Introduction to the Models and Tools for Social Networks

1. Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann Krause, Ben Michael Pogodzinski, Bo Yan, Min Sun, I-Chen, Chong Min Kim

2. Abstract • Many quantitative analyses in the social sciences are applied to data regarding characteristics of people, but not to data describing interactions among people. But interactions play an important role in affecting people’s behavior and beliefs that cannot be explained purely in terms of individual attributes or organizational context. In this workshop we will focus on analyzing social network data (who interacts with whom) so that we can relate people's interactions with what they think and do. We draw on statistical concepts that account for the unusual nature of network data as well as substantive theories across the social sciences to specify and interpret social network models. • Topics include models of influence through a social network, choices in a social network, clustering and graphical representations; ethical issues and IRB, and software. Throughout examples are given using simple toy data and analyses in published papers. • Students taking this workshop should have roughly one year of applied statistics so that they are extremely comfortable with the general linear model (regression and ANOVA), and analysis of 2x2 tables.

9. Overview • Introduction • Overview • What Are Social Networks? • Representations of Social Networks: Sociomatrix • Representations: Notation • Representations: Sociogram • Characteristics of Social Network Data • Ego Centric Data • Favorites • Barry Wellman on Misconceptions • Doreian: Social Network Effects added to other... • Breiger: Tracking Network Analysis from Metaph... • Mine Frank: Integrating Social Networks into Models and G... • Personal • Two Fundamental Processes Involving Human Social Networks • Selection and Influence • Causality • Scramble Exercise • Influence • Selection • Graphical representations • Centrality • Ethics • Resources

10. What Are Social Networks? • A set of actors and the ties (resource flows) or relations (stable states) among them. • close colleagues (relation) among teachers (actors) • help (tie) one teacher (actor) provides to another • communication (tie) between people (actors) in an organization • friendships (relation) among politicians (actors) • links (relation) among web sites (actors) • referrals (tie) among social service agencies (actors) • For me: actors must • have agency • Able to take deliberate action • Actor network theory ? Can artifacts have agency and take deliberate action? • More than BookFace

11. Format of Network Data (W) Your name: Lisa Jones (person 1) Please indicate who helped you with computers at xxx and the frequency with which you interact with each person. Name Yearly Monthly Weekly Daily Bob Jones_(2)________ 1 2 3 4 Sue Meyer_(3)________ 1 2 3 4 ____________________ 1 2 3 4 ____________________ 1 2 3 4 Data entered (nominator, nominee, frequency) 1 2 2 1 3 4 Your name: Bob Jones (person 2) Please who helped you with computersat xxx and the frequency with which you interact with each person. Name Yearly Monthly Weekly Daily 1. Lisa Jones_(1)________ 1 2 3 4 2. Lin Freeman (4)_______ 1 2 3 4 3. ____________________ 1 2 3 4 4. ____________________ 1 2 3 4 Data entered (nominator, nominee, frequency) 2 1 2 2 4 3

12. Friendships among the French financial elite Edgelist 1 13 211 21112 1 17 1545463790 1 19 1|......111.| 25 14 25|..1....11.| 25 19 14|.1.1.1.11.| 14 25 15|..1..1.11.| 14 15 4|.......11.| 14 26 26|..11...11.| 14 17 13|1......11.| 14 19 17|1111111.11| 15 14 19|11111111..| 15 26 20|.......1..| 15 17 15 19 4 17 4 19 Representations of Social Networks Matrix

13. Representations: Notation • xij, takes a value of 1 if i nominates j, 0 otherwise: x1 25=0, x1 13=1 • Ken uses: • wii’, takes a value of 1 if i nominates i’, 0 otherwise: w1 25=0, w1 13=1

14. Representations: Sociogram Lines indicate friendships: solid within subgroups, dotted between subgroups. numbers represent actors Rgt,Cen,Soc,Non = political parties; B=Banker, T=treasury; E=Ecole National D’administration Frank, K.A. & Yasumoto, J. (1998). "Linking Action to Social Structure within a System: Social Capital Within and Between Subgroups." American Journal of Sociology, Volume 104, No 3, pages 642-686

18. Characteristics of Social Network Data • Directionality • If A nominates B as a bully, B may not nominate A as a bully • Valued relations • How frequently does teacher A interact with teacher B? • Multiple relations • Are students friends, romantic partners, coursemates? • Centricity • Sociocentric: whole social network • Egocentric: each person and their own network • Modes • One mode: actor to actor • Friendship, bullying • Two mode: actors and events • Students and the courses they attend • Ceo’s and the boards they are members of

19. Ego Centric Data Wellman, B.A. and Frank, K.A. 2001. "Network Capital in a Multi-Level World: Getting Support from Personal Communities." pages 233-274 in Social Capital: Theory and Research, Nan Lin, Ron Burt and Karen Cook. (Eds.). Chicago: Aldine De Gruyter

20. Frank, K.A., Muller, C., Schiller, K., Riegle-Crumb, C., Strassman-Muller, A., Crosnoe, R., Pearson J. 2008. “The Social Dynamics of Mathematics CourseTaking in high school.” American Journal of Sociology, Vol 113 (6): 1645-1696.

21. Two mode: actors and events

22. Favorites:Barry Wellman on Misconceptions

23. Favorites:Doreian: Social Network Effects added to other Effects • Inner causes: psychological motivation • Ascriptive effects: gender • Social network effects: centrality in group • Doreian, Patrick (2001). “Causality in Social network Analysis.” Sociological Methods and Research, Vol 30, No. 1, 81-114.

24. Favorites:Breiger: Tracking Network Analysis from Metaphor to Application • Great review of theoretical motivations for network analysis dating back to Marx, Durkheim, Cooley • Includes emphasis on cognition • Breiger, R.L. “The Analysis of Social Networks.” Pp. 505–526 in Handbook of Data Analysis, edited by Melissa Hardy and Alan Bryman. London: Sage Publications, 2004. http://www.u.arizona.edu/~breiger/NetworkAnalysis.pdf

25. MineFrank: Integrating Social Networks into Models and Graphical Representations • Multilevel models • Accounts for nesting of people within groups (e.g., students within schools) • Effects of groups modeled at the group level (e.g., effect of school restructuring on achievement • Assumptions • Groups independent of each other • People within groups independent of each other. Hmmmmmmmm. • People within schools influence each other • Student to student • Teacher to teacher • Teacher to student • People within schools select interaction partners • Adolescents’ friends and peers • Teachers’ close colleagues • Frank, K. A. 1998. "The Social Context of Schooling: Quantitative Methods". Review of Research in Education 23, chapter 5: 171-216.

26. Social Processes in Schools

27. Personal • I started my work with Valerie Lee, my dissertation chair was Tony Bryk, and my first faculty mentor was Steve Raudenbush. • Raudenbush, S. W., and A.S. Bryk. 2002 Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage. • This article is my recognition of their influences and then pushing to networks • Charles Bidwell played a strong roll • Aaron Pallas, Steve Raudenbush and Noah Friedkin as editors

28. Two Fundamental Processes Involving Human Social Networks • Influence: Change in actors’ beliefs or behaviors as a result of interaction with others • Teachers’ change uses of computers as a result of use of others’ around them (Frank, Zhao and Borman 2004) • Adolescents’ change effort in school in response to peers’ effort (Frank et al 2008, AJS; ) • Selection: Actors choose with whom to interact as a function of the characteristics of the chooser, chosen, and the dyad • Teachers choose to help others with technology based on close collegial ties (Frank and Zhao 2005) • French bankers choose whom to take supportive or hostile action against based on friendship structure (Frank and Yasumoto, 1998) • Who does one child nominate as a bully? • Each process relates social network to beliefs or behaviors Frank, K.A., & Fahrbach, K. (1999). "Organizational Culture as a Complex System: balance and Information in Models of Influence and Selection." Special issue of Organization Science on Chaos and Complexity, Vol 10, No. 3, pp. 253-277.

29. Selection and Influence Leenders, R. (1995). Structure and influence: Statistical models for the dynamics of actor attributes, network structure and their interdependence. Amsterdam: Thesis Publishers. • Selection and Influence always present • Ignore them at your peril! – biased / wrong estimates Change in Behavior Behavior | Influence selection Relations | Change in Relations 0 1 2 3 Time

30. Causality • Is it selection or influence? • Do people choose to interact with others like themselves (selection) or do they change • Birds of a feather flock together • Beliefs/behaviors based on interactions with others (influence)? • She’s hanging out with the wrong crowd! • Need longitudinal data!!!!!!! • Influence • With whom did you talk over the last week: asked at week 2 (12) • What are your beliefs? (asked at week 1) • What are your beliefs (asked at week 2) • Selection • With whom did you talk over the last week: asked at week 1 (0 1) • With whom did you talk over the last week: asked at week 2 (1 2) • What are your beliefs? (asked at week 1, or asked at weeks 1 and 2 and take the average)

31. Scramble Exercise • Think: Identify a network • Actors • Relations • Directionality, Valued relations, Multiple relations, Modality, Centricity • Process and bases of Influence • why would one person be influenced by another? • Process and bases of Selection • why would one person choose to interact with a specific other? • Form: Meet and share in groups of 3-4 • Others: Question bases for making inferences • Scramble: Form new group of 3-4 people • Matchmaker (at lunch): Identify matches of interest between members of first and second group

32. Statistical Issues • Dependencies among observations • A  B depends on • B  A • BC, C A • The return of multilevel models • Pairs within nominators and nominees • Alters within egos • People within subgroups within organizations • Sample and population (?!) • Need special techniques

33. Overview • Introduction • Influence • Influence: How Interactions Affect Beliefs and Behaviors • The Formal Model of Influence -- the Network Effect • Influence in Words (for teachers’ use of computers) • Exposure: Graphical Representation • Model and Equation: Toy Data • For Actor 3: • Influence Exercise • Influence Model with Toy Data Software • Questions about W: Timing • Studies of Teachers’ Implementation of Innovation • Measures of Y: Use of Computers • Format of Network Data (W) • General Influence Model in Empirical Example • Definitions of Social Capital (Individual Level) • Social Capital and the Network Effect • Modification: Capacity to Convey Resource • Longitudinal Model • Effects of Social Capital on Implementation of Computers ... • Importance of Controlling for the Prior: Longitudinal Data • Selection • Graphical Representations • Centrality • Ethics • Resources

34. Influence: How Interactions Affect Beliefs and Behaviorshttp://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547 (0-7:52) Research questions How does a teacher’s interactions affect her implementation of innovations? How does a banker’s interactions affect her profitability? How does an adolescent’s interactions affect her delinquency, alcohol use or engagement in school? Theoretical Mechanisms (see Frank and Fahrbach, 1999) Frank, K.A., & Fahrbach, K. (1999). "Organizational Culture as a Complex System: balance and Information in Models of Influence and Selection." Special issue of Organization Science on Chaos and Complexity, Vol 10, No. 3, pp. 253-277. Normative/conformity : change to conform to others around Information: change based on new information Dual processes: both apply Friedkin, Noah (2002). Social Influence Network Theory: Toward a Science of Strategic Modification of Interpersonal Influence Systems. In National Academy Press: Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers (2003). http://www.nap.edu/books/0309089522/html/ Overview

35. The Formal Model of Influence -- the Network Effect • wii’ Network. Extent of relation between i and i’, as perceived by i. • yit • Outcome. An attitude or behavior of actor i at time t • ∑i’wii’yi’t-1.. • Exposure. Sum of attributes of others to whom actor iis related at t-1. • yit= ρ∑i’wii’t-1tyi’t-1 +γ yit-1 +eit • Model. Errors are assumed iid normal, with mean zero and variance (σ2).

36. Influence in Words (for technology use) • Use of technology time 2i= • ρ[use of first colleague time 1] + • ρ[use of second colleague time 1] + • ρ[use of third colleaguetime 1] + • γ(use time 1)i + • error time 2i

37. Exposure: Graphical Representation

38. Model and Equation: Toy Data Y2 ρWY1 + γY1 + E2 = intercept+ 2 2 1 -.5 -2 -.5 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 x x x x x x 2.4 2.6 1.1 -.5 -3 - 1 0 x 2.4=0 1 x 2.6=2.6 0 x 1.1=0 1 x 6-.5=-.5 0 x -3 =0 1 x – 1=-1 Total =(1.1)/3 =.37 2.4 2.6 1.1 -.5 -3 - 1 .029 -.093 .094 -.027 -.025 .022 0 1 0 1 0 1 =.116+(.125) = + (.67) +

39. For Actor 3: y3 time 2= intercept+ ρ(y2 time 1+ y4 time 1+y6 time 1)/3 + γ y3 time 1 + e3 time 2 1=.116+.125*(2.6-.5-1)/3 + .67(1.1) + .094

40. Influence Exercise Assume Bob talks to Sue with frequency 1, to Lisa with frequency 3 and not at all to Jane. Last year (at time 1), Sue’s organic farming implementation behavior was a 9, Lisa’s was a 5 and Jane’s was 2. What is the mean of the exposure of Bob to his peers regarding organic farming? Hint ( Mean=sum/n, but what should n be?) Specify a model with two sources of exposure (e.g., within versus between subgroups) Influence answers

41. Influence Model with Toy Data Softwarehttp://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547(7:52-32:51) • http://www.msu.edu/~kenfrank/software.htm#Influence_Models_ • Influence program using means and merges in spss • (7:52-21:20) • Spss tutorials • http://www.stanford.edu/group/ssds/cgi-bin/drupal/files/Guides/software_docs_reading_raw_data_SPSS.pdf • http://www.hmdc.harvard.edu/projects/SPSS_Tutorial/spsstut.shtml • influence program using proc means and merges in sas • (21:20-32:51) • Sas tutorial: http://www.ats.ucla.edu/stat/sas/ • Influence program using means and merges in stata [save and uncompress] • Stata tutorial: http://www.ats.ucla.edu/stat/stata/

42. Exercise: Modifications to the Influence Model (SPSS) • Is influence increased if we weight exposure by the in-degree (number of times nominated) of the person influencing (i’)? • Change: COMPUTE exposure=relate * yvar1 • To: COMPUTE exposure=relate * yvar1*(indeg+1) • Is influence stronger of we take the sum instead of the mean? • Change: /exposure_mean_1=MEAN(exposure) • To: /exposure_sum_1=SUM(exposure) • Use exposure_sum_1 in the regression • What if you didn’t control for the prior? • Change: /METHOD=ENTER exposure_mean_1 yvar1. • To /METHOD=ENTER exposure_mean_1. • Does coefficient for exposure term depend on prior (interaction term)? • run influence for technology

43. Exercise: Modifications to the Influence Model (SAS) • Is influence increased if we weight exposure by the in-degree (number of times nominated) of the person influencing (i’)? • Set useattr=1; • Is influence stronger of we take the sum instead of the mean? • Change: mean=totinfl • To: sum=totinfl • What if you didn’t control for the prior? • Change: model yvar2=totinfl yvar1; • To: model yvar2=totinfl ; • Does coefficient for exposure term depend on prior (interaction term) • run influence for technology

44. Questions about W: Timing • Should we use simultaneous or staggered behavior? • Yt=ρWYt • accounts for all direct and indirect (or primary, secondary, tertiary, etc) effects • hard to estimate (Y on both sides) • Christakis and Fowler • http://www.nytimes.com/2009/09/13/magazine/13contagion-t.html?_r=1&pagewanted=1&ref=magazine • Yt=ρWYt-1 • easier to estimate • Only direct effects • et=ρWet • Autocorrelated disturbances – exposed to the same effects • Charles Manski’s reflection problem

45. Observational studies with controls for pretests work better than you think Shadish et al (JASA 2008) • Quantify how much biased removed by statistical control using pretests in a given setting • Sample: Volunteer undergraduates • Outcome: Math and vocabulary tests • Treatment: • basic didactic, • showing transparencies • defining math concepts • OLS Regression with pretests removes 84% to 94% of bias relative to RCT!! • Propensity by strata not quite as good • See also Concato et al., 2000 for a comparable example in medical research

46. OLS might not work • So what would it take to change an inference? • How strong must a confound be to reduce estimated effect below a threshold for making an inference? • https://www.msu.edu/~kenfrank/research.htm#causal • Related to: how bad would your sample have to be to invalidate your inference?

47. Questions about W:Cohesion versus Structural Equivalence • Cohesion -- direct connections/communication Examples: Students’ educational and aspirations decisions are influenced through direct discussions Adolescents’ delinquency is influenced by the delinquency of their friends • Structural Equivalence -- common roles/comparison & comparison Examples Students who occupy similar positions defined by curricular tracks may develop similar educational aspirations Businesses who sell to similar others may adopt similar practices • Direct Influence versus Indirect Influence (Leenders) • Are you influenced by those who you do not talk to, but with whom you share intermediaries?

48. Redundant Effects through A Network

49. Questions about W: Row Normalization and Interpretation of Influence • Divide values by row marginal • Different transformation for each subject • Changes metric to “influence units” • Access of one unit of expertise of one influence unit increases number of uses of computers by xx per year. • Theoretical meaning of “influence units” versus frequency of interaction • Could you model “influence unit” with a selection model?

50. Articles on Causality