolution of network and actor attributes Model 5: Co-evolution of network and actor attributes

21 Analysis Results: Model 1 – Endogenous Evolution of Network (Creating Ties) Objective function ParametersEstimates Standard Errors Convergencet-statistics Density (out- degree) -1.96* Reciprocity1.18* Transitivity0.25* * Significant at 0.05 level

22 Analysis Results: Model 1 – Endogenous Evolution of Network (Creating Ties) Objective function Utility (actor i's friendship network) Utility (actor i's friendship network) = x (# of outgoing friendship ties of actor i) x (# of reciprocated friendship ties of actor i) 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. 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 If the tie is reciprocated, there is also a benefit of 1.18, thus the net cost of a reciprocated tie is 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 additional benefit of Since there may be multiple such triplets, the net value of one particular friendship tie may become positive. 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 additional benefit of Since there may be multiple such triplets, the net value of one particular friendship tie may become positive.

23 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 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 reciprocate friendship ties with other members over time. (social exchange) Team members tend to be friends with their friends’ friends over time. (balance) Team members tend to be friends with their friends’ friends over time. (balance) IJIJ X IJIJ I K J I K J Time 1Time 2

24 Analysis Results: Model 2 – Endogenous Evolution of Network (Maintaining and Dissolving Ties) Objective + Endowment function ParametersEstimates Standard Errors Convergencet-statistics Density (out- degree) Reciprocity Breaking reciprocated relation

25 Analysis Results: Model 3 –Exogenous Influence of Actor Attribute on Network Evolution ParametersEstimates Standard Errors Convergencet-statistics Density (out- degree) -0.94* AT similarity 0.59* AT alter -0.41* AT ego * Significant at 0.05 level

26 Analysis Results: Model 3 – Exogenous Influence of Actor Attribute on Network Evolution Utility (actor i's friendship network) Utility (actor i's friendship network) = x (# of outgoing friendship ties of actor i) x (# of actor i’s friendship ties with other actors who have similar levels of team attachment) 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 attached. 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 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 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 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.

27 Analysis Results: Model 3 – Exogenous Influence of Actor Attribute on Network Evolution Team members tend NOT to be friends with other members over time. 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. 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. Over time, team members tend to be friends with other members who report to have low levels of team attachment. IJIJ X Time 1Time 2 HAT LAT HAT LAT IHAT JLAT IHAT JLAT

28 Analysis Results: Model 4 Influence of Network on Evolution of Actor Attributes ParametersEstimates Standard Errors Convergencet-statistics Density (out- degree) -0.49* Behavior AT tendency (“intercept term” – preference for attachment) Behavior AT similarity * Significant at 0.05 level

29 Analysis Results: Model 5 – Coevolution of Network + Attributes * Significant at 0.05 level ParametersEstimates Standard Errors Convergencet-statistics Density (out- degree) Reciprocity1.18* Transitivity0.23* AT similarity AT alter -0.51* Behavior AT tendency Behavior AT similarity

30 Analysis Results: Model 5 – Co-evolution of Network + Actor Attributes Utility (actor i's friendship network) Utility (actor i's friendship network) = x (# of outgoing friendship ties of actor i) x (# of reciprocated friendship ties of actor i) x (# of transitive friendship triplets in which actor i is the focal actor) x (sum of attachment scores for actor i’s 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 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 i>j>k to a direct tie i>k (i.e., when the triplet i,j,k is a transitive triplet), there is an additional benefit of 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 additional benefit 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 of the alter, the cost of establishing a friendship tie from actor i to the alter increases by 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.

31 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 reciprocate friendship ties with other members over time. Team members tend to be friends with their friends’ friends 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. Over time, team members tend to be friends with other members who report to have low levels of team attachment. I J K I J K Time 1Time 2 IHAT JLAT IHAT JLAT IJIJ

32 Theoretical & Analytical Issues I Additional theoretical mechanisms: contagion by structural equivalence (influence), theories of collective action (selection), cognitive theories (cognitive social structures). 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. 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. Time scale for “behavioral” changes may be lower than for network relations.

33 Theoretical & Analytical Issues II Additional analysis using 97 more teams and 2 more relations: advice and adversarial between project teams. 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). 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). Meta-analysis across multiple teams versus one large data set of multiple teams (Andrea Knecht and Chris Baerveldt).

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