Home reflection Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann.

home reflection 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 1

home reflectionAbstract  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. 2

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Kindred Britain 9 http://news.stanford.edu/news/2013/august/kindred-britain-database-082613.html

10 http://www.nytimes.com/interactive/2013/02/20/movies/among-the-oscar-contenders-a- host-of-connections.html

home reflectionOverview  Introduction Introduction  Overview Overview  What Are Social Networks? What Are Social Networks? What Are Social Networks?  Representations of Social Networks: Sociomatrix Representations of Social Networks: Sociomatrix Representations of Social Networks: Sociomatrix  Representations: Notation Representations: Notation Representations: Notation  Representations: Sociogram Representations: Sociogram Representations: Sociogram  Characteristics of Social Network Data Characteristics of Social Network Data Characteristics of Social Network Data  Ego Centric Data Ego Centric Data Ego Centric Data  Favorites  Barry Wellman on Misconceptions Barry Wellman on Misconceptions Barry Wellman on Misconceptions  Doreian: Social Network Effects added to other... Doreian: Social Network Effects added to other... Doreian: Social Network Effects added to other...  Breiger: Tracking Network Analysis from Metaph... Breiger: Tracking Network Analysis from Metaph... Breiger: Tracking Network Analysis from Metaph...  Mine Frank: Integrating Social Networks into Models and G... Mine Frank: Integrating Social Networks into Models and G... Mine Frank: Integrating Social Networks into Models and G...  Personal Personal  Two Fundamental Processes Involving Human Social Networks Two Fundamental Processes Involving Human Social Networks Two Fundamental Processes Involving Human Social Networks  Selection and Influence Selection and Influence Selection and Influence  Causality Causality  Scramble Exercise Scramble Exercise Scramble Exercise  Influence Influence  Selection Selection  Graphical representations Graphical representations Graphical representations  Centrality Centrality  Ethics  Resources Resources 11

home reflectionReflection  What part is most confusing to you?  Why?  More than one interpretation?  Talk with one other, share

home reflection 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 cites (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?  http://en.wikipedia.org/wiki/Actor%E2%80%93network_theory http://en.wikipedia.org/wiki/Actor%E2%80%93network_theory  More than BookFace 13

home reflection 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)________1234 Sue Meyer_(3)________1234 ____________________1234 Data entered (nominator, nominee, frequency) 1 2 2 1 3 4 Your name: Bob Jones (person 2) Please who helped you with computers at xxx and the frequency with which you interact with each person. Name Yearly Monthly Weekly Daily 1.Lisa Jones_(1)________1234 2. Lin Freeman (4)_______ 1234 3. ____________________1234 4. ____________________1234 Data entered (nominator, nominee, frequency) 2 1 2 2 4 3 14

Representations of Social Networks Friendships among the French financial elite Edgelist Edgelist 1 13 1 13 211 21112 1 17 211 21112 1 17 1545463790 1 19 1545463790 1 19 1|......111.| 25 14 1|......111.| 25 14 25|..1....11.| 25 19 25|..1....11.| 25 19 14|.1.1.1.11.| 14 25 14|.1.1.1.11.| 14 25 15|..1..1.11.| 14 15 15|..1..1.11.| 14 15 4|.......11.| 14 26 4|.......11.| 14 26 26|..11...11.| 14 17 26|..11...11.| 14 17 13|1......11.| 14 19 13|1......11.| 14 19 17|1111111.11| 15 14 17|1111111.11| 15 14 19|11111111..| 15 26 19|11111111..| 15 26 20|.......1..| 15 17 20|.......1..| 15 17 15 19 15 19 4 17 4 17 4 19 4 19 15 125141542613171920 1111 25111 1411111 151111 411 261111 13111 17111111111 1911111111 201 Matrix

home reflection Representations: Notation  x ij, takes a value of 1 if i nominates j, 0 otherwise: x 1 25 =0, x 1 13 =1  Ken uses:  w ii’, takes a value of 1 if i nominates i’, 0 otherwise: w 1 25 =0, w 1 13 =1  ii’ represents the fact that it’s the same people, but in different roles, either as sender or receiver 16

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 17

home reflection 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 20

home reflection 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 21

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. 22

Two mode: actors and events 23

One-Mode Projection vs Two Mode data Field, S. *Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. (2006). "Identifying Social Contexts in Affiliation Networks: Preserving the Duality of People and Events. Field, S. *Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. (2006). "Identifying Social Contexts in Affiliation Networks: Preserving the Duality of People and Events. Social Networks 28:97- 123

Favorites: Barry Wellman on Misconceptions 25

home reflection 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. 26

home reflection 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 http://www.u.arizona.edu/~breiger/NetworkAnalysis.pdf 27

home reflection Mine Frank: 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. Frank, K. A. 1998. "The Social Context of Schooling: Quantitative Methods". Review of Research in Education 23, chapter 5: 171-216. Frank, K. A. 1998. "The Social Context of Schooling: Quantitative Methods". Review of Research in Education 23, chapter 5: 171-216.   Frank, K. A., S. Maroulis, D. Belman, and M. D. Kaplowitz. 2011. The social embeddedness of natural resource extraction and use in small fishing communities. Pages 309-332 in W. W. Taylor, A. J. Lynch, and M. G. Schechter, editors. Sustainable fisheries: multi-level approaches to a global problem. American Fisheries Society, Bethesda, Maryland. Frank, K. A., S. Maroulis, D. Belman, and M. D. Kaplowitz. 2011. The social embeddedness of natural resource extraction and use in small fishing communities. Pages 309-332 in W. W. Taylor, A. J. Lynch, and M. G. Schechter, editors. Sustainable fisheries: multi-level approaches to a global problem. American Fisheries Society, Bethesda, Maryland.     Frank, K.A. 2011. Social Network Models for Natural Resource Use and Extraction. Social networks and natural resource management: Uncovering the social fabric of environmental governance. Pp. 180-205. Örjan Bodin & Christina Prell editors. Cambridge: Cambridge University Press. Frank, K.A. 2011. Social Network Models for Natural Resource Use and Extraction. Social networks and natural resource management: Uncovering the social fabric of environmental governance. Pp. 180-205. Örjan Bodin & Christina Prell editors. Cambridge: Cambridge University Press. 28

Social Processes in Schools 29

home reflectionPersonal  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. 2002Hierarchical 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 30

home reflection 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. 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. See notes for other papers 31

home reflection Selection and Influence  Selection and Influence always present  Ignore them at your peril! – biased / wrong estimates Influence selection 01 2 3 Time Change in Behavior Change in Relations Behavior | Relations | Leenders, R. (1995). Structure and influence: Statistical models for the dynamics of actor attributes, network structure and their interdependence. Amsterdam: Thesis Publishers. 32

home reflectionCausality  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) 33

home reflection Scramble Exercise  Think: Identify a network  Actors  Relations or ties  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 34

home reflection 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 35

home reflectionOverview  Introduction Introduction  Influence Influence  Influence: How Interactions Affect Beliefs and Behaviors Influence: How Interactions Affect Beliefs and Behaviors Influence: How Interactions Affect Beliefs and Behaviors  The Formal Model of Influence -- the Network Effect The Formal Model of Influence -- the Network Effect The Formal Model of Influence -- the Network Effect  Influence in Words (for teachers’ use of computers) Influence in Words (for teachers’ use of computers) Influence in Words (for teachers’ use of computers)  Exposure: Graphical Representation Exposure: Graphical Representation Exposure: Graphical Representation  Model and Equation: Toy Data Model and Equation: Toy Data Model and Equation: Toy Data  For Actor 3: For Actor 3: For Actor 3:  Influence Exercise Influence Exercise Influence Exercise  Influence Model with Toy Data Software Influence Model with Toy Data Software Influence Model with Toy Data Software  Questions about W: Timing Questions about W: Timing Questions about W: Timing  Studies of Teachers’ Implementation of Innovation Studies of Teachers’ Implementation of Innovation Studies of Teachers’ Implementation of Innovation  Measures of Y: Use of Computers Measures of Y: Use of Computers Measures of Y: Use of Computers  Format of Network Data (W) Format of Network Data (W) Format of Network Data (W)  General Influence Model in Empirical Example General Influence Model in Empirical Example General Influence Model in Empirical Example  Definitions of Social Capital (Individual Level) Definitions of Social Capital (Individual Level) Definitions of Social Capital (Individual Level)  Social Capital and the Network Effect Social Capital and the Network Effect Social Capital and the Network Effect  Modification: Capacity to Convey Resource Modification: Capacity to Convey Resource Modification: Capacity to Convey Resource  Longitudinal Model Longitudinal Model Longitudinal Model  Effects of Social Capital on Implementation of Computers... Effects of Social Capital on Implementation of Computers... Effects of Social Capital on Implementation of Computers...  Importance of Controlling for the Prior: Longitudinal Data Importance of Controlling for the Prior: Longitudinal Data Importance of Controlling for the Prior: Longitudinal Data  Selection Selection  Graphical Representations Graphical Representations Graphical Representations  Centrality Centrality  Ethics  Resources Resources 36

home reflection Influence: How Interactions Affect Beliefs and Behaviors video (0-7:52) video 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. 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 Competition (Burt) Competition (Burt) 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/ http://www.nap.edu/books/0309089522/html/ Overview 37

The Formal Model of Influence -- the Network Effect  w ii’ Network. Extent of relation between i and i’, as perceived by i.  y it  Outcome. An attitude or behavior of actor i at time t  ∑ i’ w ii’ y i’t-1..  Exposure. Sum of attributes of others to whom actor i is related at t-1.  y it = ρ ∑ i’ w ii’t-1  t y i’t-1 +γ y it-1 +e it  Model. Errors are assumed iid normal, with mean zero and variance (σ2). 38

Influence in Words (for technology use) Use of technology time 2 i = ρ[use of first colleague time 1] + ρ[use of second colleague time 1] + ρ[use of third colleaguetime 1] + ρ[use of third colleague time 1] + γ(use time 1) i + error time 2 i 39

Exposure: Graphical Representation 40

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 ρ WY 1 2.4 2.6 1.1 -.5 -3 - 1 γY1γY1 Y2Y2 2 1 -.5 -2 -.5 = intercept+ =.116+(.125) + ++ E 2 2.4 2.6 1.1 -.5 -3 - 1 Model and Equation: Toy Data.029 -.093.094 -.027 -.025.022 + (.67) 0 1 0 1 0 1 0 1 0 1 0 1 x 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 = 41

home reflection For Actor 3: y 3 time 2 = intercept+ ρ( y 2 time 1 + y 4 time 1 +y 6 time 1 )/3 + γ y 3 time 1 + e 3 time 2 1=.116+.125*(2.6-.5-1)/3 +.67(1.1) +.094 42

home reflection Data structure in spss to make exposure term 43 wpair totinfl i i’w

home reflection 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 44

home reflection Influence Model with Toy Data Software video (7:52-32:51) video  http://www.msu.edu/~kenfrank/software.htm#Influence_Models_ http://www.msu.edu/~kenfrank/software.htm#Influence_Models_  Influence program using means and merges in spss Influence program using means and merges in spss Influence program using means and merges in spss  Note that nominator is i, nominee is i’ and w is relate.  (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.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 http://www.hmdc.harvard.edu/projects/SPSS_Tutorial/spsstut.shtml  influence program using proc means and merges in sas influence program using proc means and merges in sas 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] Influence program using means and merges in stata Influence program using means and merges in stata  Stata tutorial: http://www.ats.ucla.edu/stat/stata/ http://www.ats.ucla.edu/stat/stata/ 45

home reflection 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.  run influence for technology 46

home reflection 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 ;  run influence for technology 47

home reflection Questions about W: Timing  Should we use simultaneous or staggered behavior?  Y t =ρWY t  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 http://www.nytimes.com/2009/09/13/magazine/13contagion- t.html?_r=1&pagewanted=1&ref=magazine http://www.nytimes.com/2009/09/13/magazine/13contagion- t.html?_r=1&pagewanted=1&ref=magazine  Y t =ρWY t-1  easier to estimate  Only direct effects  e t =ρWe t  Autocorrelated disturbances – exposed to the same effects  Charles Manski’s reflection problem 48

home reflection Examples of Influence Models Sun, M., Penuel, W., Frank, K.A., and Gallagher, A. Forthcoming. “Shaping Professional Development to Promote the Diffusion of Instructional Expertise among Teachers”. Education, Evaluation and Policy Analysis. Sun, Min., Frank, K.A., Penuel, W. and Kim, Chong Min. 2013. “How External Institutions Penetrate Schools through Formal and Informal Leaders”. Educational Administration Quarterly 49(4), 610- 644.Sun, Min., Frank, K.A., Penuel, W. and Kim, Chong Min. 2013. “How External Institutions Penetrate Schools through Formal and Informal Leaders”. Educational Administration Quarterly 49(4), 610- 644. http://eaq.sagepub.com/content/early/2013/03/18/0013161X12468148http://eaq.sagepub.com/content/early/2013/03/18/0013161X12468148 Frank*, K.A., Penuel*, W.R., Sun, M. Kim, C., and Singleton, C. 2013. “The Organization as a Filter of Institutional Diffusion. Teacher’s College Record. *Authors listed alphabetically – equal authorship. Volume 115(1). http://www.tcrecord.org/Content.asp?ContentID=16742Frank*, K.A., Penuel*, W.R., Sun, M. Kim, C., and Singleton, C. 2013. “The Organization as a Filter of Institutional Diffusion. Teacher’s College Record. *Authors listed alphabetically – equal authorship. Volume 115(1).http://www.tcrecord.org/Content.asp?ContentID=16742 Frank, K.A., Zhao, Y., Penuel, W.R., Ellefson, N.C., and Porter, S. 2011. Focus, Fiddle and Friends: Sources of Knowledge to Perform the Complex Task of Teaching. Sociology of Education, Vol 84(2): 137-156. Youngs, P., Frank, K.A., and Pogodzinski, B. 2011. The Role of Mentors and Colleagues in Beginning Elementary and Middle School Teachers’ Language Arts Instruction. Chapter 8 in Sean Kelly, Editor. Understanding Teacher Effects. New York: Teachers’ College Press. Penuel, W.R., Frank, K.A., and Krause, A. 2010. Between Leaders and Teachers: Using Social Network Analysis to Examine the Effects of Distributed Leadership. Pages 159-178 in Alan J. Daly editor. Social Network Theory and Educational Change. Cambridge: Harvard University Press. Penuel, W. R., Riel, M., Joshi, A., & Frank, K. A. 2010. The alignment of the informal and formal supports for school reform: Implications for improving teaching in schools.Educational Administration Quarterly, 46(1), 57-95.Educational Administration Quarterly Frank, K. A., Zhao, Y., and Borman (2004). Social Capital and the Diffusion of Innovations within Organizations: Application to the Implementation of Computer Technology in Schools." Sociology of Education, 77: 148-171. Zhao, Y. and Frank, K. A., (2003). "An Ecological Analysis of Factors Affecting Technology Use in Schools." American Educational Research Journal, 40(4): 807-840. 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. 49

Concerns about Causality 50 Outcome behavior Prior behavior Behavior of network members selection influence

Answer: Control for Prior Behavior! 51 There are heightened concerns about potential dependencies in estimating any social network model (e.g., Robins et al., 2007; Steglich, Snijders and Pearson, 2010 ). Regarding model 91) estimated influence is biased if the errors are not independent of the network exposure term (see Ord, 1975, equations 1.2-1.4); the estimate of influence will be positively biased if there is some unexplained aspect of enforcement behavior that is related to the network exposure. The most compelling source of such dependencies would be if people choose to interact with others whose behaviors are similar to their own, known as selection in the network literature. Those who tended to engage in enforcement at time 1 might have chosen to interact with similar others between time 1 and time 2, and also would have been inclined to engage in enforcement behaviors at time 2. Because the network exposure term is likely confounded with prior enforcement behavior, model 1 includes a control for prior enforcement behavior. A second concern in the influence model would arise if the model of a fisherman’s behaviors was a function of the contemporaneous behaviors of his/her network members. This would essentially put the outcome on both sides of the model in which case the errors would be directly related to the exposure term. It is for this reason that we model enforcement behavior as a function of the previous behaviors of others in one’s network. This avoids creating dependenices beteween the errors and predictors by putting the same variables on both sides of the model. Even given our approach there may still be concerns about omitted variables that create dependencies between the errors and the exposure term. Therefore we quantify the robustness of our inferences to potential omitted variables (Frank, 2000 ). Steglich, Christian E.G. Tom A.B. Snijders, and Michael Pearson (2010). Dynamic Networks and Behavior: Separating Selection from Influence. Sociological Methodology, 40, 329-392.Dynamic Networks and Behavior: Separating Selection from Influence. Ord, Keith. "Estimation methods for models of spatial interaction."Journal of the American Statistical Association 70.349 (1975): 120-126. Robins, Garry L., Tom A.B. Snijders, Peng Wang, Mark Handcock, and Philippa Pattison. Recent developments in exponential random graph (p*) models for social networks. Social Networks 29 (2007), 192- 215.Recent developments in exponential random graph (p*) models for social networks

Verify with Simulation (student Ran Xu) 52

home reflection Must Control for Prior 54

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home reflection 56 Must Control for Prior

home reflection Christakis & Fowler: Contagion of Obesity 57

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home reflection C&F: Methods 59 Lagged controls?

home reflection Christakis & Fowler Model  Should we use simultaneous or staggered behavior?  They use both:  y it = ρ 1 ∑ i’ w ii’t y i’t /∑ i’ w ii’t + ρ 2 ∑ i’ w ii’t y i’t-1 /∑ i’ w ii’t + γ y it-1 +e it  Obesity 2000 =ρ 1 obesity of friends 2000 +ρ 2 obesity of friends 1997 + γ own obesity it-1 +e t :  Lyons: ρ 1 and ρ 2 have opposite signs. Hmmmm.  Collinearity problems? 60

Christakis and Fowler Debate: Lyons 61

home reflection Lyons, Russell The spread of evidence-poor medicine via flawed social-network analysis, Stat., Politics, Policy 2, 1 (2011), Article 2. DOI: 10.2202/2151-7509.1024 See Andrew Gelman: http://themonkeycage.org/blog/2011/06/10/1-lyonss-statistical-critiques-seem- reasonable-to-me-there-could-well-be-something-important-that-im-missing-but-until-i-hear-otherwise- for-example-in-a-convincing-reply-by-christakis-and-f/http://themonkeycage.org/blog/2011/06/10/1-lyonss-statistical-critiques-seem- reasonable-to-me-there-could-well-be-something-important-that-im-missing-but-until-i-hear-otherwise- for-example-in-a-convincing-reply-by-christakis-and-f/ Critique of Christakis and Fowler “influence” model pages 5-6

home reflection Christakis & Fowler Model  Should we use simultaneous or staggered behavior?  They use both:  y it = ρ 1 ∑ i’ w ii’t y i’t /∑ i’ w ii’t + ρ 2 ∑ i’ w ii’t y i’t-1 /∑ i’ w ii’t + γ y it-1 +e it  Obesity 2000 =ρ 1 obesity of friends 2000 +ρ 2 obesity of friends 1997 + γ own obesity it-1 +e t  Same data on right and left hand sides of model  Lyons: ρ 1 and ρ 2 have opposite signs: hmmm  Collinearity problems? 63

home reflection C&F: Methods 64 directionality

home reflection Christakis & Fowler: Directionality Results 65 Are they statistically different from one another? No.

66 Articles on Causality

Articles on Causality 69

home reflection It’s all in how you talk about it!  Do best method you can  Include relevant controls!  But science is as much in the nature of the discourse as the method  Virtue epistemology  Greco, 2009; Kvanig, 2003; Sosa, 2007  What would it take to invalidate the inference?  How much bias must be present to invalidate an inference?  https://www.msu.edu/~kenfrank/research.htm#causal https://www.msu.edu/~kenfrank/research.htm#causal   Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460. Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460.

home reflection Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460. Abstract Abstract We contribute to debate about causal inferences in educational research in two ways. First, we quantify how much bias there must be in an estimate to invalidate an inference. Second, we utilize Rubin’s causal model (RCM) to interpret the bias necessary to invalidate an inference in terms of sample replacement. We apply our analysis to an inference of a positive effect of Open Court Curriculum on reading achievement from a randomized experiment, and an inference of a negative effect of kindergarten retention on reading achievement from an observational study. We consider details of our framework, and then discuss how our approach informs judgment of inference relative to study design. We conclude with implications for scientific discourse. We contribute to debate about causal inferences in educational research in two ways. First, we quantify how much bias there must be in an estimate to invalidate an inference. Second, we utilize Rubin’s causal model (RCM) to interpret the bias necessary to invalidate an inference in terms of sample replacement. We apply our analysis to an inference of a positive effect of Open Court Curriculum on reading achievement from a randomized experiment, and an inference of a negative effect of kindergarten retention on reading achievement from an observational study. We consider details of our framework, and then discuss how our approach informs judgment of inference relative to study design. We conclude with implications for scientific discourse. Keywords: causal inference; Rubin’s causal model; sensitivity analysis; observational studies

home reflection Questions about W: Cohesion versus Structural Equivalence 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? 73 Leenders, R.Th.A.J., 2002, ““Modeling Social Influence through Network Autocorrelation: Constructing the Weight Matrix.”” Social Networks, 24: 21-47. Available via science direct: http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5969&_auth=y&_acct=C000050221&_versio n=1&_urlVersion=0&_userid=10&md5=0dbd43b8d4784bc1532be7b6c056be81

home reflection Redundant Effects through A Network 74

home reflection 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? 75

home reflection Studies of Teachers’ Implementation of Innovation video (32:51-40:00) video  Enumerated network within elementary schools  Network questions: e.g., “who has helped you use computers in the last year”  Longitudinal  2 measures of use of computers a year apart  Multiple studies:  Technology, 6 schools across nation (1999-2000)  Technology in 26 schools in one state (2002-2003)  Reforms in 21 schools in one state (2004-2005)  Collective Efficacy in 41 schools in two states (2005- 2006) 76

home reflection Measures of Y: Use of Computers Teacher’s Use of Technology at Time 2 (α=.94) I use computers to help me... Never Yearly Monthly Weekly Daily 1 2 |3 4 5 introduce new material into the curriculum. 1 2 |34 5 guide student communication. 1 2 |3 4 5 model an idea or activity. 1 2 |34 5 connect the curriculum to real world tasks. 1 23 | 4 5 teach the required curriculum. 1 2 3 | 4 5 motivate students. | indicates mean response Expertise (α=.76): Use at time 1 for teacher and student purposes (e.g., to help students communicate) Total number of applications with which the teacher was familiar at time 2 extent to which the teacher reported being able to operate computers at time 2 How confident the teacher felt with computers at time 2 77

home reflection 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)________1234 Sue Meyer_(3)________1234 ____________________1234 Data entered (nominator, nominee, frequency) 1 2 2 1 3 4 Your name: Bob Jones (person 2) Please who helped you with computers at xxx and the frequency with which you interact with each person. Name Yearly Monthly Weekly Daily 1.Lisa Jones_(1)________1234 2. Lin Freeman (4)_______ 1234 3. ____________________1234 4. ____________________1234 Data entered (nominator, nominee, frequency) 2 1 2 2 4 3 78

home reflection General Influence Model in Empirical Example Y=ρWY  Y: Teacher’s use of computers in classroom (in times used per year)  W: help or talk about technology (in days per year)  ρ: network effect of interaction on use of computers Frank, K. A., Zhao, Y., and Borman (2004). Social Capital and the Diffusion of Innovations within Organizations: Application to the Implementation of Computer Technology in Schools." Sociology of Education, 77: 148-171. 79

Exposure to Expertise of Others 80

home reflection Questions regarding W  Take sum or Mean?  Timing?  Cohesion versus structural equivalence  Social capital as a guide 81

home reflection Definitions of Social Capital Alejandro Portes (1998 "Social Capital: Its Origins and Applications in Modern Sociology." Annual Review of Sociology, Vol 24, pages 1-24, page 7): “...the consensus is growing in the literature that social capital stands for the ability of actors to secure benefits by virtue of membership in social networks or other social structures.” (emphasis added) See also Nan Lin: (1999. Building a network theory of social capital. Connections, 22(1), 28-51.): Refers to social capital as “Investment in social relations by individuals through which they gain access to embedded resources to enhance expected returns of instrumental or expressive actions. (emphasis added) 82

Social Capital and the Network Effect Social Capital= potential to access resources through social relations Resource =Expertise Social relation=relation with colleague, help from teacher i’ to teacher I is the tie marking when the resource flows 83

Modification: Capacity to Convey Resource Knoke: account for probability that resource is conveyed through any interaction Proxy for ability to convey help: amount of help provided to others 84

home reflection Longitudinal Model  y i t =intercept+ρ∑ i’ w ii’ t-1→t y i’ t-1 x ∑ i w ii’ +γy it-1  Take sum (resources accessed)  Partial control for selection of similar or valuable others by including y it-1  Continuity through γ. 85

Effects of Social Capital on Implementation of Computers in the Classroom 86

Importance of Controlling for the Prior: Longitudinal Data 87

home reflection Metric Based on Expertise/Day  WY is an interaction:  units = days per year x expertise  Solution 1: interpret standardized coefficients  Network effect as strong as perceptions  Solution 2:  Divide by number of days in a year: WY/365,  new metric is access to expertise per day .23WY =.23Help x Expertise=84Help x Expertise/365  Access of one unit of expertise per day increases number of uses of computers by 84 per year.  Solution 3: If you use the mean for the exposure term, and the interactions are unweighted, then the metric for the exposure term is the same as for one’s own prior belief/behavior, and you can compare the coefficient for exposure with the coefficient for the prior. 88

home reflection Your own Influence Model A) A)Identify a network in which you are interested B) Characterize the theoretical processes of influence that occur in the network. Through what mechanisms due actors influence each other? What is conveyed through a tie or relation that could change an actor’s belief or behavior? C) write down a model of influence 1) How should W be specified -- what is the relation? 2) What is the time interval during which interaction occurs With a partner III) Critique the other person’s influence model A) Does the model capture the theoretical influence processes? If not, what needs to be added or modified? B) Does the time interval seem reasonable? C) Is the process based on cohesion or structural equivalence? D) How would you measure the variables, w and y in your model? 89

home reflectionOverview  Introduction Introduction  Influence Influence  Selection Selection  Selection: How Actors Choose Others with whom to Interact Selection: How Actors Choose Others with whom to Interact Selection: How Actors Choose Others with whom to Interact  Selection Model Selection Model Selection Model  Selection Exercise Selection Exercise Selection Exercise  Estimation of Selection Model Estimation of Selection Model Estimation of Selection Model  The p1 Approach The p1 Approach The p1 Approach  Visual Representations of p2 Model Visual Representations of p2 Model Visual Representations of p2 Model  Reciprocity: Wii’ (as yij) Wi’i (as yji) Modeled Simultan... Reciprocity: Wii’ (as yij) Wi’i (as yji) Modeled Simultan... Reciprocity: Wii’ (as yij) Wi’i (as yji) Modeled Simultan...  Basic Selection Model (p2) Basic Selection Model (p2) Basic Selection Model (p2)  Toy Data Toy Data Toy Data  Setting up p2 Setting up p2 Setting up p2  Example Output for p2 for Toy Data see also http://stat.g... Example Output for p2 for Toy Data see also http://stat.g... Example Output for p2 for Toy Data see also http://stat.g...  Selection model (p2): Toy Data Selection model (p2): Toy Data Selection model (p2): Toy Data  Prediction for Pair (2,5) Selection Model (p2): Toy Data  Selection Application Transition from Social Exchange to quasi ties... Selection Application Transition from Social Exchange to quasi ties... Selection Application Transition from Social Exchange to quasi ties...  Alternatives for Running p2 Alternatives for Running p2 Alternatives for Running p2  Graphical Representations Graphical Representations Graphical Representations  Centrality Centrality  Ethics  Resources Resources 90

home reflection Examples of Research Questions How do farmers decide to whom to provide help? How do bankers decide to whom to loan money? How do social service agencies choose other agents to refer clients to? 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. 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. Balance seeking/homophily -- seeking to interact with others like yourself Information seekingGoal oriented, Reduce uncertainty, Power oriented, Better understanding, Curiosity, Inoculate Constraints on exposure (Frank et al 2013) Evidence of Effects Adolescents select friends who are like themselves Teachers who want to be innovative interact with other innovators Selection: How Actors Choose Others with whom to Interact video : (0:00-19:40) video Overview 91

home reflection Examples of Selection Frank, K.A., Muller, C., Mueller, A.S., 2013. The Embeddedness of Adolescent Friendship Nominations: The Formation of Social Capital in Emergent Network Structures. American Journal of Sociology, Vol 119(1):216-253.Frank, K.A., Muller, C., Mueller, A.S., 2013. The Embeddedness of Adolescent Friendship Nominations: The Formation of Social Capital in Emergent Network Structures. American Journal of Sociology, Vol 119(1):216-253. Media hits: Atlantic; Huffington Post; Huffington Post (Op-ed); US News and World Report; Yahoo; Health Day; RedOrbit;The Times of India; MSUToday: Psych Central: Positions and Promotions; Deccan Chronicle: wood radio: Fox Chicago: local news channels (south Carolina): Science Daily;National Science FoundationAtlanticHuffington PostHuffington Post (Op-ed)US News and World ReportYahoo;Health DayRedOrbitThe Times of IndiaMSUToday:Psych Central:Positions and PromotionsDeccan Chronicle:wood radio:Fox Chicago:local news channels (south Carolina):Science DailyNational Science Foundation Spillane, J., Kim, Chong Min, Frank, K.A. 2012. “Instructional Advice and Information Providing and Receiving Behavior in Elementary Schools: Exploring Tie Formation as a Building Block in Social Capital Development.” American Educational Research Journal. Vol 49 no. 6 1112-1145 Crosnoe, Robert, Anna Strassman-Mueller, and Frank, K.A. 2008. “Gender, Body Size, and Social Relations in American High Schools.” Social Forces 86: 1189-1216. Frank, K. A. and Zhao, Y. (2005). "Subgroups as a Meso-Level Entity in the Social Organization of Schools." Chapter 10, pages 279-318. Book honoring Charles Bidwell's retirement, edited by Larry Hedges and Barbara Schneider. New York: Sage publications. 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 92

home reflection Selection Model Absolute value of difference in attributes Represents the effect of difference in attribute 93

home reflection The Logistic Regression Model The "logit" model solves these problems: ln[p/(1-p)] =  0 +  1 X  p is the probability that the event Y occurs, p(Y=1)  [range=0 to 1]  p/(1-p) is the "odds ratio"  [range=0 to ∞]  ln[p/(1-p)]: log odds ratio, or "logit“  [range=-∞ to +∞] 94

Interpretation of Ogive  The logistic distribution constrains the estimated probabilities to lie between 0 and 1.  The estimated probability is: p = e (  0 +  1X) /[1 + e (  0 +  1X ) ]  if you let  0 +  1 X =0, then p =.50  as  0 +  1 X gets really big, p approaches 1  as  0 +  1 X gets really small, p approaches 0 96

home reflection Selection Exercise A) Write a model for whether two actors talked as a function of whether they are of different race and whether they are of different gender. w ii’ represents whether i and i’ talked, y i represents the gender of i (0 if male, 1 if female), and z i represents the race of i (0 if white, 1 if African American) (You’ll need one term for effects associated with gender, and another for race) 97

home reflection Selection Exercise B) Assume that Bob and Lisa are African American and that Jane and Bill are white. Bill and Bob are Male and Lisa and Jane are female. Calculate the independent variables based on difference of race and gender for Bob with each of his interaction partners: (Bob, Lisa): different gender = _______; different race = _________ (Bob, Jane): different gender =_______; different race = _________ (Bob, Bill): different gender = _______; different race =__________ 98

home reflection Selection Exercise C) Assuming the values of the θ ’s are negative and that the effect of race is stronger than that of gender, who is Bob most likely to talk to? D) Include a term capturing the interaction of similarity of race and gender Selection answers 99

Estimation of Selection Model Use the example of w ii’ being whether one teacher helped another Naive: logistic regression: Similarity of attributes captured by -|y i t-h - y i’ t-h |. Likelihood function: p(A and B) = p(A)×p(B) if A and B are independent. NO! Help ii’ is not independent of Help ii” ! 100

The p 1 Approach W i’i =0 W i’i =1 W ii’ =0 Cell A (reciprocity) Cell B W ii’ =1 Cell C Cell D (reciprocity) W ii’ =0 Model as 4 cells, A,B,C,D instead of just W ii’ =0 Holland, Paul W. and S. Leinhardt. 1981. "An Exponential Family of Probability Distributions for Directed Graphs." Journal of American Statistical Association 76(373):33-49. 101

Estimation via p* 102

Visual representations of p2 model control for dependencies associated with nominator and nominee video : (12:41-19:40) video Van Duijn, M.A.J. (1995). Estimation of a random effects model for directed graphs. In: Snijders, T.A.B. (Ed.) SSS '95. Symposium Statistische Software, nr. 7. Toeval zit overal: programmatuur voor random-coefficient modellen [Chance is omnipresent: software for random coefficient models], p. 113-131. Groningen, iec ProGAMMA. SOFTWARE http://stat.gamma.rug.nl/stocnet/ Lazega, E. and van Duijn, M (1997). “Position in formal structure, personal characteristics and choices of advisors in a law firm: a logistic regression model for dyadic network data.” Social Networks, Vol 19, pages 375- 397. 103

Reciprocity: W ii’ (as y ij ) W i’i (as y ji ) Modeled Simultaneously (Lazega and Van Duijn 1997) 104

Selection Model (p2) Pair Level (i,i’) Sender Level (i) or nominator Receiver Level (i’) or nominee u i ~N(0,τ u ) V i’ ~N(0,τ v ) Difference In attribute reciprocity Sender attribute Receiver attribute Sender variance Receiver variance 105

Boots and Shoes: aligning my notation with Marijtje’s Level 1 Pair Level (i,i’) Difference In attribute reciprocity 106 z Pair Level (j,i) Modeling density

Boots and Shoes: aligning my notation with Marijtje’s Level 2 Sender (i) Receiver (j) u i ~N(0,τ u ) V i’ ~N(0,τ v ) attribute variance 107 covariance Nominator (i) nominee (i’)

home reflection Setting up p2 video : (19:40-42:25) video video 0) make square network data file out of list using makemat.sas will put file called c:\stocnet\network\matrix.dat 1) Using Van Duijn’s p2: go to: http://stat.gamma.rug.nl/stocnet/ http://stat.gamma.rug.nl/stocnet/ go to downloads and save stocnet to desktop. Unzip stocnet file Run setup in the unzipped folder run stocnet.exe Manual available @ http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf Skip running p2 108

home reflection 109

home reflection Accessing data  Toy network data for p2 Toy network data for p2 Toy network data for p2  Put in c:\stocnet\networks\toyw.dat  Optional: Toy dyadic attribute Toy dyadic attributeToy dyadic attribute  Put in c:\stocnet\networks\toywpre.dat  Toy attribute data for p2 Toy attribute data for p2 Toy attribute data for p2  Put in c:\stocnet\actfiles\toyatt.dat 110

home reflection Running p2  Start a new session by 1.Click on “Start with new session” 2.Then hit the “Apply” button 111

home reflection Running p2  Click on the “Data” icon to add data. 112

home reflection Running p2 Click on the “Add…” button. 1) add network data collt1.dat 2) add network data coll21.dat 3) add actor data indiv.dat 113

home reflection Running p2 Once you finish adding data, click on the “Apply” button first. Then, you can click on the “View” button to view data. 114

home reflection Running p2  Click on the “Model” icon 115

home reflection Running p2  Select the p2 model 116

home reflection Running p2  Click on the “Data specification” button 117

home reflection Running p2 put network1 (toydata) into digraph put file1 (indiv) into selected attributes 118

home reflection Running p2: Model Specification 119 Density is pair level for us

Visual Representations of Selection Models 120

Selection Model (p2) Pair Level (i,i’) Sender Level (i) Receiver Level (i’) u i ~N(0,τ u ) V i’ ~N(0,τ v ) Difference In attribute reciprocity Sender attribute Receiver attribute Sender variance Receiver variance 121

Toy Data Network (w) Attribute y1 y2 223212223212 total 122 Total 1 2 3 3 1 2

W |Y i -Y i’ | 123

home reflection Example Output for p2 for Toy Data see also http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf P2MCMC RW ml mv testtoy.out October 13, 2009, 11:36:25 AM @1 General Information: Digraph: C:\stocnet\temp\~toyw.dat @1 General Information: Digraph: C:\stocnet\temp\~toyw.dat October 13, 2009, 11:36:25 AM Number of valid tie indicator observations: 45 @1Descriptives: GroupObserved Initial Tie variables Digraph Number of ties Reciprocal ties Mutliplex ties Exchange ties Size Size Present Missing Size Size Present Missing 1 6 6 30 0 ~toyw.dat 12 10 - - 6 6 30 0 ~toyw.dat 12 10 - - 124

Variances or Random Effects @1 Random effects: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 () sender variance : 0.4323 0.4288 0.05 0.08 0.18 0.29 0.51 1.69 2.67 ( τ u ) sender variance : 0.4323 0.4288 0.05 0.08 0.18 0.29 0.51 1.69 2.67 () receiver variance: 4.9249 7.4311 0.05 0.08 0.24 2.37 6.76 25.69 37.16 ( τ v ) receiver variance: 4.9249 7.4311 0.05 0.08 0.24 2.37 6.76 25.69 37.16 () covariance -0.3081 1.7522 -6.96 -5.24 -0.52 0.01 0.29 2.58 5.21 ( τ uv ) covariance -0.3081 1.7522 -6.96 -5.24 -0.52 0.01 0.29 2.58 5.21 125 Sender Level (i) Receiver Level (i’) u i ~N(0,.43) v i ~N(0,4.9) 125

Selection model (p2): Toy Data Pair level (i,i’) Sender Level (i) Receiver Level (i’) u i ~N(0,.43) v i ~N(0,4.9) 126

home reflection Regression Coefficients: Density, or Pair Level @1 Fixed effects: @2 Overall effects: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 Density ~toyw.dat: 3.7863 2.6904 -1.71 -1.10 1.76 3.46 5.36 11.46 11.85 Density ~toyw.dat: 3.7863 2.6904 -1.71 -1.10 1.76 3.46 5.36 11.46 11.85 Reciprocity ~toyw.dat: 3.7586 2.3022 -1.35 -0.30 2.16 3.67 4.99 9.24 10.33 Reciprocity ~toyw.dat: 3.7586 2.3022 -1.35 -0.30 2.16 3.67 4.99 9.24 10.33@2 Specific covariate effects: @3 Sender covariates: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 Attribute2 0.3084 0.6322 -0.74 -0.67 -0.21 0.29 0.77 1.55 1.62 Attribute2 0.3084 0.6322 -0.74 -0.67 -0.21 0.29 0.77 1.55 1.62@3 Density covariates: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 abs_diff_Attribute1 -2.3816 1.0525 -5.60 -5.28 -3.03 -2.41 -1.55 -0.68 -0.32 abs_diff_Attribute1 -2.3816 1.0525 -5.60 -5.28 -3.03 -2.41 -1.55 -0.68 -0.32 This last term models wither difference in attribute 1 predicts density. 127 0 is contained within the 95% interval of the posterior distribution, not statistically significant

home reflection Regression Coefficients: Sender Effects @1 Fixed effects: @2 Overall effects: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 Density ~toyw.dat: 3.7863 2.6904 -1.71 -1.10 1.76 3.46 5.36 11.46 11.85 Density ~toyw.dat: 3.7863 2.6904 -1.71 -1.10 1.76 3.46 5.36 11.46 11.85 Reciprocity ~toyw.dat: 3.7586 2.3022 -1.35 -0.30 2.16 3.67 4.99 9.24 10.33 Reciprocity ~toyw.dat: 3.7586 2.3022 -1.35 -0.30 2.16 3.67 4.99 9.24 10.33@2 Specific covariate effects: @3 Sender covariates: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 Attribute2 0.3084 0.6322 -0.74 -0.67 -0.21 0.29 0.77 1.55 1.62 Attribute2 0.3084 0.6322 -0.74 -0.67 -0.21 0.29 0.77 1.55 1.62@3 Density covariates: parameter standard quantiles from sample parameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5 estimate error 0.5 2.5 25 50 75 97.5 99.5 abs_diff_Attribute1 -2.3816 1.0525 -5.60 -5.28 -3.03 -2.41 -1.55 -0.68 -0.32 abs_diff_Attribute1 -2.3816 1.0525 -5.60 -5.28 -3.03 -2.41 -1.55 -0.68 -0.32 This last term models wither difference in attribute 1 predicts density. 128

Selection model (p2): Toy Data Pair level (i,i’) Sender Level (i) Receiver Level (i’) u i ~N(0,.43) v i ~N(0,4.9) Bigger difference  less interaction High Reciprocity Big y2  more interaction 129

Combined Selection model (p2): Toy Data Pair level (i,i’) Sender Level (i) u i ~N(0,.43) 130

Add Dyadic Covariate 131

Specify P2 Model 132

P2 Data Specification 133

P2 Model Specification 134

Modify Parameters for Quick Estimation 135

Prediction for Pair (2,5) Selection Model (p2): Toy Data Pair level (2,5) Actual value: W 2,5 =0 136

home reflection Keeping Terms Straight in p2 Q: Who helps you with math? Sender=person who nominates others =person who receives help =expansiveness Receiver = person who is nominated by others = person who provides help =attractiveness

home reflection Keeping Terms Straight in p2 Q: Who gave you cigarettes? Sender=person who nominates others =person who receives cigarettes =expansiveness Receiver = person who is nominated by others = person who provides cigarettes =attractiveness

home reflection Exercise for P2  How can you make an inference about the effect of similarity of an attribute  What happens to the similarity of attribute when you control for time 1?  Try putting in the model:  Difference in attribute1+attribute1 on sender+attribute1 on receiver  Did it work?  What is the difference between putting in difference in attribute instead of absolute value of the difference?

home reflection Marijtje Van Duijn’s P2 in her own words  http://www.gmw.rug.nl/~steglich/dynamics/ workshop/sienap2ergm.pdf http://www.gmw.rug.nl/~steglich/dynamics/ workshop/sienap2ergm.pdf http://www.gmw.rug.nl/~steglich/dynamics/ workshop/sienap2ergm.pdf  Data sets: http://www.stats.ox.ac.uk/~snijders/siena/s 50_data.htm http://www.stats.ox.ac.uk/~snijders/siena/s 50_data.htm http://www.stats.ox.ac.uk/~snijders/siena/s 50_data.htm  Try s50: 50 teenage girls, friendships at 3 time points: http://www.stats.ox.ac.uk/~snijders/siena/s50_ data.htm http://www.stats.ox.ac.uk/~snijders/siena/s50_ data.htm http://www.stats.ox.ac.uk/~snijders/siena/s50_ data.htm 

home reflection Substance use Example

home reflection

home reflection Look at full report variances

home reflection Alternatives for Running p2 In sas: download Sam Field’s p2 via sas from my web site: http://www.msu.edu/~kenfrank/software.htm#Selection_Mo dels:_p2 http://www.msu.edu/~kenfrank/software.htm#Selection_Mo dels:_p2 download glimmix from my web site and save to c:\ run glimmix.sas in sas run Sam’s program (p2_explore.sas) Note it generates its own ego and alter files (see data i and data j) and network data (a5), but these could be read in. Can also do using Peter Hoff’s R routine http://www.stat.washington.edu/hoff/Code/GBME/. For R, go to http://cran.cnr.berkeley.edu/ http://www.stat.washington.edu/hoff/Code/GBME/.http://cran.cnr.berkeley.edu/ http://www.stat.washington.edu/hoff/Code/GBME/.http://cran.cnr.berkeley.edu/ Tutorial in Exponential Random Graph Models Tutorial in Exponential Random Graph Models https://statnet.csde.washington.edu/trac/wiki/Sunbelt2013 145

home reflection Introduction to statnet Introduction to statnet 146

home reflection Using statnet  Overview Overview  Access R Access R Access R  Running R 147

home reflection 148

home reflection Basic statnet setup 149 statnet community statnet tutorialstatnet tutorial.

Basic ERGM in statnet from statnet tutorial statnet tutorialstatnet tutorial 150

151 Spillane, J., Kim, Chong Min, Frank, K.A. 2012. “Instructional Advice and Information Providing and Receiving Behavior in Elementary Schools: Exploring Tie Formation as a Building Block in Social Capital Development.” Americ an Educational Research Journal. Vol 49 no. 6 1112-1145

Concerns about Causality 155 Outcome: help from i’ to i Prior help from i’ to i Similarity of behavior between i’ and i Influence selection

156. For every pair of school staff i and j, if i turned to j for advice about instruction the i  j relationship was assigned a value of 1 and 0 otherwise.

Selection Application Transition from Social Exchange to Systemic Exchange Via Quasi-Ties video : (42:25-48:00) video video Frank, K.A. 2009 Quasi-Ties: Directing Resources to Members of a Collective American Behavioral Scientist. 52: 1613-1645 159

p2 extended model Quasi-tie 160

Interaction of Close Colleagues and Identification of the Potential Provider on the Provision of Help: Evidence of a Quasi-Tie 161

Cross Nested Multilevel Poisson Regression (i.e., p2 social network model) of Extent (# of days per year) to which i’ Helped i Quasi-tie 162

home reflection Examples of Selection Frank, K.A., Muller, C., Mueller, A.S., 2013. The Embeddedness of Adolescent Friendship Nominations: The Formation of Social Capital in Emergent Network Structures. American Journal of Sociology, Vol 119(1):216-253.Frank, K.A., Muller, C., Mueller, A.S., 2013. The Embeddedness of Adolescent Friendship Nominations: The Formation of Social Capital in Emergent Network Structures. American Journal of Sociology, Vol 119(1):216-253. Media hits: Atlantic; Huffington Post; Huffington Post (Op-ed); US News and World Report; Yahoo; Health Day; RedOrbit;The Times of India; MSUToday: Psych Central: Positions and Promotions; Deccan Chronicle: wood radio: Fox Chicago: local news channels (south Carolina): Science Daily;National Science FoundationAtlanticHuffington PostHuffington Post (Op-ed)US News and World ReportYahoo;Health DayRedOrbitThe Times of IndiaMSUToday:Psych Central:Positions and PromotionsDeccan Chronicle:wood radio:Fox Chicago:local news channels (south Carolina):Science DailyNational Science Foundation ppt Spillane, J., Kim, Chong Min, Frank, K.A. 2012. “Instructional Advice and Information Providing and Receiving Behavior in Elementary Schools: Exploring Tie Formation as a Building Block in Social Capital Development.” American Educational Research Journal. Vol 49 no. 6 1112-1145 Crosnoe, Robert, Anna Strassman-Mueller, and Frank, K.A. 2008. “Gender, Body Size, and Social Relations in American High Schools.” Social Forces 86: 1189-1216. Frank, K. A. and Zhao, Y. (2005). "Subgroups as a Meso-Level Entity in the Social Organization of Schools." Chapter 10, pages 279-318. Book honoring Charles Bidwell's retirement, edited by Larry Hedges and Barbara Schneider. New York: Sage publications. 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 642-686 163

home reflectionOverview  Introduction Introduction  Influence Influence  Selection Selection  Graphical Representations Graphical Representations Graphical Representations  KliqueFinder KliqueFinder  Step 1) Criteria for Determining defining clusters Step 1) Criteria for Determining defining clusters Step 1) Criteria for Determining defining clusters  Step 2) Maximizing Criterion Step 2) Maximizing Criterion Step 2) Maximizing Criterion  Step 3) Examine evidence of clusters Step 3) Examine evidence of clusters Step 3) Examine evidence of clusters  Step 4) Evaluating the performance of the algorithm : Did... Step 4) Evaluating the performance of the algorithm : Did...Step 4) Evaluating the performance of the algorithm : Did...  Crystalized sociogram of Close Collegial Ties Crystalized sociogram of Close Collegial Ties Crystalized sociogram of Close Collegial Ties  Ripple Plot Ripple Plot Ripple Plot  Running KliqueFinder Running KliqueFinder Running KliqueFinder  Centrality Centrality  Ethics  Resources Resources 164

home reflection KliqueFinder: Identifying Clusters in Network Data Go to: https://www.msu.edu/user/k/e/kenfrank/web/resources. htm#KliqueFinder https://www.msu.edu/user/k/e/kenfrank/web/resources. htm#KliqueFinder https://www.msu.edu/user/k/e/kenfrank/web/resources. htm#KliqueFinder Based on:   Frank. K.A. 1995. Identifying Cohesive Subgroups. Social Networks (17): 27-56 Frank. K.A. 1995. Identifying Cohesive Subgroups. Social Networks (17): 27-56   Frank, K. 1996. Mapping interactions within and between cohesive subgroups. Social Networks 18: 93-119. Frank, K. 1996. Mapping interactions within and between cohesive subgroups. Social Networks 18: 93-119.   *Field, S. *Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. (2006). "Identifying Social Contexts in Affiliation Networks: Preserving the Duality of People and Events. Social Networks 28:97-123 * coequal first authorship *Field, S. *Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. (2006). "Identifying Social Contexts in Affiliation Networks: Preserving the Duality of People and Events.  https://www.msu.edu/user/k/e/kenfrank/web/research.htm#representation https://www.msu.edu/user/k/e/kenfrank/web/research.htm#representation 165

home reflection 166

home reflection Scenarios for the Network analyst For each of the scenarios below, identify the theoretical processes at work write down what model or tool you would employ to evaluate the theory. describe what data you would collect to apply the model or tool to describe what estimation procedure/tool you would use. Sally is concerned that her daughter is experimenting with alcohol and thinks it is because her daughter’s friends are experimenting. Sally wonders generally if adolescents tend to drink more if their friends drink alcohol. Michael wants to understand the social structure of his synagogue (church). He has an idea that there are certain sets of people who interact with each other, and, if he could understand what those sets of people are, he might better be able to tailor programs of the synagogue to be more effective. How could Michael use the information above track the diffusion of new beliefs or behaviors in his synagogue? Pennie wants to know under what conditions one social service agency would allocate resources to another. Is it because they have a history of doing so, they share clients, they deal with similar issues, etc. What clustering among social service agencies might emerge as a result of the processes above? 167

Centrality: The Strength of the Connection between an Actor and the Network   Freeman, L. C. (1978/1979). Centrality in social networks conceptual clarification. Social Networks, 1, 215-239.   Degree: number of ties to node i   Betweeness: proportion of geodisics (connecting paths) between j and k that go through i.   Closeness: total number of edges required to link i to all others   See http://www.soc.duke.edu/~jmoody77/s884/syllabus_09.htm http://www.soc.duke.edu/~jmoody77/s884/syllabus_09.htm   Bonacich (1972): eigen vector   The centrality of a given person (ei) depends on the centrality of the people to whom the person is tied (wii’=1 if i and i’ are related, 0 otherwise):   The elements in e then represent the components of the eigen vector of W – do a factor analysis of W e i is the centrality of actor i. w ii is the network data. λ is a constant 168

Bonacich Centrality Revised 169

home reflection Critique of Centrality  Individualistic, not view of network  Does not explicitly account for resources flowing through ties  Structural  Empirically, centrality often not a strong predictor of individual outcomes (exception: Ron Burt’s work)  Can model actor in-degree or out-degree using p2  Can model effect of network ties + resources using influence 170

home reflection Centralization -- the Centrality of the System   How does the pattern of communication in organization A differ from that in organization B, and how are these patterns formed by characteristics external to the organization?   Freeman: distribution of centrality   Compare measures against the maximal measure in the graph   -- but what if there is more than one actor who is highly extreme in centrality? 171

Barnett G., & Rice, R.: warp. (1985, Longitudinal Non-Euclidean Networks: Applying Galileo, Social Networks, pages 287-322): 172 Let S represent distances. Actor 1 is too central. Cannot plot in 2 dimensions

First Find Scalar Product 173 S’S=Cartesian coordinates Let S represent distances Diagonal represents centrality, hjgh value  less central

Calculate Warp from S’S 174 Eigen values of are { -5.02; 13.96 ; 83.05 } http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert2.htm Warp b =3.74+9.11/(-2.24+3.74+9.11)=4.59 Warp a =(13.96+83.05)/(13.96-5.02+83.05)=1.05

Calculating Warp from S (doesn’t really work) 175 Eigen values of are {-.22, 9.2, -9} http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert2.htm Warp b =3.03/3.03-3-.46=-.44, negative? Warp a =9.2/(-.22+9.2-9)=undefined

home reflection Centralization & Centrality in KliqueFinder  KliqueFinder produces a measure of Warp.  Starts with distances defined by  Maximum value in network / observed value  E.g. maximum is 4 and a particular tie is 1, then distance is 4/1=4.  These are the distances used in the MDS to produce the sociograms (see “running KliqueFinder ppt”)  Obtains eigen values  within each cluster based on raw data within cluster  Between clusters based on 1/density of ties between clusters  Density=average value in a given block  Warp =sum of positive eigen values/sum of all eigen values  Note it does not use the square toot of the eigen values  Output into xxxxxx.bcord (9th element) and into netdraw as node attribute for groups, called “centrality”  Centrality for individuals is distance to the center of their subgroup (radius). 176

home reflectionOverview  Introduction Introduction  Influence Influence  Selection Selection  Graphical Representations Graphical Representations Graphical Representations  Centrality Centrality  Ethics  Confidentiality/Ethical issues in Collecting Network Data  The SRI/KliqueFinder Solution to confidentiality.  Actual relations not revealed Actual relations not revealed Actual relations not revealed  Resources Resources 177

home reflectionOverview  Introduction Introduction  Influence Influence  Selection Selection  Graphical Representations Graphical Representations Graphical Representations  Centrality Centrality  Ethics  Resources Resources  Logistics of Data Collection Logistics of Data Collection Logistics of Data Collection  Organizing data entry Organizing data entry Organizing data entry  Resources for Networks: Books Resources for Networks: Books Resources for Networks: Books  Resources for Networks: Web Resources for Networks: Web Resources for Networks: Web  Resources: Clearinghouses Resources: Clearinghouses Resources: Clearinghouses  Resources: Individual web Pages Resources: Individual web Pages Resources: Individual web Pages 178

home reflection Logistics of Data Collection   Need for longitudinal data to disentangle selection from influence   (Matsueda and Anderson 1998; Leenders 1995).   Time constraints: how long does a network question take?   Without roster: 2-3 minutes   With roster: 5-10 minutes (depending on size of network)   High response rates (70% or more) needed to characterize system, influence   incentives: school, individual   administer in collective settings (e.g., staff meeting)   do not be perceived to be affiliated with principal   Network data without survey?   Sensors   Participation in events (two-mode)   on-line e-mails   web links   Marsden in Carrington et al., follow up on   Marsden, Peter V. 1990. “Network Data and Measurement.” Annual Review of Sociology 16: 435-463. 179

check out: http://www.classroomsociometrics.com/ check out: http://www.classroomsociometrics.com/ Organizing data entry check out: http://www.classroomsociometrics.com/ check out: http://www.classroomsociometrics.com/ 180

home reflection Confidentiality/Ethical issues in Collecting Network Data   Need names on survey   Data can be confidential but not anonymous (especially for longitudinal)  http://www.u.arizona.edu/~breiger/2005BreigerIntroEthics.pdf  R.L. Breiger, “Ethical Dilemmas in Social Network Research: Introduction to Special Issue.” Social Networks 27 / 2 (2005): 89 – 93. Read it online. http://www.u.arizona.edu/~breiger/2005BreigerIntroEthics.pdf http://www.u.arizona.edu/~breiger/2005BreigerIntroEthics.pdf   (All issues of social networks available via science direct)   Who benefits from network analysis? Who bears the cost?   Kadushin, Charles “Who benefits from network analysis: ethics of social network research” Social Networks 27 / 2 (2005): Pages 139-153. chapter 11 of Understanding Social Networks   Issues to raise when dealing with Human Subjects Board:   Klovdahl, Alden S. Social network research and human subjects protection: Towards more effective infectious disease control Pages 119-137   Hint on Human Subjects boards: they like precedents. Once you have one network study accepted, refer to it when submitting others!   https://www.msu.edu/~kenfrank/social%20network/irb%20with%20network%20data.htm https://www.msu.edu/~kenfrank/social%20network/irb%20with%20network%20data.htm 181 video video : >rich media >vodcast>podcast>Course Portal (1:23:41-1:28)rich mediavodcastpodcastCourse Portal

home reflection The SRI/KLiqueFinder Solution to confidentiality: aggregate to subgroups 1) Provide information about who is in which cluster as well as information regarding the resources embedded in each cluster. Resources could be information, expertise, material resources, etc. Benefit: reveals location of resources relative to social; structure Protection: does not reveal specific responses because all information is at the cluster level. 2) Provide locations from in a sociogram unique for each respondent, indicating where that person is located (“you are here”). But figure does not include the lines from a sociogram, so respondents cannot infer others’ responses. Benefit: Respondents then use this as a guide to individual behavior for identifying further resources or information. Protection: Specific responses of others not revealed, so confidentiality preserved. See: Using subgroups for feedback to respondents and in a proposalUsing subgroups for feedback to respondents and in a proposal 182

home reflection 183

home reflection Reliability and Validity of Network Items  Most likely to recall:  Frequent, routinized interactions  Missing weak ties?  Instrument  Prompt with roster  Mix roster & extra nominations (targeted subsets)  Adam Douglas Henry, Mark Lubell, and Michael McCoy (2012). “Survey-Based Measurement of Public Management and Policy Networks.” Journal of Policy Analysis and Management, 31(2): 432-452.  Fatigue:  Order effects matter 184

home reflection Scenarios for the Network Analyst: Ethical Considerations For your previous answer to each of the scenarios below, identify who would benefit from the analysis, who bears the costs how confidentiality of subjects could be protected Sally is concerned that her daughter is experimenting with alcohol and thinks it is because her daughter’s friends are experimenting. Sally wonders generally if adolescents tend to drink more if their friends drink alcohol. Michael wants to understand the social structure of his synagogue. He has an idea that there are certain sets of people who interact with each other, and, if he could understand what those sets of people are, he might better be able to tailor programs of the synagogue to be more effective. How could Michael use the information above track the diffusion of new beliefs or behaviors in his synagogue? Pennie wants to know under what conditions one social service agency would allocate resources to another. Is it because they have a history of doing so, they share clients, they deal with similar issues, etc. What clustering among social service agencies might emerge as a result of the processes above? 185

home reflection Resources for Networks: Books Kadushin, Charles. (2012). Understanding Social Networks: Theories, Concepts, and Findings. Oxford: Oxford University Press.Kadushin, Charles. (2012). Understanding Social Networks: Theories, Concepts, and Findings. Oxford: Oxford University Press. Peter J. Carrington, John Scott, Stanley Wasserman “Models and Methods in Social Network Analysis” Cambridge, order from Amazon on-line. Wasserman, S., & Faust, K. (2005). Social networks analysis: Methods and applications. New York: Cambridge University. Go to Amazon to order electronically. Freeman, Linton (2004). The Development of Social Network Analysis: A Study in the Sociology of Science. Empirical Press of Vancouver, BC, Canada http//www.booksurge.com/product.php3?bookID=GPUB01133-00001 Scott, J., 1992, Social Network Analysis. Newbury Park CA: Sage. Wellman, Barry and S.D. Berkowitz, 1997. Social Structures: A Network Approach.(updated edition) Greenwich, CT: JAI Press. 186

home reflection Resources for Networks: Courses and Introductions Introductory On the Web Borgatti’s slide show: http://www.analytictech.com/networks/intro/index.html Kadushin’s intro http://www.charleskadushin.com/ Barry Wellman’s intro: Social Network Analysis: An Introduction http://www.chass.utoronto.ca/~wellman/publications/index.html David Knoke’s intro to social network methods: http://www.soc.umn.edu/%7Eknoke/pages/SOC8412.htm Wasserman, S., & Faust, K. (1994). Social networks analysis: Methods and applications. New York: Cambridge University. Jim Moody’s course: http://www.soc.duke.edu/~jmoody77/s884/syllabus_09.htm http://www.soc.duke.edu/~jmoody77/s884/syllabus_09.htm 187

home reflection General Resources   International social network analysis web page: http://www.insna.org/ http://www.insna.org/  Syllabi:: http://www.ksg.harvard.edu/netgov/html/sna_courses_ev ents.htm http://www.ksg.harvard.edu/netgov/html/sna_courses_ev ents.htm http://www.ksg.harvard.edu/netgov/html/sna_courses_ev ents.htm   Labs  http://sna.stanford.edu/rlabs.php http://sna.stanford.edu/rlabs.php 188

home reflection Resources: Individual Web Pages   Individual Web Pages :  http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4  Phil Bonacich http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4 http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4  http://www.u.arizona.edu/~breiger/)  Ron Breiger (http://www.u.arizona.edu/~breiger/): http://www.u.arizona.edu/~breiger/   Ronald Burt (google Ron Burt):   http://www.chicagobooth.edu/faculty/bio.aspx?person_id=12824623104 http://www.chicagobooth.edu/faculty/bio.aspx?person_id=12824623104  http://www.msu.edu/~kenfrank/  Ken Frank http://www.msu.edu/~kenfrank/ http://www.msu.edu/~kenfrank/   Linton Freemanh http://moreno.ss.uci.edu/lin.htmlhttp://moreno.ss.uci.edu/lin.html   James Moody http://www.soc.duke.edu/~jmoody77/http://www.soc.duke.edu/~jmoody77/   Mark Newman: http://www-personal.umich.edu/~mejn/http://www-personal.umich.edu/~mejn/   Tom Snijders http://www.stats.ox.ac.uk/~snijders/http://www.stats.ox.ac.uk/~snijders/  http://www.chass.utoronto.ca/~wellman/  Barry Wellman: http://www.chass.utoronto.ca/~wellman/ http://www.chass.utoronto.ca/~wellman/ 189

home reflection Resources data  http://snap.stanford.edu/index.html http://snap.stanford.edu/index.html  Stanford, large data sets  http://datamob.org/datasets/tag/social-networks http://datamob.org/datasets/tag/social-networks  Multiple potential sources (including Enron)  http://www-personal.umich.edu/~mejn/netdata/ http://www-personal.umich.edu/~mejn/netdata/  Mark newman  http://vlado.fmf.uni-lj.si/pub/networks/data/UciNet/UciData.htm http://vlado.fmf.uni-lj.si/pub/networks/data/UciNet/UciData.htm  UCINET  http://www.nd.edu/~networks/resources.htm http://www.nd.edu/~networks/resources.htm  Barabasi  http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/20541 http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/20541  National Social Life, Health, and Aging Project (NSHAP)  http://moreno.ss.uci.edu/data.html http://moreno.ss.uci.edu/data.html  Linton freeman’s web page, scan for attributes if you want to combine network data with attributes 190

home reflection Resources Exercise  Find 2 web resources not listed above and post them on angel 191

Influence Exercise: Answers 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 was a 9, Lisa’s was a 5 and Jane’s was 2. What is the mean exposure of Bob to his peers regarding organic farming? Sum=1x9+3x5+0x2=24 N= 2 (number Bob talks to) or 3 (number of people) or 4 (number of interactions)? Hmmmmmm. Mean = 24/2=12 or 24/3=8 or 24/4=6. Or, use the sum? Specify a model with two sources of exposure (e.g., within versus between subgroups Let s ii’ =1 if i and i’ are in the same subgroup, 0 otherwise Return to influence 192

home reflection Selection Answers 193

home reflection Selection Answers 194 Note: variable is 1 if different gender, 0 if same gender. Could also make it: 1 if same gender, 0 if different gender

C Selection answers Return to selection D 195 For Bob and Jane:.4-.2(1)-.5(1)= -.3

home reflection Resources Exercise  Find 2 web resources not listed above and post them on angel 196

home reflection Bounds on ρ (Based in part on dissertation by Jiqiang Xu)  Ord says 1/λ min < ρ < 1/λ max, λ is an eigen value  likelihood =G[OLS, ∑ a ln(1-ρλ a )]  Alternative: eigen values and eigen vectors (V):  λV =WV → V =(1/ λ)WV  Perfect fit if ρ=1/ λ,  eigen value λ a  with Y = corresponding eigen vector, V a 197

W= Y= OLS estimate of ρ = 1.21, R 2 =.97 OLS estimate of ρ =.5, R 2 =.99 198

home reflection Substantive Restriction on Y  1/λ min < ρ < 1/λ max to confine to largest component  What if there are multiple components?  Separate estimate of ρ in each component, average over components?  Standardize: z(ρ)= p/(1/λ max -1/λ min ) 199

Find the network model Try to relate this regression to one of our network models. How does her analysis take into account ties among people? How could you extend? 200

Measure of Bridging Capital 201

Try to relate this regression to one of our network models. How does her analysis take into account ties among people? How could you extend? 202

Prior to workshop 204 1)Standard statistical software package: Sas, spss or stata 2) KliqueFinder: –http://hlmsoft.net/wkf/http://hlmsoft.net/wkf/ –Follow instructions to install. Put in c:\kliqfind –Mac users: vmware fusion, Windows 7, 32 bit: http://store.vmware.com/store/vmware/pd/productID.165310200/Curr ency.USD/ http://store.vmware.com/store/vmware/pd/productID.165310200/Curr ency.USD/ https://www.msu.edu/~kenfrank/resources.htm#KliqueFinder quick power point on how to use KliqueFinder 3) Stocnet http://stat.gamma.rug.nl/stocnet/ http://stat.gamma.rug.nl/stocnet/ 4) Statnet: https://statnet.csde.washington.edu/trachttps://statnet.csde.washington.edu/trac 5) These slides : Overview of network tools Overview of network tools see also “workshop materials” 6) KNOW REGRESSION! model building, predicted values, errors and inference, assumptions

Background Readings 205 Frank, K.A. Lo, Y., Sun, M., (2014). “Social network analysis of the influences of educational reforms on teachers’ practices and interactions.” Zeitschrift für Erziehungswissenschaft. Volume 17, Issue 3. Attached. Frank, K.A., Kim, C., and Belman, D. 2010. “Utility Theory, Social Networks, and Teacher Decision Making.” Pages 223-242 in Alan J. Daly editor. Social Network Theory and Educational Change. Cambridge: Harvard University Press. Frank, K. A., S. Maroulis, D. Belman, and M. D. Kaplowitz. 2011. The social embeddedness of natural resource extraction and use in small fishing communities. Pages 309-332 in W. W. Taylor, A. J. Lynch, and M. G. Schechter, editors. Sustainable fisheries: multi-level approaches to a global problem. American Fisheries Society, Bethesda, Maryland. Frank, K.A. 2011. Social Network Models for Natural Resource Use and Extraction. Social networks and natural resource management: Uncovering the social fabric of environmental governance. Pp. 180-205. Örjan Bodin & Christina Prell editors. Cambridge: Cambridge University Press. Frank, K. A. (1998). "The Social Context of Schooling: Quantitative Methods" Review of Research in Education, Vol, 23, chapter 5Frank, K. A. (1998). "The Social Context of Schooling: Quantitative Methods" Review of Research in Education, Vol, 23, chapter 5 They are all very similar (only read one), and include reviews of the literature. I have listed them in the order of priority for learning purposes.

home reflection Plan of Activities Day 1 of 2 day workshop 9-10:15: Introduction to social network analysis 10:15-10:45 scramble exercise (introductions) 10:45-11 break 11-12 introduction to influence model Includes exercise 12-1 Lunch make introductions from scramble exercise! 1-1:45 application of the influence model 1:45-2:30 introduction to selection model Includes exercise 2:30-2:45 Break 2:45-3:30 application of the selection model 3:30-3:4:30 Clustering an graphical representations includes interactive exercise 4:30-5 set up for second day [download videos] 206

home reflection Plan of Activities Day 2: Software  9-9:15: Break into groups to focus on  Influence, selection, graphical representations  9:15-10:15 Watch video demonstration and try basics  10:15-12 supported experimentation and exploration  12-1: lunch  1-2: example demonstration of theoretical models  2-3:30 supported experimentation with models 207

Home reflection Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann.

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Presentation on theme: "Home reflection Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann."— Presentation transcript:

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Home reflection Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann.

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Presentation on theme: "Home reflection Introduction to the Models and Tools for Social Networks Kenneth Frank, College of Education and Fisheries and Wildlife Help from: Ann."— Presentation transcript:

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About project

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