Introduction to the Models and Tools Introduction to the Models and Tools for Social Networksfor Social Networks

Kenneth Frank, College of Education and Kenneth Frank, College of Education and Fisheries and WildlifeFisheries and Wildlife

Help from: Ann Krause, Ben Michael Help from: Ann Krause, Ben Michael Pogodzinski, Bo Yan, Min Sun, I-Chen, Pogodzinski, Bo Yan, Min Sun, I-Chen,

Chong Min Kim Chong Min Kim

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AbstractAbstract Many quantitative analyses in the social sciences are applied to data Many quantitative analyses in the social sciences are applied to data

regarding characteristics of people, but not to data describing interactions regarding characteristics of people, but not to data describing interactions among people. But interactions play an important role in affecting people’s among people. But interactions play an important role in affecting people’s behavior and beliefs that cannot be explained purely in terms of individual behavior and beliefs that cannot be explained purely in terms of individual attributes or organizational context. In this workshop we will focus on attributes or organizational context. In this workshop we will focus on analyzing social network data (who interacts with whom) so that we can relate 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 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 concepts that account for the unusual nature of network data as well as substantive theories across the social sciences to specify and interpret social substantive theories across the social sciences to specify and interpret social network models. network models.

Topics include models of influence through a social network, choices in a Topics include models of influence through a social network, choices in a social network, clustering and graphical representations; ethical issues and social network, clustering and graphical representations; ethical issues and IRB, and software. Throughout examples are given using simple toy data and IRB, and software. Throughout examples are given using simple toy data and analyses in published papers.analyses in published papers.

Students taking this workshop should have roughly one year of applied Students taking this workshop should have roughly one year of applied statistics so that they are extremely comfortable with the general linear model statistics so that they are extremely comfortable with the general linear model (regression and ANOVA), and analysis of 2x2 tables. (regression and ANOVA), and analysis of 2x2 tables.

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OverviewOverview Introduction

Overview What Are Social Networks?

Representations of Social Networks: Sociomatrix Representations: Notation Representations: Sociogram

Characteristics of Social Network Data Ego Centric Data

FavoritesFavorites 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 EthicsEthics Resources

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What Are Social Networks?What Are Social Networks?

A set of actors and the ties (resource flows) or relations A set of actors and the ties (resource flows) or relations (stable states) among them.(stable states) among them. close colleagues (relation) among teachers (actors)close colleagues (relation) among teachers (actors) help (tie) one teacher (actor) provides to another help (tie) one teacher (actor) provides to another communication (tie) between people (actors) in an organizationcommunication (tie) between people (actors) in an organization friendships (relation) among politicians (actors)friendships (relation) among politicians (actors) links (relation) among web sites (actors)links (relation) among web sites (actors) referrals (tie) among social service agencies (actors)referrals (tie) among social service agencies (actors)

For me: actors must For me: actors must have agencyhave agency Able to take deliberate actionAble to take deliberate action Actor network theory ? Can artifacts have agency and take Actor network theory ? Can artifacts have agency and take

deliberate action?deliberate action? More than BookFaceMore than BookFace

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Format of Network Data (W)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 DailyBob Jones_(2)________ 1 2 3 4Sue Meyer_(3)________ 1 2 3 4____________________ 1 2 3 4____________________ 1 2 3 4Data entered (nominator, nominee, frequency)1 2 21 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)________ 1 2 3 42. Lin Freeman (4)_______ 1 2 3 43. ____________________ 1 2 3 44. ____________________ 1 2 3 4Data entered (nominator, nominee, frequency)2 1 22 4 3

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Representations of Social NetworksRepresentations of Social NetworksFriendships among the French financial eliteFriendships among the French financial elite

EdgelistEdgelist

1 131 13 211 21112 1 17211 21112 1 17 1545463790 1 191545463790 1 19

1|......111.| 25 14 1|......111.| 25 14

25|..1....11.| 25 1925|..1....11.| 25 19

14|.1.1.1.11.| 14 2514|.1.1.1.11.| 14 25

15|..1..1.11.| 14 1515|..1..1.11.| 14 15

4|.......11.| 14 264|.......11.| 14 26

26|..11...11.| 14 1726|..11...11.| 14 17

13|1......11.| 14 1913|1......11.| 14 19

17|1111111.11| 15 1417|1111111.11| 15 14

19|11111111..| 15 2619|11111111..| 15 26

20|.......1..| 15 1720|.......1..| 15 17 15 1915 19 4 174 17 4 194 19

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1 25 14 15 4 26 13 17 19 20

1 1 1 1

25 1 1 1

14 1 1 1 1 1

15 1 1 1 1

4 1 1

26 1 1 1 1

13 1 1 1

17 1 1 1 1 1 1 1 1 1

19 1 1 1 1 1 1 1 1

20 1

Matrix

Representations: NotationRepresentations: Notation

xxijij, takes a value of 1 if , takes a value of 1 if ii nominates  nominates jj  , , 0 0

otherwise: xotherwise: x1 251 25=0, x=0, x1 131 13=1=1

Ken uses:Ken uses:wwii’ii’, takes a value of 1 if , takes a value of 1 if ii nominates  nominates i’, i’, 0 0

otherwise: wotherwise: w1 251 25=0, w=0, w1 131 13=1=1

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Representations: SociogramRepresentations: 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 1414

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Characteristics of Social Network DataCharacteristics of Social Network Data

DirectionalityDirectionality If A nominates B as a bully, B may not nominate A as a bullyIf A nominates B as a bully, B may not nominate A as a bully

Valued relationsValued relations How frequently does teacher A interact with teacher B?How frequently does teacher A interact with teacher B?

Multiple relationsMultiple relations Are students friends, romantic partners, coursemates?Are students friends, romantic partners, coursemates?

CentricityCentricity Sociocentric: whole social networkSociocentric: whole social network Egocentric: each person and their own networkEgocentric: each person and their own network

ModesModes One mode: actor to actor One mode: actor to actor

Friendship, bullyingFriendship, bullying Two mode: actors and eventsTwo mode: actors and events

Students and the courses they attendStudents and the courses they attend Ceo’s and the boards they are members of Ceo’s and the boards they are members of

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Ego Centric DataEgo 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

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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.

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Two mode: actors and events

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Favorites:Favorites:Barry Wellman on MisconceptionsBarry Wellman on Misconceptions

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Favorites:Favorites:Doreian: Social Network Effects added to Doreian: Social Network Effects added to

other Effectsother Effects Inner causes: psychological motivationInner causes: psychological motivation Ascriptive effects: genderAscriptive effects: gender Social network effects: centrality in groupSocial network effects: centrality in group Doreian, Patrick (2001). “Causality in Doreian, Patrick (2001). “Causality in

Social network Analysis.” Social network Analysis.” Sociological Sociological Methods and ResearchMethods and Research, Vol 30, No. 1, 81-, Vol 30, No. 1, 81-114.114.

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Favorites:Favorites:Breiger: Tracking Network Analysis from Breiger: Tracking Network Analysis from

Metaphor to ApplicationMetaphor to Application Great review of theoretical motivations for Great review of theoretical motivations for

network analysis dating back to Marx, network analysis dating back to Marx, Durkheim, CooleyDurkheim, Cooley

Includes emphasis on cognition Includes emphasis on cognition Breiger, R.L. “The Analysis of Social Breiger, R.L. “The Analysis of Social

Networks.” Pp. 505–526 in Handbook of Networks.” Pp. 505–526 in Handbook of Data Analysis, edited by Melissa Hardy Data Analysis, edited by Melissa Hardy and Alan Bryman. London: Sage and Alan Bryman. London: Sage Publications, 2004. Publications, 2004. http://www.u.arizona.edu/~breiger/NetworkAnalysis.pdf

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MineMineFrank: Integrating Social Networks into Models and Frank: Integrating Social Networks into Models and

Graphical RepresentationsGraphical Representations

Multilevel modelsMultilevel models Accounts for nesting of people within groups (e.g., students within Accounts for nesting of people within groups (e.g., students within

schools)schools) Effects of groups modeled at the group level (e.g., effect of school Effects of groups modeled at the group level (e.g., effect of school

restructuring on achievementrestructuring on achievement AssumptionsAssumptions

Groups independent of each otherGroups independent of each other People within groups independent of each other. Hmmmmmmmm.People within groups independent of each other. Hmmmmmmmm.

People within schools influence each otherPeople within schools influence each other Student to studentStudent to student Teacher to teacherTeacher to teacher Teacher to studentTeacher to student

People within schools select interaction partnersPeople within schools select interaction partners Adolescents’ friends and peersAdolescents’ friends and peers Teachers’ close colleaguesTeachers’ close colleagues

Frank, K. A. 1998. "The Social Context of Schooling: Quantitative Methods". Review of Research in Education 23, chapter 5: 171-216.

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Social Processes in SchoolsSocial Processes in Schools

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PersonalPersonal

I started my work with Valerie Lee, my I started my work with Valerie Lee, my dissertation chair was Tony Bryk, and my first dissertation chair was Tony Bryk, and my first faculty mentor was Steve Raudenbush. faculty mentor was Steve Raudenbush. Raudenbush, S. W., and A.S. Bryk. 2002Raudenbush, S. W., and A.S. Bryk. 2002

Hierarchical linear models: Applications and data Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: analysis methods (2nd ed.). Thousand Oaks, CA: Sage.Sage.

This article is my recognition of their influences This article is my recognition of their influences and then pushing to networksand then pushing to networks Charles Bidwell played a strong rollCharles Bidwell played a strong roll Aaron Pallas, Steve Raudenbush and Noah Friedkin Aaron Pallas, Steve Raudenbush and Noah Friedkin

as editorsas editors

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Two Fundamental Processes Involving Two Fundamental Processes Involving Human Social Networks Human Social Networks

Influence: Change in actors’ beliefs or behaviors as a result of Influence: Change in actors’ beliefs or behaviors as a result of interaction with othersinteraction with others Teachers’ change uses of computers as a result of use of others’ Teachers’ change uses of computers as a result of use of others’

around them (Frank, Zhao and Borman 2004)around them (Frank, Zhao and Borman 2004) Adolescents’ change effort in school in response to peers’ effort (Frank Adolescents’ change effort in school in response to peers’ effort (Frank

et al 2008, AJS; )et al 2008, AJS; ) Selection: Actors choose with whom to interact as a function of the Selection: Actors choose with whom to interact as a function of the

characteristics of the chooser, chosen, and the dyadcharacteristics of the chooser, chosen, and the dyad Teachers choose to help others with technology based on close Teachers choose to help others with technology based on close

collegial ties (Frank and Zhao 2005)collegial ties (Frank and Zhao 2005) French bankers choose whom to take supportive or hostile action French bankers choose whom to take supportive or hostile action

against based on friendship structure (Frank and Yasumoto, 1998)against based on friendship structure (Frank and Yasumoto, 1998) Who does one child nominate as a bully?Who does one child nominate as a bully?

Each process relates social network to beliefs or behaviorsEach 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. 2828

Selection and InfluenceSelection and Influence

Selection and Influence always presentSelection and Influence always present Ignore them at your peril! – biased / wrong estimatesIgnore them at your peril! – biased / wrong estimates

Influ

ence

selection

0 1 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.

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CausalityCausality

Is it selection or influence?Is it selection or influence? Do people choose to interact with others like themselves (selection) or Do people choose to interact with others like themselves (selection) or

do they changedo they change Birds of a feather flock togetherBirds of a feather flock together

Beliefs/behaviors based on interactions with others (influence)? Beliefs/behaviors based on interactions with others (influence)? She’s hanging out with the wrong crowd!She’s hanging out with the wrong crowd!

Need longitudinal data!!!!!!!Need longitudinal data!!!!!!! Influence Influence

With whom did you talk over the last week: asked at week 2 (1With whom did you talk over the last week: asked at week 2 (12)2) What are your beliefs? (asked at week 1)What are your beliefs? (asked at week 1) What are your beliefs (asked at week 2)What are your beliefs (asked at week 2)

SelectionSelection With whom did you talk over the last week: asked at week 1 (0With whom did you talk over the last week: asked at week 1 (0 1) 1) With whom did you talk over the last week: asked at week 2 (1With whom did you talk over the last week: asked at week 2 (1 2) 2) What are your beliefs? (asked at week 1, or asked at weeks 1 and 2 and What are your beliefs? (asked at week 1, or asked at weeks 1 and 2 and

take the average)take the average)

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Scramble ExerciseScramble Exercise

Think: Identify a networkThink: Identify a network ActorsActors RelationsRelations

Directionality, Valued relations, Directionality, Valued relations, Multiple relations, Modality, Multiple relations, Modality, CentricityCentricity

Process and bases of Influence Process and bases of Influence why would one person be influenced by another?why would one person be influenced by another?

Process and bases of SelectionProcess and bases of Selection why would one person choose to interact with a specific other?why would one person choose to interact with a specific other?

Form: Meet and share in groups of 3-4Form: Meet and share in groups of 3-4 Others: Question bases for making inferencesOthers: Question bases for making inferences

Scramble: Form new group of 3-4 peopleScramble: Form new group of 3-4 people Matchmaker (at lunch): Identify matches of interest Matchmaker (at lunch): Identify matches of interest

between members of first and second groupbetween members of first and second group

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Statistical IssuesStatistical Issues

Dependencies among observationsDependencies among observations A A B B dependsdepends on on

B B A A BBC, CC, C A A

The return of multilevel modelsThe return of multilevel models Pairs within nominators and nomineesPairs within nominators and nominees Alters within egosAlters within egos People within subgroups within organizationsPeople within subgroups within organizations

Sample and population (?!)Sample and population (?!) Need special techniquesNeed special techniques

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OverviewOverview 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 EthicsEthics Resources

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Influence: How Interactions Affect Beliefs and BehaviorsInfluence: How Interactions Affect Beliefs and Behaviors http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547 (0-7:52) (0-7:52)

Research questionsResearch questionsHow does a teacher’s interactions affect her implementation of innovations?How does a teacher’s interactions affect her implementation of innovations?How does a banker’s interactions affect her profitability?How does a banker’s interactions affect her profitability?How does an adolescent’s interactions affect her delinquency, alcohol use or How does an adolescent’s interactions affect her delinquency, alcohol use or engagement in school?engagement in school?

Theoretical Mechanisms (see Frank and Fahrbach, 1999)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 aroundNormative/conformity : change to conform to others aroundInformation: change based on new informationInformation: change based on new informationDual processes: both applyDual processes: both apply

Friedkin, Noah (2002). Social Influence Network Theory: Toward a Science of Strategic Modification Friedkin, Noah (2002). Social Influence Network Theory: Toward a Science of Strategic Modification of Interpersonal Influence Systems. In National Academy Press: Dynamic Social Network of Interpersonal Influence Systems. In National Academy Press: Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers (2003). Modeling and Analysis: Workshop Summary and Papers (2003). http://www.nap.edu/books/0309089522/html/

Overview3434

The Formal Model of Influence -- the The Formal Model of Influence -- the Network Effect Network Effect

wwii’ii’

Network. Extent of relation between Network. Extent of relation between ii and and i’i’, as perceived by , as perceived by ii. .

yyitit Outcome. An attitude or behavior of actor Outcome. An attitude or behavior of actor ii at time at time tt

∑∑i’i’wwii’ii’yyi’t-1.. i’t-1..

Exposure. Sum of attributes of others to whom actor Exposure. Sum of attributes of others to whom actor i i is related is related at t-1. at t-1.

yyit it = = ρρ∑∑i’i’wwii’t-1ii’t-1ttyyi’t-1 i’t-1 ++γ γ yyit-1 it-1 +e+eitit

Model. Model. Errors are assumed iid normal, with mean zero and Errors are assumed iid normal, with mean zero and variance (σ2). variance (σ2).

' ' 1 1' 1

n

it ii i t it iiy w y y e

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Influence in Words Influence in Words (for technology use)(for technology use)

Use of technology time Use of technology time 22ii==

ρρ[[use of first colleague time use of first colleague time 1]1] + +ρρ[[use of second colleague time use of second colleague time 1]1] + +ρρ[[use of third colleagueuse of third colleague time time 1]1] + +γγ((use time use time 1)1)ii + +

error time error time 22ii

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Exposure to Expertise of Others for Computer Use

A

B

C

D

C

Exposure: Graphical RepresentationExposure: Graphical Representation

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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

ρWY1

2.42.61.1-.5-3- 1

γY1Y2

221-.5-2-.5

= intercept+

=.116+(.125)

+

+ + E2

2.42.61.1-.5-3- 1

Model and Equation: Toy DataModel and Equation: Toy Data

.029-.093.094-.027-.025.022

+ (.67)

0 1 0 1 0 1

0 1 0 1 0 1

x x x x x x

0 x 2.4=0 1 x 2.6=2.60 x 1.1=0 1 x 6-.5=-.50 x -3 =0 1 x – 1=-1 Total =(1.1)/3 =.37

=

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For Actor 3:For Actor 3:

yy3 time 23 time 2= intercept+ = intercept+ ρρ((yy2 time 12 time 1+ y+ y4 time 14 time 1+y+y6 time 16 time 1)/3 + )/3 + γγ y y3 time 1 3 time 1 + e+ e3 3

time 2time 2

1=.116+.125*(2.6-.5-1)/3 + .67(1.1) + .0941=.116+.125*(2.6-.5-1)/3 + .67(1.1) + .094

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Influence ExerciseInfluence Exercise

Assume Bob talks to Sue with frequency 1, to Lisa with frequency 3 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 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. implementation behavior was a 9, Lisa’s was a 5 and Jane’s was 2.

What is the What is the meanmean of the exposure of Bob to his peers regarding of the exposure of Bob to his peers regarding organic farming? organic farming?

Hint ( Mean=sum/n, but what should Hint ( Mean=sum/n, but what should nn be?) be?)

Specify a model with two sources of exposure (e.g., within versus Specify a model with two sources of exposure (e.g., within versus between subgroups)between subgroups)

Influence answers

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Influence Model with Toy Data SoftwareInfluence Model with Toy Data Softwarehttp://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547

(7:52-32:51)(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) (7:52-21:20) Spss tutorialsSpss 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) (21:20-32:51) Sas tutorial: http://www.ats.ucla.edu/stat/sas/Sas tutorial: http://www.ats.ucla.edu/stat/sas/

Influence program using means and merges in stata [save and uncompress] [save and uncompress] Stata tutorial: Stata tutorial: http://www.ats.ucla.edu/stat/stata/

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Exercise: Modifications to the Influence Exercise: Modifications to the Influence Model (SPSS)Model (SPSS)

Is influence increased if we weight exposure by the in-degree (number of Is influence increased if we weight exposure by the in-degree (number of times nominated) of the person influencing (i’)?times nominated) of the person influencing (i’)? Change: COMPUTE exposure=relate * yvar1Change: COMPUTE exposure=relate * yvar1 To: COMPUTE exposure=relate * yvar1*(indeg+1)To: COMPUTE exposure=relate * yvar1*(indeg+1)

Is influence stronger of we take the sum instead of the mean?Is influence stronger of we take the sum instead of the mean? Change: /exposure_mean_1=MEAN(exposure)Change: /exposure_mean_1=MEAN(exposure) To: /exposure_sum_1=SUM(exposure)To: /exposure_sum_1=SUM(exposure) Use exposure_sum_1 in the regressionUse exposure_sum_1 in the regression

What if you didn’t control for the prior?What if you didn’t control for the prior? Change: /METHOD=ENTER exposure_mean_1 yvar1.Change: /METHOD=ENTER exposure_mean_1 yvar1. To /METHOD=ENTER exposure_mean_1.To /METHOD=ENTER exposure_mean_1.

Does coefficient for exposure term depend on prior (interaction term)?Does coefficient for exposure term depend on prior (interaction term)? run influence for technologyrun influence for technology

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Exercise: Modifications to the Influence Exercise: Modifications to the Influence Model (SAS)Model (SAS)

Is influence increased if we weight exposure by the in-Is influence increased if we weight exposure by the in-degree (number of times nominated) of the person degree (number of times nominated) of the person influencing (i’)?influencing (i’)? Set useattr=Set useattr=1; 1;

Is influence stronger of we take the sum instead of the mean?Is influence stronger of we take the sum instead of the mean? Change: mean=totinfl Change: mean=totinfl To: sum=totinfl To: sum=totinfl

What if you didn’t control for the prior?What if you didn’t control for the prior? Change: model yvar2=totinfl yvar1;Change: model yvar2=totinfl yvar1; To: model yvar2=totinfl ;To: model yvar2=totinfl ;

Does coefficient for exposure term depend on prior (interaction Does coefficient for exposure term depend on prior (interaction term)term)

run influence for technologyrun influence for technology

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Questions about W: TimingQuestions about W: Timing

Should we use simultaneous or staggered behavior?Should we use simultaneous or staggered behavior? YYtt==ρρWYWYt t

accounts for all direct and indirect (or primary, secondary, tertiary, accounts for all direct and indirect (or primary, secondary, tertiary, etc) effectsetc) effects

hard to estimate (Y on both sides)hard to estimate (Y on both sides) Christakis and FowlerChristakis and Fowler

http://www.nytimes.com/2009/09/13/magazine/13contagion-t.html?_r=1&pagewanted=1&ref=magazine

YYtt==ρρWYWYt-1 t-1

easier to estimateeasier to estimate Only direct effectsOnly direct effects

eett==ρρWeWett

Autocorrelated disturbances – exposed to the same effectsAutocorrelated disturbances – exposed to the same effects Charles Manski’s reflection problemCharles Manski’s reflection problem

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Observational studies with controls for Observational studies with controls for pretests work better than you think pretests work better than you think

Shadish et al (JASA 2008)Shadish et al (JASA 2008) Quantify how much biased removed by statistical control using Quantify how much biased removed by statistical control using

pretests in a given setting pretests in a given setting Sample: Volunteer undergraduatesSample: Volunteer undergraduates Outcome: Math and vocabulary testsOutcome: Math and vocabulary tests Treatment: Treatment:

basic didactic, basic didactic, showing transparenciesshowing transparencies defining math conceptsdefining 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

OLS might not workOLS might not work

So what would it take to change an So what would it take to change an inference?inference? How strong must a confound be to reduce How strong must a confound be to reduce

estimated effect below a threshold for making estimated effect below a threshold for making an inference?an inference?

https://www.msu.edu/~kenfrank/research.htm#causal

Related to: how bad would your sample have to be to Related to: how bad would your sample have to be to invalidate your inference?invalidate your inference?

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Questions about W:Questions about W:Cohesion versus Structural EquivalenceCohesion versus Structural Equivalence

Cohesion -- direct connections/communicationCohesion -- direct connections/communicationExamples:Examples:

Students’ educational and aspirations decisions are influenced through Students’ educational and aspirations decisions are influenced through direct discussions direct discussions Adolescents’ delinquency is influenced by the delinquency of their Adolescents’ delinquency is influenced by the delinquency of their friendsfriends

Structural Equivalence -- common roles/comparison & comparisonStructural Equivalence -- common roles/comparison & comparisonExamples Examples

Students who occupy similar positions defined by curricular tracks may Students who occupy similar positions defined by curricular tracks may develop similar educational aspirations develop similar educational aspirations Businesses who sell to similar others may adopt similar practicesBusinesses who sell to similar others may adopt similar practices

Direct Influence versus Indirect Influence (Leenders)Direct Influence versus Indirect Influence (Leenders) Are you influenced by those who you do not talk to, but with whom Are you influenced by those who you do not talk to, but with whom

you share intermediaries?you share intermediaries?

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Redundant Effects through A NetworkRedundant Effects through A Network

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Questions about W: Row Normalization Questions about W: Row Normalization and Interpretation of Influenceand Interpretation of Influence

Divide values by row marginalDivide values by row marginal Different transformation for each subjectDifferent transformation for each subject

Changes metric to “influence units” Changes metric to “influence units” Access of one unit of expertise of one Access of one unit of expertise of one influence unitinfluence unit

increases number of uses of computers by xx per increases number of uses of computers by xx per year.year.

Theoretical meaning of “influence units” versus Theoretical meaning of “influence units” versus frequency of interactionfrequency of interaction Could you model “influence unit” with a selection Could you model “influence unit” with a selection

model?model?

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Articles on CausalityArticles on Causality

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Lyons, RussellThe spread of evidence-poor medicine via flawed social-network analysis, Stat., Politics, Policy 2, 1 (2011), Article 2. DOI: 10.2202/2151-7509.1024See 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/

Critique ofChristakis and Fowler“influence” model pages 5-6

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Articles on CausalityArticles on Causality

Articles on CausalityArticles on Causality

5353

Studies of Teachers’ Implementation of InnovationStudies of Teachers’ Implementation of Innovation http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547

(32:51)40:00)(32:51)40:00)

Enumerated network within elementary schoolsEnumerated network within elementary schools Network questions: e.g., “who has helped you Network questions: e.g., “who has helped you

use computers in the last year”use computers in the last year” LongitudinalLongitudinal

2 measures of use of computers a year apart2 measures of use of computers a year apart Multiple studies:Multiple studies:

Technology, 6 schools across nation (1999-2000)Technology, 6 schools across nation (1999-2000) Technology in 26 schools in one state (2002-2003)Technology in 26 schools in one state (2002-2003) Reforms in 21 schools in one state (2004-2005)Reforms in 21 schools in one state (2004-2005) Collective Efficacy in 41 schools in two states (2005-Collective Efficacy in 41 schools in two states (2005-

2006)2006)

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Measures of Y: Use of ComputersMeasures 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 | 3 4 5 guide student communication. 1 2 | 3 4 5 model an idea or activity. 1 2 | 3 4 5 connect the curriculum to real world tasks. 1 2 3 | 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 2extent to which the teacher reported being able to operate computers at time 2How confident the teacher felt with computers at time 2

5555

Format of Network Data (W)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 DailyBob Jones_(2)________ 1 2 3 4Sue Meyer_(3)________ 1 2 3 4____________________ 1 2 3 4____________________ 1 2 3 4Data entered (nominator, nominee, frequency)1 2 21 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)________ 1 2 3 42. Lin Freeman (4)_______ 1 2 3 43. ____________________ 1 2 3 44. ____________________ 1 2 3 4Data entered (nominator, nominee, frequency)2 1 22 4 3

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General Influence Model in Empirical ExampleGeneral Influence Model in Empirical Example

Y=Y=ρρWYWY Y: Teacher’s use of computers in Y: Teacher’s use of computers in

classroom (in times used per year)classroom (in times used per year) W: help or talk about technology (in days W: help or talk about technology (in days

per year)per year) ρρ: network effect of interaction on use of : network effect of interaction on use of

computerscomputers

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.

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A

B

C

D

Help from CC

Exposure to Expertise of OthersExposure to Expertise of Others

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Questions regarding WQuestions regarding W

Take sum or Mean?Take sum or Mean? Timing?Timing? Cohesion versus structural equivalenceCohesion versus structural equivalence Social capital as a guideSocial capital as a guide

5959

Definitions of Social CapitalDefinitions 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)

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Social Capital and the Network Social Capital and the Network EffectEffect

Social Capital=Social Capital=

potential to access resources through social potential to access resources through social relationsrelations

Resource =Expertise Resource =Expertise

Social relation=help from teacher i’ to teacher i.Social relation=help from teacher i’ to teacher i.

' ' 1' 1help expertise

n

ii i ti 6161

Modification: Capacity to Convey Modification: Capacity to Convey ResourceResource

Knoke: account for probability that resource is Knoke: account for probability that resource is conveyed through any interactionconveyed through any interaction

Proxy for ability to convey help: amount of help Proxy for ability to convey help: amount of help provided to othersprovided to others

' ' 1' 1help expertise x total help provided by i'

n

ii i ti

6262

Longitudinal ModelLongitudinal Model

yyii t t=intercept+=intercept+ρ∑ρ∑i’i’wwii’ii’ t-1→t t-1→tyyi’i’ t-1 t-1 x x ∑∑iiwwii’ii’ + +γγyyiit-1t-1

Take sum (resources accessed)Take sum (resources accessed) Partial control for selection of similar Partial control for selection of similar

or valuable others by including or valuable others by including yyiit-1t-1

Continuity through Continuity through γγ..

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Effects of Social Capital on Implementation of Computers in the Effects of Social Capital on Implementation of Computers in the ClassroomClassroom

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Importance of Controlling for the Prior: Longitudinal DataImportance of Controlling for the Prior: Longitudinal Data

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Metric Based on Expertise/DayMetric Based on Expertise/Day

WY is an interaction: WY is an interaction: units = days per year units = days per year x x expertise expertise

Solution 1: interpret standardized coefficientsSolution 1: interpret standardized coefficients Network effect as strong as perceptionsNetwork effect as strong as perceptions

Solution 2:Solution 2: Divide by number of days in a year: WY/365,Divide by number of days in a year: WY/365,

new metric is access to expertise per daynew metric is access to expertise per day .23WY =.23.23WY =.23HelpHelpxxExpertise=84HelpExpertise=84HelpxxExpertise/365Expertise/365 Access of one unit of expertise per day increases Access of one unit of expertise per day increases

number of uses of computers by 84 per year.number of uses of computers by 84 per year.

6666

Your own Influence ModelA) Identify a network in which you are interested

B) Characterize the theoretical processes of influence that occur in the network. Throughwhat 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

I) Compare your representations of social structure

II) Compare your calculations for the example influence model

III) Critique the other person’s influence model

A) Does the model capture the theoretical influence processes? If not, what needs to beadded 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?

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OverviewOverview Introduction Influence Selection

Selection: How Actors Choose Others with whom to Interact Selection Model Selection Exercise Estimation of Selection Model

The p1 Approach Visual Representations of p2 Model Reciprocity: Wii’ (as yij) Wi’i (as yji) Modeled Simultan... Basic Selection Model (p2) Toy Data Setting up p2 Example Output for p2 for Toy Data see also http://stat.g... Selection model (p2): Toy Data Prediction for Pair (2,5) Selection Model (p2): Toy DataPrediction for Pair (2,5) Selection Model (p2): Toy Data Selection Application Transition from Social Exchange to quasi ties ... Alternatives for Running p2

Graphical Representations Centrality EthicsEthics Resources

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Examples of Research QuestionsExamples of Research Questions

How do farmers decide to whom to provide help?How do farmers decide to whom to provide help?How do bankers decide to whom to loan money?How do bankers decide to whom to loan money?How do social service agencies choose other agents to refer clients to?How do social service agencies choose other agents to refer clients to?

Theoretical Mechanisms (see Frank and Fahrbach, 1999)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.

Balance seeking/homophily -- seeking to interact with others like yourself Balance seeking/homophily -- seeking to interact with others like yourself

Information seekingInformation seeking Goal orientedGoal oriented , , Reduce uncertainty , Power orientedReduce uncertainty , Power oriented , , Better Better understandingunderstanding , , Curiosity, Curiosity, InoculateInoculate

Evidence of EffectsEvidence of Effects

Adolescents select friends who are like themselvesAdolescents select friends who are like themselvesTeachers who want to be innovative interact with other innovatorsTeachers who want to be innovative interact with other innovators

Selection: How Actors Choose Others with whom to InteractSelection: How Actors Choose Others with whom to Interact

http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd-491e-bf30-0b2377f332a6

: (0:00-19:40): (0:00-19:40)

Overview6969

Selection ModelSelection Model

Absolute value of difference in attributes

'0 1 '

'

( )log

1 ( )ii

i iii

p wy y

p w

Represents the effect of difference in attribute

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The Logistic Regression ModelThe Logistic Regression Model

The "logit" model solves these problems:The "logit" model solves these problems:

ln[p/(1-p)] = ln[p/(1-p)] = 00 + + 11X X

p is the probability that the event Y occurs, p is the probability that the event Y occurs, p(Y=1) p(Y=1) [range=0 to 1][range=0 to 1]

p/(1-p) is the "odds ratio" p/(1-p) is the "odds ratio" [range=0 to ∞][range=0 to ∞]

ln[p/(1-p)]: log odds ratio, or "logit“ln[p/(1-p)]: log odds ratio, or "logit“ [range=-∞ to +∞][range=-∞ to +∞]

7171

x

x

e

exyP

1)(

7272

Interpretation of OgiveInterpretation of Ogive

The logistic distribution constrains the The logistic distribution constrains the estimated probabilities to lie between 0 and estimated probabilities to lie between 0 and 1. 1.

The estimated probability is:The estimated probability is:

p = 1/[1 + ep = 1/[1 + e((00 + + 11X )X )] ]

if you let if you let 00 + + 11X =0, then p = .50 X =0, then p = .50

as as 00 + + 11X gets really big, p approaches 1 X gets really big, p approaches 1

as as 00 + + 11X gets really small, p approaches 0X gets really small, p approaches 0

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Selection ExerciseSelection Exercise

A) Write a model for whether two actors talked as A) Write a model for whether two actors talked as a function of whether they are of different race a function of whether they are of different race and whether they are of different gender.and whether they are of different gender.

wwii’ii’ represents whether represents whether ii and  and i’ i’ talked, talked,

yyii represents the gender of represents the gender of ii (0 if male, 1 if female), (0 if male, 1 if female), and and

zzii represents the race of represents the race of i i (0 if white, 1 if African (0 if white, 1 if African American)American)

(You’ll need one term for effects associated with (You’ll need one term for effects associated with gender, and another for race)gender, and another for race)

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Selection ExerciseSelection Exercise

B) Assume that Bob and Lisa are African B) Assume that Bob and Lisa are African American and that Jane and Bill are white. Bill American and that Jane and Bill are white. Bill and Bob are Male and Lisa and Jane are female.and Bob are Male and Lisa and Jane are female.

Calculate the independent variables based on Calculate the independent variables based on difference of race and gender for Bob with each difference of race and gender for Bob with each of his interaction partners:of his interaction partners:

(Bob, Lisa): different gender = _______; (Bob, Lisa): different gender = _______; different race = _________ different race = _________(Bob, Jane): different gender =_______; (Bob, Jane): different gender =_______; different race = _________ different race = _________(Bob, Bill): different gender = _______; (Bob, Bill): different gender = _______; different race =__________ different race =__________

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Selection ExerciseSelection Exercise

C) Assuming the values of the C) Assuming the values of the θθ’s are ’s are negative and that the effect of race is negative and that the effect of race is stronger than that of gender, who is Bob stronger than that of gender, who is Bob most likely to talk to?most likely to talk to?

D) Include a term capturing the interaction of D) Include a term capturing the interaction of similarity of race and gendersimilarity of race and gender

Selection answers 7777

Estimation of Selection ModelEstimation of Selection Model

Use the example of wUse the example of wii’ii’ being whether one being whether one

teacher helped another teacher helped another

Naive: logistic regression:Naive: logistic regression:

Similarity of attributes captured by -|Similarity of attributes captured by -|yyi t-hi t-h - y - yi’ t-hi’ t-h| .| .

Likelihood function: p(A and B) = p(A)×p(B) Likelihood function: p(A and B) = p(A)×p(B) if A if A and B are independent. and B are independent. NO! NO!

HelpHelpii’ii’ is not independent of Helpis not independent of Helpii”ii” !!

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The pThe p11 Approach Approach

WWi’i i’i =0=0 WWi’i i’i =1=1

WWii’ ii’ =0=0 Cell ACell A

(reciprocity)(reciprocity)

Cell BCell B

WWii’ ii’ =1=1 Cell CCell C Cell DCell D

(reciprocity)(reciprocity)

Model as 4 cells, A,B,C,D instead of just WWii’ii’ =0 =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.

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Estimation via p*Estimation via p*

8080

Visual representations of p2 modelVisual representations of p2 modelcontrol for dependencies associated with nominator and nomineecontrol for dependencies associated with nominator and nominee

http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd-491e-bf30-0b2377f332a6

: (12:41-19:40): (12:41-19:40)

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.

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Reciprocity: WReciprocity: Wii’ ii’ (as y(as yijij) W) Wi’i i’i (as y(as yjiji)) Modeled Simultaneously Modeled Simultaneously

(Lazega and Van Duijn 1997)(Lazega and Van Duijn 1997)

8282

Selection Model (p2)Selection Model (p2)

'0 0 ' 1 ' '

'

( )log

1 ( )ii

i i i i i iii

p wy y w

p w

0 00 01i

i i iy u '

0 ' 00 01 ' 'i

i i iy v

Pair Level (i,i’)

Sender Level (i) or nominator

Receiver Level (i’) or nominee

ui ~N(0,τu)

Vi’ ~N(0,τv)

Difference In attribute reciprocity

Sender attribute

Receiver attribute

Sender variance

Receiver variance

8383

Boots and Shoes:Boots and Shoes:aligning my notation with Marijtje’saligning my notation with Marijtje’s

Level 1Level 1

'0 0 ' 1 ' '

'

( )log

1 ( )ii

i i i i i iii

p wy y w

p w

Pair Level (i,i’)

Difference In attribute reciprocity

8484

( )log

1 ( )ij

i j i j jiij

p yy y y

p y

z

Pair Level (j,i)

Modeling density

Boots and Shoes:Boots and Shoes:aligning my notation with Marijtje’saligning my notation with Marijtje’s

Level 2Level 2

0 00 01i

i i iy u

'0 ' 00 01 ' '

ii i iy v

Sender (i)

Receiver (j)

ui ~N(0,τu)

Vi’ ~N(0,τv)

attribute

attribute

variance

variance

8585

1i i ix A

2j j jx B

covariance

Nominator (i)

nominee (i’)

Setting up p2Setting up p2

http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd-491e-bf30-0b2377f332a6

: (19:40-42:25): (19:40-42:25)0) make square network data file out of list using makemat.sas will put 0) make square network data file out of list using makemat.sas will put file called file called

c:\stocnet\network\matrix.datc:\stocnet\network\matrix.dat

1) Using Van Duijn’s p2:1) Using Van Duijn’s p2:go to: go to: http://stat.gamma.rug.nl/stocnet/go to downloads and save stocnet in c:\stocnet (follow directions if you go to downloads and save stocnet in c:\stocnet (follow directions if you

install somewhere else).install somewhere else).

Unzip into c:\stocnetUnzip into c:\stocnetrun stocnet.exerun stocnet.exe

Manual available @ Manual available @ http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf

Skip running p2

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Toy dataToy data

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0 1 1 0 0 01 0 1 0 0 00 1 0 1 0 00 0 0 0 1 10 0 0 1 0 00 0 1 1 0 0

Outcome network data at time tSave in c:\stocnet\networks\toyw.dat

0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0

Optional: network data at t-1Save in c:\stocnet\networks\pretoyw.dat

2.4 2 2.6 2 1.1 1 -.5 -.5 -3 -2 -1 -.5

Attributes (1 & 2)Save in c:\stocnet\actfiles\toyatt.dat

To convert edgelist data for p2 (using sas):KLiqueFinder can also convert an edgelist to p2 data: set option 14 in printo to a 1. output will be in xxxxxx.dat, where “xxxxxx” are the 1st 6 characters of your filename

Running p2Running p2

Start a new session byStart a new session by1.1. Click on “Start with new session”Click on “Start with new session”

2.2. Then hit the “Apply” buttonThen hit the “Apply” button

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Running p2Running p2

Click on the “Data” icon to add data.Click on the “Data” icon to add data.

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Running p2Running p2

Click on the Click on the “Add…” button.“Add…” button.1) add network 1) add network data collt1.datdata collt1.dat2) add network 2) add network data coll21.datdata coll21.dat3) add actor data 3) add actor data indiv.datindiv.dat

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Running p2Running p2

Once you finish Once you finish adding data, click adding data, click on the “Apply” on the “Apply” button first.button first.

Then, you can Then, you can click on the “View” click on the “View” button to view button to view data.data.

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Running p2Running p2

Click on the “Model” iconClick on the “Model” icon

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Running p2Running p2

Select the p2 modelSelect the p2 model

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Running p2Running p2

Click on the “Data specification” buttonClick on the “Data specification” button

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Running p2Running p2put network1 (toydata) into digraphput network1 (toydata) into digraph

put file1 (indiv) into selected attributesput file1 (indiv) into selected attributes

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Running p2Running p2 Specify model with actor attributes on Specify model with actor attributes on

network parametersnetwork parameters

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Density is pair level for us

Visual Representations of Selection Visual Representations of Selection ModelsModels

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Selection Model (p2)Selection Model (p2)

'0 0 ' 1 ' '

'

( )log

1 ( )ii

i i i i i iii

p wy y w

p w

0 00 01i

i i iy u '

0 ' 00 01 ' 'i

i i iy v

Pair Level (i,i’)

Sender Level (i)

Receiver Level (i’)

ui ~N(0,τu)

Vi’ ~N(0,τv)

Difference In attribute reciprocity

Sender attribute

Receiver attribute

Sender variance

Receiver variance

9999

Toy DataToy DataNetwork (w) Attribute

y1 y2

2

2

3

2

1

2

total

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Total 1 2 3 3 1 2

W

|Yi-Yi’ |

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Example Output for p2 for Toy DataExample Output for p2 for Toy Datasee also http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdfsee also http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf

P2MCMC RW ml mvP2MCMC RW ml mv

testtoy.outtesttoy.out

October 13, 2009, 11:36:25 AMOctober 13, 2009, 11:36:25 AM

@1@1

General Information:General Information:

Digraph: C:\stocnet\temp\~toyw.datDigraph: C:\stocnet\temp\~toyw.dat

@1@1

General Information:General Information:

Digraph: C:\stocnet\temp\~toyw.datDigraph: C:\stocnet\temp\~toyw.dat

October 13, 2009, 11:36:25 AMOctober 13, 2009, 11:36:25 AM

Number of valid tie indicator observations: 45Number of valid tie indicator observations: 45

@1@1

Descriptives:Descriptives:

GroupGroup Observed Initial Tie variables Digraph Number of ties Observed Initial Tie variables Digraph Number of ties Reciprocal ties Mutliplex ties Exchange tiesReciprocal ties Mutliplex ties Exchange ties

Size Size Present MissingSize Size Present Missing

11

6 6 30 0 ~toyw.dat 12 10 - -6 6 30 0 ~toyw.dat 12 10 - -

102102

VariancesVariances@1@1Random effects:Random effects: parameter standard quantiles from sampleparameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5estimate error 0.5 2.5 25 50 75 97.5 99.5

((τu) sender variance : 0.4323 0.4288 0.05 0.08 0.18 0.29 0.51 1.69 2.67 ) sender variance : 0.4323 0.4288 0.05 0.08 0.18 0.29 0.51 1.69 2.67

((τv) receiver variance: 4.9249 7.4311 0.05 0.08 0.24 2.37 6.76 25.69 37.16 ) receiver variance: 4.9249 7.4311 0.05 0.08 0.24 2.37 6.76 25.69 37.16

((τuv) covariance -0.3081 1.7522 -6.96 -5.24 -0.52 0.01 0.29 2.58 5.21 ) covariance -0.3081 1.7522 -6.96 -5.24 -0.52 0.01 0.29 2.58 5.21

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Selection model (p2): Toy DataSelection model (p2): Toy Data

'0 0 ' ' '

'

( )log -2.38 3.76

1 ( )ii

i i i i i iii

p wy y w

p w

0 3.79 .308i i iy u

0 ' '3.79 [not modeled]i iv

Pair level (i,i’)

Sender Level (i)

Receiver Level (i’)

ui ~N(0,.43)

vi ~N(0,4.9)

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Regression CoefficientsRegression Coefficients

@1@1Fixed effects:Fixed effects:

@2@2Overall effects:Overall effects: parameter standard quantiles from sampleparameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5estimate 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@2Specific covariate effects:Specific covariate effects:

@3@3Sender covariates:Sender covariates: parameter standard quantiles from sampleparameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5estimate 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@3Density covariates:Density covariates: parameter standard quantiles from sampleparameter standard quantiles from sample estimate error 0.5 2.5 25 50 75 97.5 99.5estimate 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.This last term models wither difference in attribute 1 predicts density.

105105

0 is contained within the 95% interval of the posterior distribution

Selection model (p2): Toy DataSelection model (p2): Toy Data

'0 0 ' ' '

'

( )log + -2.38 3.76

1 ( )ii

i i i i i iii

p wy y w

p w

0 3.79 .308i i iy u

0 ' '3.79 [not modeled]i iv

Pair level (i,i’)

Sender Level (i)

Receiver Level (i’)

ui ~N(0,.43)

vi ~N(0,4.9)

Bigger difference more interaction

High Reciprocity

Big y2 more interaction

106106

Combined Selection model (p2): Toy DataCombined Selection model (p2): Toy Data

'' '

'

( )log 3.79 .308 + -2.38 3.76

1 ( )ii

i i i i i iii

p wy u y y w

p w

0 3.79 .308i i iy u

Pair level (i,i’)

Sender Level (i)

ui ~N(0,.43)

Θ0i’

107107

Add Dyadic CovariateAdd Dyadic Covariate

108108

Specify P2 ModelSpecify P2 Model

109109

P2 Data SpecificationP2 Data Specification

110110

P2 Model SpecificationP2 Model Specification

111111

Modify Parameters for Quick EstimationModify Parameters for Quick Estimation

112112

Prediction for Pair (2,5) Selection Model Prediction for Pair (2,5) Selection Model (p2): Toy Data(p2): Toy Data

2,5

2 2 5 5,2

2,5

-5.1

2,5 -5.1

p(w )log =3.79+.308×2 -2.38 2 --2 +3.760

1-p(w )

=3.79+.308×2-2.38×4+3.760(0)=-5.1,

ep(w )= =.006

1+e

Pair level (2,5)

Actual value: W2,5=0

113113

Keeping Terms Straight in p2Keeping Terms Straight in p2

Q: Who helps you with math?Q: Who helps you with math?SenderSender =person who nominates others=person who nominates others

=person who receives help =person who receives help

=expansiveness=expansiveness

Receiver Receiver = person who is nominated by others = person who is nominated by others

= person who provides help = person who provides help

=attractiveness=attractiveness

Keeping Terms Straight in p2Keeping Terms Straight in p2

Q: Who gave you cigarettes?Q: Who gave you cigarettes?

SenderSender =person who nominates others=person who nominates others

=person who receives cigarettes=person who receives cigarettes

=expansiveness=expansiveness

Receiver Receiver = person who is nominated by others = person who is nominated by others

= person who provides cigarettes= person who provides cigarettes

=attractiveness=attractiveness

Exercise for P2Exercise for P2

How can you make an inference about the How can you make an inference about the effect of similarity of an attributeeffect of similarity of an attribute

What happens to the similarity of attribute What happens to the similarity of attribute when you control for time 1?when you control for time 1?

Try putting in the model:Try putting in the model: Difference in attribute1+attribute1 on Difference in attribute1+attribute1 on

sender+attribute1 on receiversender+attribute1 on receiver Did it work? Did it work?

What is the difference between putting in What is the difference between putting in difference in attribute instead of absolute difference in attribute instead of absolute value of the difference? value of the difference?

Marijtje Van Duijn’s P2 in her own wordsMarijtje Van Duijn’s P2 in her own words

http://www.gmw.rug.nl/~steglich/dynamics/workshop/sienap2ergm.pdf

Data sets: Data sets: http://www.stats.ox.ac.uk/~snijders/siena/s50_data.htm Try s50: 50 teenage girls, friendships at 3 Try s50: 50 teenage girls, friendships at 3

time points: time points: http://www.stats.ox.ac.uk/~snijders/siena/s50_data.htm

Look at full reportLook at full report

variances

Alternatives for Running p2Alternatives for Running p2

In sas:In sas:download Sam Field’s p2 via sas from my web site:download Sam Field’s p2 via sas from my web site:http://www.msu.edu/~kenfrank/software.htm#Selection_Models:_p2

download glimmix from my web site and save to c:\download glimmix from my web site and save to c:\run glimmix.sas in sasrun glimmix.sas in sasrun Sam’s program (p2_explore.sas)run Sam’s program (p2_explore.sas)Note it generates its own ego and alter files (see data Note it generates its own ego and alter files (see data ii and and

data data jj) and network data () and network data (a5a5), but these could be read in.), but these could be read in.

Can also do using Peter Hoff’s R routine Can also do using Peter Hoff’s R routine http://www.stat.washington.edu/hoff/Code/GBME/. For For R, go to http://cran.cnr.berkeley.edu/R, go to http://cran.cnr.berkeley.edu/

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Selection ApplicationSelection ApplicationTransition from Social Exchange to Systemic Exchange Via Quasi-TiesTransition from Social Exchange to Systemic Exchange Via Quasi-Ties

http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd-491e-bf30-0b2377f332a6

: (42:25-48:00): (42:25-48:00)

Frank, K.A. 2009 Quasi-Ties: Directing Resources to Members of a Collective

American Behavioral Scientist.  52: 1613-1645 123123

p2 extended modelp2 extended model

Quasi-tie

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

125125

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

Quasi-tie

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OverviewOverview

Introduction Influence Selection Graphical Representations

KliqueFinder Step 1) Criteria for Determining defining clusters Step 2) Maximizing Criterion Step 3) Examine evidence of clusters Step 4) Evaluating the performance of the algorithm : Did... Crystalized sociogram of Close Collegial Ties

Ripple Plot Running KliqueFinder

Centrality EthicsEthics Resources

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KliqueFinder: KliqueFinder: Identifying Clusters in Network DataIdentifying Clusters in Network Data

Go to: Go to: https://www.msu.edu/user/k/e/kenfrank/web/resources.htm#KliqueFinder

Based on:Based on: FrankFrank, K. 1996. “Mapping interactions within and between cohesive , K. 1996. “Mapping interactions within and between cohesive

subgroups.” subgroups.” Social Networks Social Networks 18: 93-119.18: 93-119. FrankFrank. K.A. 1995. “Identifying Cohesive Subgroups.” . K.A. 1995. “Identifying Cohesive Subgroups.” Social NetworksSocial Networks (17): (17):

27-56.27-56. *Field, S. **Field, S. *Frank, K.A.Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. 2006. , Schiller, K, Riegle-Crumb, C, and Muller, C. 2006.

“Identifying Social Contexts in Affiliation Networks: Preserving the Duality of “Identifying Social Contexts in Affiliation Networks: Preserving the Duality of People and Events. People and Events. Social NetworksSocial Networks 28:97-123. * co first authors. 28:97-123. * co first authors.

https://www.msu.edu/user/k/e/kenfrank/web/research.htm#representation

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129129

Scenarios for the Network analystScenarios for the Network analyst

For each of the scenarios below, For each of the scenarios below, identify the theoretical processes at workidentify the theoretical processes at workwrite down what model or tool you would employ to evaluate the theory. 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 data you would collect to apply the model or tool to describe what estimation procedure/tool you would use.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 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. 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 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 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.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?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 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.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? What clustering among social service agencies might emerge as a result of the processes above?

130130

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 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

' '' 1

n

i ii iie w e e We

ei is the centrality of actor i. wii is the network data. λ is a constant

131131

Bonacich Centrality Revised

132132

Critique of CentralityCritique of Centrality

Individualistic, not view of networkIndividualistic, not view of network Does not explicitly account for resources Does not explicitly account for resources

flowing through tiesflowing through ties structuralstructural

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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?

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Barnett G., & Rice, R.: warp. (1985, Longitudinal Non-Euclidean Networks: Applying Galileo, Social

Networks, pages 287-322):

135135

Calculating Warp: Still not sure how this Calculating Warp: Still not sure how this works?works?

EIGEN FACTOR VALUE ------- ------- 1: 13.238 2: -1.000 3: -12.238 ======= ======= 26.475

WARP=175/(175-1-149)=175/25=7

136136

OverviewOverview

Introduction Influence Selection Graphical Representations Centrality EthicsEthics

Confidentiality/Ethical issues in Collecting Confidentiality/Ethical issues in Collecting Network Data Network Data

The SRI/KliqueFinder Solution to confidentiality.The SRI/KliqueFinder Solution to confidentiality. Actual relations not revealed

Resources

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OverviewOverview

Introduction Influence Selection Graphical Representations Centrality EthicsEthics Resources

Logistics of Data Collection Organizing data entry Resources for Networks: Books Resources for Networks: Web Resources: Clearinghouses Resources: Individual web Pages

138138

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.

139139

Organizing data entrycheck out: check out:

http://www.classroomsociometrics.com/http://www.classroomsociometrics.com/

140140

Confidentiality/Ethical issues in Collecting Network Data

Need names on survey

Data can be confidential but not anonymous (especially for longitudinal)

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.pdfhttp://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

141141Video: >rich media >vodcast>podcast>Course Portal (1:23:41-1:28)

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; structureProtection: 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.

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Scenarios for the Network Analyst: Scenarios for the Network Analyst: Ethical ConsiderationsEthical Considerations

For your previous answer to each of the scenarios below, identify For your previous answer to each of the scenarios below, identify who would benefit from the analysis, who would benefit from the analysis, who bears the costswho bears the costshow confidentiality of subjects could be protectedhow 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 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. 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 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 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.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?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 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.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? What clustering among social service agencies might emerge as a result of the processes above?

144144

Resources for Networks: Books

• Kadushin, Charles. (2012). Understanding Social Networks: Theories, Kadushin, Charles. (2012). Understanding Social Networks: Theories, Concepts, and Findings. Oxford: Oxford University Press.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.

145145

Resources for Networks: Courses Resources for Networks: Courses and Introductionsand Introductions

Introductory On the WebBorgatti’s slide show:

http://www.analytictech.com/networks/intro/index.htmlhttp://www.analytictech.com/networks/intro/index.html

Kadushin’s introhttp://www.charleskadushin.com/

Barry Wellman’s intro:Social Network Analysis: An Introductionhttp://www.chass.utoronto.ca/~wellman/publications/index.html

David Knoke’s intro to social network methods: http://www.soc.umn.edu/%7Eknoke/pages/SOC8412.htmhttp://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

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General ResourcesGeneral Resources International social network analysis web page:

http://www.insna.org/

Syllabi:Syllabi:: : http://www.ksg.harvard.edu/netgov/html/sna_courses_evhttp://www.ksg.harvard.edu/netgov/html/sna_courses_events.htments.htm

147147

Resources: Individual Web PagesResources: Individual Web Pages Individual Web Pages :

Phil Bonacich http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4

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

Ken Frank http://www.msu.edu/~kenfrank/http://www.msu.edu/~kenfrank/

Linton Freemanh http://moreno.ss.uci.edu/lin.html

James Moody http://www.soc.duke.edu/~jmoody77/

Mark Newman: http://www-personal.umich.edu/~mejn/

Tom Snijders http://www.stats.ox.ac.uk/~snijders/

Barry Wellman: http://www.chass.utoronto.ca/~wellman/http://www.chass.utoronto.ca/~wellman/

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Resources dataResources data

http://snap.stanford.edu/index.htmlhttp://snap.stanford.edu/index.html Stanford, large data setsStanford, large data sets

http://datamob.org/datasets/tag/social-networkshttp://datamob.org/datasets/tag/social-networks Multiple potential sources (including Enron)Multiple potential sources (including Enron)

http://www-personal.umich.edu/~mejn/netdata/http://www-personal.umich.edu/~mejn/netdata/ Mark newmanMark newman

http://vlado.fmf.uni-lj.si/pub/networks/data/UciNet/UciData.htmhttp://vlado.fmf.uni-lj.si/pub/networks/data/UciNet/UciData.htm UCINETUCINET

http://www.nd.edu/~networks/resources.htmhttp://www.nd.edu/~networks/resources.htm BarabasiBarabasi

http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/20541http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/20541 National Social Life, Health, and Aging Project (NSHAP)National Social Life, Health, and Aging Project (NSHAP)

http://www.insna.org/software/data.htmlhttp://www.insna.org/software/data.html INSNA pageINSNA page

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Resources ExerciseResources Exercise

Find 2 web resources not listed above and Find 2 web resources not listed above and post them on angelpost them on angel

150150

Influence Exercise: AnswersInfluence Exercise: Answers

Assume Bob talks to Sue with frequency 1, to Lisa with frequency 3 and not at all to 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 Jane. Last year (at time 1), Sue’s organic farming implementation was a 9, Lisa’s was a 5 and Jane’s was 2. a 5 and Jane’s was 2.

What is the What is the meanmean exposure of Bob’s to his peers regarding delinquency? exposure of Bob’s to his peers regarding delinquency? Sum=1x9+3x5+0x2=24Sum=1x9+3x5+0x2=24

N= 2 (number Bob talks to) or 3 (number of people) or 4 (number of N= 2 (number Bob talks to) or 3 (number of people) or 4 (number of interactions)? Hmmmmmm.interactions)? Hmmmmmm.

Mean = 24/2=12 or 24/3=8 or 24/4=6. Mean = 24/2=12 or 24/3=8 or 24/4=6.

Or, use the sum?Or, use the sum?

Specify a model with two sources of exposure (e.g., within versus between subgroupsSpecify a model with two sources of exposure (e.g., within versus between subgroupsLet sLet sii’ ii’ =1 if i and i’ are in the same subgroup, 0 otherwise=1 if i and i’ are in the same subgroup, 0 otherwise

yit ρwithinni 1,ii

siiwii yi t 1 ρbetweenni 1,i i

(1 sii )wiiyi t 1 γyi t 1 eit .yit ρwithinni 1,ii

siiwii yi t 1 ρbetweenni 1,i i

(1 sii )wiiyi t 1 γyi t 1 eit .

Return to influence 151151

Selection AnswersSelection Answers

'0 1 ' 2 '

'

( )log

1 ( )ii

i i i iii

p wy y z z

p w

152152

Selection AnswersSelection AnswersB) Assume Bob that and Lisa are African American and that Jane and Bill arewhite. Bill and Bob are Male and Lisa and Jane are female.

Calculate the independent variables based on race and gender for Bobwith each of his interaction partners:

(Bob, Lisa): different gender = |0-1|=1; different race = |1-1|=0

(Bob, Jane): different gender = |0-1|=1 ; different race = |1-0|=1

(Bob, Bill): different gender = |0-0|=0 ; different race = |1-0|=1

B) Assume Bob that and Lisa are African American and that Jane and Bill are

153153

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 answersSelection answers

Return to selection

D

154154

For Bob and Jane: .4-.2(1)-.5(1)= -.3

Resources ExerciseResources Exercise

Find 2 web resources not listed above and Find 2 web resources not listed above and post them on angelpost them on angel

155155

Bounds on Bounds on ρρ(Based in part on dissertation by Jiqiang (Based in part on dissertation by Jiqiang

Xu)Xu) Ord says 1/Ord says 1/λλminmin < < ρρ < 1/ < 1/λλmaxmax , , λλ is an eigen value is an eigen value

likelihood =G[OLS, ∑likelihood =G[OLS, ∑aaln(1-ln(1-ρλρλaa)])]

Alternative: eigen values and eigen vectors (V):Alternative: eigen values and eigen vectors (V): λλV =WV → V =(1/ V =WV → V =(1/ λλ)WV)WV

Perfect fit if Perfect fit if ρρ=1/ =1/ λλ, , eigen value eigen value λλaa

with Y = corresponding eigen vector, Vwith Y = corresponding eigen vector, Vaa

156156

40|0000

04|0000

10|4430

00|3403

00|2044

00|0234

03.

06.

54.

50.

50.

46.

9999

9999

1.

01.

01.

1.

40|0000

04|0000

10|4430

00|3403

00|2044

00|0234

W=

W=Y=

Y=OLS estimate of ρ = 1.21, R2=.97

OLS estimate of ρ = .5, R2=.99

157157

Substantive Restriction on YSubstantive Restriction on Y

1/1/λλminmin < < ρρ < 1/ < 1/λλmax max to confine to largest to confine to largest

componentcomponent What if there are multiple components?What if there are multiple components?

Separate estimate of Separate estimate of ρρ in each component, in each component, average over components?average over components?

Standardize: z(Standardize: z(ρρ)= p/(1/)= p/(1/λλmaxmax -1/ -1/λλminmin))

158158

Find the network modelFind 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?

159159

Measure of Bridging CapitalMeasure of Bridging Capital

160160

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?

161161

162162

Prior to workshopPrior to workshop

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1)Standard statistical software packageSas, spss or stata

2) KliqueFinder:–http://pikachu.harvard.edu/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/Currency.USD/

3) Stocnet

http://stat.gamma.rug.nl/stocnet/

4) These slides

https://www.msu.edu/user/k/e/kenfrank/web/resources.htm

see “workshop materials”

5) quick power point on how to use KliqueFinder

6) KNOW REGRESSION!

model building, predicted values, errors and inference, assumptions

Plan of Activities Day 1 of 2 day Plan of Activities Day 1 of 2 day workshopworkshop

9-10:15: Introduction to social network analysis9-10:15: Introduction to social network analysis

10:15-10:45 scramble exercise (introductions)10:15-10:45 scramble exercise (introductions)

10:45-11 break10:45-11 break

11-12 introduction to influence model11-12 introduction to influence model

Includes exerciseIncludes exercise

12-1 Lunch 12-1 Lunch

make introductions from scramble exercise!make introductions from scramble exercise!

1-1:45 application of the influence model1-1:45 application of the influence model

1:45-2:30 introduction to selection model1:45-2:30 introduction to selection model

Includes exerciseIncludes exercise

2:30-2:45 Break2:30-2:45 Break

2:45-3:30 application of the selection model2:45-3:30 application of the selection model

3:30-3:4:30 Clustering an graphical representations3:30-3:4:30 Clustering an graphical representations

includes interactive exerciseincludes interactive exercise

4:30-5 set up for second day [download videos]4:30-5 set up for second day [download videos]

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Plan of Activities Day 2: SoftwarePlan of Activities Day 2: Software 9-9:15: Break into groups to focus on 9-9:15: Break into groups to focus on

Influence, selection, graphical representationsInfluence, selection, graphical representations

9:15-10:15 Watch video demonstration and try 9:15-10:15 Watch video demonstration and try basicsbasics

10:15-12 supported experimentation and 10:15-12 supported experimentation and explorationexploration

12-1: lunch12-1: lunch 1-2: example demonstration of theoretical models1-2: example demonstration of theoretical models 2-3:30 supported experimentation with models2-3:30 supported experimentation with models

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Research on networks in educationResearch on networks in education

on teachers:on teachers:    Jim SpillaneJim Spillane Peter YoungsPeter Youngs Cynthia CoburnCynthia Coburn Alan DalyAlan Daly Min SunMin Sun Chong Min KimChong Min Kim Nienke MoolenaarNienke Moolenaar Ben PogodzinskiBen Pogodzinski Bill PenuelBill Penuel Russell ColeRussell Cole Jonathan SupovitzJonathan Supovitz Kara FinniganKara Finnigan Kara JacksonKara Jackson Paul CobbPaul Cobb Tom SmithTom Smith      

On adolescent networks On adolescent networks on schoolson schools

   Bill CarbonaroBill Carbonaro Jim MoodyJim Moody Yu XieYu Xie Chandra MuellerChandra Mueller Ann Strassman MullerAnn Strassman Muller Derek KreigerDerek Kreiger

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