Dynamic Social Network Analysis <ul><li>René Veenstra </li></ul><ul><li>Department of Sociology  </li></ul><ul><li>http://...
The basics <ul><li>What is a network? </li></ul><ul><ul><li>A  graph  in which… </li></ul></ul><ul><ul><li>we have a  set ...
Network data <ul><li>We commonly use matrices containing the ties </li></ul><ul><li>Example: </li></ul><ul><ul><li>a 1  ha...
Non-directed and directed graphs <ul><li>Non-directed </li></ul><ul><ul><li>e.g., romantic relationship, marriage ties </l...
Network parameters: Degree <ul><li>In-degree:  </li></ul><ul><ul><li>number of ties  directed at  the node </li></ul></ul>...
Network parameters <ul><li>Number of possible lines </li></ul><ul><ul><li>non-directed: n (n-1)/2 </li></ul></ul><ul><ul><...
Network parameters: closure <ul><li>Transitivity  (usually positive) </li></ul><ul><ul><li>measure of triads </li></ul></u...
Evolution of social networks <ul><li>Single observations are snapshots </li></ul><ul><ul><li>Result of untraceable history...
SIENA: Actor oriented approach <ul><li>Analyzing longitudinal changes in networks </li></ul><ul><li>At certain moments in ...
Purpose of statistical modeling <ul><li>Investigate network evolution as function of: </li></ul><ul><ul><li>Structural net...
Example data of Ernest Hodges <ul><li>167 male actors (predominantly Hispanic and low SES background) </li></ul><ul><li>Ti...
Tie Changes Between Wave 1 and 2 <ul><li>Period 0=>0 0=>1 1=>0 1=>1 Missing </li></ul><ul><li>1 ==> 2 22842 847 896 1610 1...
Prevalence of Weapon Carrying <ul><li>T1 T2 </li></ul><ul><li>( N =164) ( N =138) </li></ul><ul><li>0 times 72.6% 69.6% </...
SIENA Estimates and Standard Errors <ul><li>Network Effects: Est. SE </li></ul><ul><li>1. Outdegree  -1.411 (0.065) *** </...
SIENA Estimates and Standard Errors <ul><li>Behavioral tendencies: Est. SE </li></ul><ul><li>7. Weapon Carrying Linear -1....
 
 
 
 
 
One-week Summer Course in Kansas <ul><li>Kansas University Summer Institute in Statistics </li></ul><ul><li>one-week cours...
SNA Community <ul><li>Handbooks </li></ul><ul><li>Wasserman, S. & Faust, K. (1994).  Social Network Analysis: Methods and ...
Thank you for your attention Software and manual: http://stat.gamma.rug.nl/siena/
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Social Network Analysis

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  • Social Network Analysis

    1. 1. Dynamic Social Network Analysis <ul><li>René Veenstra </li></ul><ul><li>Department of Sociology </li></ul><ul><li>http://www.gmw.rug.nl/~veenstra </li></ul>
    2. 2. The basics <ul><li>What is a network? </li></ul><ul><ul><li>A graph in which… </li></ul></ul><ul><ul><li>we have a set of nodes (children, companies, web pages)… </li></ul></ul><ul><ul><li>connected by ties ( friendship relations, product exchanges, citations) </li></ul></ul><ul><li>Why do we look at networks? </li></ul><ul><ul><li>to study relational data, considering simultaneously both individuals connected by a tie </li></ul></ul><ul><ul><li>to see how ties combine: individuals are connected to others, who themselves are also connected to others </li></ul></ul><ul><ul><li>to find and highlight statistical properties that characterize structure and behavior of networked systems </li></ul></ul><ul><ul><li>to make predictions based on measured structural properties </li></ul></ul>
    3. 3. Network data <ul><li>We commonly use matrices containing the ties </li></ul><ul><li>Example: </li></ul><ul><ul><li>a 1 has a tie to a2 and a5 </li></ul></ul>0 1 1 1 1 1 a6 1 0 0 0 0 0 a5 0 0 0 0 1 1 a4 1 0 0 0 1 0 a3 0 0 0 0 0 1 a2 0 1 0 0 1 0 a1 a6 a5 a4 a3 a2 a1
    4. 4. Non-directed and directed graphs <ul><li>Non-directed </li></ul><ul><ul><li>e.g., romantic relationship, marriage ties </li></ul></ul><ul><li>Directed </li></ul><ul><ul><li>e.g., friendship nominations, bullying </li></ul></ul>
    5. 5. Network parameters: Degree <ul><li>In-degree: </li></ul><ul><ul><li>number of ties directed at the node </li></ul></ul><ul><ul><li>popularity of an actor </li></ul></ul><ul><ul><li>number of received nominations </li></ul></ul><ul><li>Out-degree: </li></ul><ul><ul><li>number of ties going from the node </li></ul></ul><ul><ul><li>activity of an actor </li></ul></ul><ul><ul><li>number of given nominations </li></ul></ul><ul><li>Isolate: </li></ul><ul><ul><li>Node without lines attached to it </li></ul></ul>
    6. 6. Network parameters <ul><li>Number of possible lines </li></ul><ul><ul><li>non-directed: n (n-1)/2 </li></ul></ul><ul><ul><li>directed: n (n-1) </li></ul></ul><ul><li>Density (ranges from 0 to 1) </li></ul><ul><ul><li>the proportion of possible lines that are actually present in the graph </li></ul></ul><ul><li>Outdegree (density = 0.5  outdegree = 0) </li></ul><ul><ul><li>models the density of the network </li></ul></ul><ul><li>Reciprocity (with friendship data usually positive) </li></ul><ul><ul><li>a mutual tie: i chooses j and j chooses i. </li></ul></ul>
    7. 7. Network parameters: closure <ul><li>Transitivity (usually positive) </li></ul><ul><ul><li>measure of triads </li></ul></ul><ul><ul><li>‘ a friend of a friend is a friend’ </li></ul></ul>
    8. 8. Evolution of social networks <ul><li>Single observations are snapshots </li></ul><ul><ul><li>Result of untraceable history </li></ul></ul><ul><ul><li>Explaining them has limited importance </li></ul></ul><ul><li>Longitudinal modeling offers promise for understanding network structure </li></ul><ul><li>Structures of relations between actors that evolve </li></ul><ul><li>Dynamics of social networks </li></ul>
    9. 9. SIENA: Actor oriented approach <ul><li>Analyzing longitudinal changes in networks </li></ul><ul><li>At certain moments in time actors can make choices, based on the evaluation of their position in the network: </li></ul><ul><ul><li>actors can change ties (selection processes) </li></ul></ul><ul><ul><li>actors can change their behavior (socialization or influence processes) </li></ul></ul><ul><li>See also: </li></ul><ul><ul><li>Steglich, C.E.G., Snijders, T.A.B., & West, P. (2006). Applying SIENA. Methodology, 48-56. </li></ul></ul><ul><ul><li>Burk, W. J., Steglich, C. E. G., & Snijders, T. A. B. (2007). Beyond dyadic interdependence. International Journal of Behavioral Development, 31, 397-404. </li></ul></ul>
    10. 10. Purpose of statistical modeling <ul><li>Investigate network evolution as function of: </li></ul><ul><ul><li>Structural network effects (e.g., reciprocity, transitivity) </li></ul></ul><ul><ul><li>Explanatory actor variables (e.g., gender, aggression, victimization) </li></ul></ul><ul><ul><li>Explanatory dyadic variables (e.g., same-gender, bullying relationship) </li></ul></ul><ul><li>All effects control for each other </li></ul><ul><li>Without structural network effects, tests of other effects would be unreliable </li></ul>
    11. 11. Example data of Ernest Hodges <ul><li>167 male actors (predominantly Hispanic and low SES background) </li></ul><ul><li>Tie = friendship </li></ul><ul><li>Actor covariates: gender, aggression, victimization, weapon carrying </li></ul><ul><li>2 measurements: one year apart </li></ul><ul><li>Dijkstra, J.K., Lindenberg, S., Veenstra, R., & Hodges, E.V.E. Selection and influence processes in weapon carrying in early adolescence. The role of status, aggression, and vulnerability. </li></ul>
    12. 12. Tie Changes Between Wave 1 and 2 <ul><li>Period 0=>0 0=>1 1=>0 1=>1 Missing </li></ul><ul><li>1 ==> 2 22842 847 896 1610 1527 ( 6%) </li></ul><ul><li>Average degree </li></ul><ul><li>T1: 0.109 </li></ul><ul><li>T2: 0.095 </li></ul><ul><li>Proportion of Reciprocated Ties: 2M/(2M+A) </li></ul><ul><li>T1: 75% (2262 / 3020) </li></ul><ul><li>T2: 70% (1718 / 2458) </li></ul>
    13. 13. Prevalence of Weapon Carrying <ul><li>T1 T2 </li></ul><ul><li>( N =164) ( N =138) </li></ul><ul><li>0 times 72.6% 69.6% </li></ul><ul><li>1 time 4.9% 5.8% </li></ul><ul><li>2-5 times 10.4% 8.7% </li></ul><ul><li>6-10 times 2.4% 2.2% </li></ul><ul><li>> 10 times 9.8% 13.8% </li></ul><ul><li>Period down up constant Missing </li></ul><ul><li>1 ==> 2 17 ( 29 steps ) 24 ( 49 steps ) 94 32 </li></ul>
    14. 14. SIENA Estimates and Standard Errors <ul><li>Network Effects: Est. SE </li></ul><ul><li>1. Outdegree -1.411 (0.065) *** </li></ul><ul><li>2. Reciprocity 1.434 (0.133) *** </li></ul><ul><li>3. Transitivity 0.024 (0.001) *** </li></ul><ul><li>Network Dynamics: </li></ul><ul><li>4. Weapon carrying similarity (selection) 0.087 (0.117) </li></ul><ul><li>Effect of weapon carrying on </li></ul><ul><li>5. Friendship nominations received 0.117 (0.033) *** </li></ul><ul><li>6. Friendship nominations given -0.065 (0.029) * </li></ul>
    15. 15. SIENA Estimates and Standard Errors <ul><li>Behavioral tendencies: Est. SE </li></ul><ul><li>7. Weapon Carrying Linear -1.100 (0.173) *** </li></ul><ul><li>8. Weapon Carrying Quadratic 0.582 (0.090) *** </li></ul><ul><li>Behavior Dynamics: </li></ul><ul><li>9. Weapon carrying similarity (influence) 3.316 (1.864) ~ </li></ul><ul><li>10. Effect of Aggression T1 2.270 (1.370) ~ </li></ul><ul><li>11. Effect of Victimization T1 -0.246 (1.187) </li></ul>
    16. 21. One-week Summer Course in Kansas <ul><li>Kansas University Summer Institute in Statistics </li></ul><ul><li>one-week course (June 15-19, 2009) &quot;Social Network Dynamics“ </li></ul><ul><li>taught by Tom Snijders </li></ul><ul><li>This will be the first workshop where the new version of SIENA implemented as an R package will be taught </li></ul><ul><li>Topics: </li></ul><ul><li>statistical analysis of network dynamics for complete networks </li></ul><ul><li>networks co-evolving with dependent actor variables </li></ul>
    17. 22. SNA Community <ul><li>Handbooks </li></ul><ul><li>Wasserman, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications . New York: Cambridge University Press. </li></ul><ul><li>Carrington, P.J., Scott, J., & Wasserman, S. (2005) (eds.) Models and methods in Social Network Analysis. New York: Cambridge University Press. </li></ul><ul><li>Journal: Social Networks </li></ul><ul><li>Conference: Sunbelt </li></ul>
    18. 23. Thank you for your attention Software and manual: http://stat.gamma.rug.nl/siena/
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