Introduction to the Models and Tools for Social Networks - PowerPoint PPT Presentation

Loading...

PPT – Introduction to the Models and Tools for Social Networks PowerPoint presentation | free to download - id: 201dce-YWU0N



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Introduction to the Models and Tools for Social Networks

Description:

Favorites: Doreian: Social Network Effects added to other Effects ... Favorites: Breiger: Tracking Network Analysis from Metaphor to Application ... – PowerPoint PPT presentation

Number of Views:457
Avg rating:3.0/5.0
Slides: 152
Provided by: CSGin7
Learn more at: http://www.msu.edu
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Introduction to the Models and Tools for Social Networks


1
Introduction to the Models and Tools for Social
Networks
  • Kenneth Frank, College of Education and Fisheries
    and Wildlife
  • Help from Ann Krause, Ben Michael Pogodzinski,
    Bo Yan, Min Sun, I-Chen
  • start camtasia and save at end

2
(No Transcript)
3
Overview
  • Introduction
  • Overview
  • What Are Social Networks?
  • Representations of Social Networks Sociomatrix
  • Representations Notation
  • Representations Sociogram
  • Characteristics of Social Network Data
  • Ego Centric Data
  • Favorites
  • Barry Wellman on Misconceptions
  • Doreian Social Network Effects added to other...
  • Breiger Tracking Network Analysis from Metaph...
  • Mine Frank Integrating Social Networks into
    Models and G...
  • Personal
  • Two Fundamental Processes Involving Human Social
    Networks
  • Selection and Influence
  • Causality
  • Scramble Exercise
  • Influence

4
What Are Social Networks?
  • A set of actors and the ties or relations 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)

5
Representations of Social Networks
  • Friendships among the French financial elite
  • Matrix
    Edgelist
  • 1 13
  • 211 21112 1 17
  • 1545463790 1 19
  • 1......111. 25 14
  • 25..1....11. 25 19
  • 14.1.1.1.11. 14 25
  • 15..1..1.11. 14 15
  • 4.......11. 14 26
  • 26..11...11. 14 17
  • 131......11. 14 19
  • 171111111.11 15 14
  • 1911111111.. 15 26
  • 20.......1.. 15 17
  • 15 19
  • 4 17

6
Representations Notation
  • xij, takes a value of 1 if i nominates j , 0
    otherwise x1 250, x1 131
  • Ken uses
  • wii, takes a value of 1 if i nominates i, 0
    otherwise w1 250, w1 131

7
Representations Sociogram
Lines indicate friendships solid within
subgroups, dotted between subgroups. numbers
represent actors Rgt,Cen,Soc,Non political
parties BBanker, Ttreasury EEcole National
Dadministration
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
8
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?
  • Modes
  • One mode actor to actor
  • Friendship, bullying
  • Two mode actors and events
  • Students and the courses they attend
  • Ceos and the boards they are members of
  • Centricity
  • Sociocentric whole social network
  • Egocentric each person and their own network

9
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
10
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.
11
FavoritesBarry Wellman on Misconceptions
12
FavoritesDoreian 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.

13
FavoritesBreiger 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. 505526 in Handbook of Data Analysis, edited
    by Melissa Hardy and Alan Bryman. London Sage
    Publications, 2004. http//www.u.arizona.edu/brei
    ger/NetworkAnalysis.pdf

14
MineFrank Integrating Social Networks into
Models and Graphical Representations
  • Multilevel models
  • Accounts for nesting of people within groups
    (e.g., students within schools)
  • Effects of groups modeled at the group level
    (e.g., effect of school restructuring on
    achievement
  • Assumptions
  • Groups independent of each other
  • People within groups independent of each other.
    Hmmmmmmmm.
  • People within schools influence each other
  • Student to student
  • Teacher to teacher
  • Teacher to student
  • People within schools select interaction partners
  • Adolescents friends and peers
  • Teachers close colleagues
  • Frank, K. A. 1998. "The Social Context of
    Schooling Quantitative Methods". Review of
    Research in Education 23, chapter 5 171-216.

15
Social Processes in Schools
16
Personal
  • I started my work with Valerie Lee, my
    dissertation chair was Tony Bryk, and my first
    faculty mentor was Steve Raudenbush.
  • Raudenbush, S. W., and A.S. Bryk.
    2002 Hierarchical linear models Applications and
    data analysis methods (2nd ed.). Thousand Oaks,
    CA Sage.
  • This article is my recognition of their
    influences and then pushing to networks
  • Charles Bidwell played a strong roll
  • Aaron Pallas, Steve Raudenbush and Noah Friedkin
    as editors

17
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.
18
Selection and Influence
Leenders, R. (1995). Structure and influence
Statistical models for the dynamics of actor
attributes, network structure and their
interdependence. Amsterdam Thesis Publishers.
  • Selection and Influence always present
  • Ignore them at your peril! biased / wrong
    estimates

Change in Behavior
Behavior
Influence
selection
Relations
Change in Relations
0 1 2 3
Time
19
Causality
  • Is it selection or influence?
  • Do people choose to interact with others like
    themselves (selection) or do they change
  • Birds of a feather flock together
  • Beliefs/behaviors based on interactions with
    others (influence)?
  • Shes 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)

20
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

21
Scramble Exercise
  • Think Identify a network
  • Actors
  • Relations
  • Directionality, Valued relations, Multiple
    relations, Modes, Centricity
  • Process and bases of Influence (e.g., normative?)
  • Process and bases of Selection (e.g.,
    homophily?)
  • Form Meet and share in groups of 3-4
  • Others Question bases for making inferences
  • Scramble Form new group of 3-4 people
  • Matchmaker Identify matches of interest between
    members of first and second group

22
Overview
  • Introduction
  • Influence
  • Influence How Interactions Affect Beliefs and
    Behaviors
  • The Formal Model of Influence -- the Network
    Effect
  • Influence in Words (for teachers use of
    computers)
  • Exposure Graphical Representation
  • Model and Equation Toy Data
  • For Actor 3
  • Influence Exercise
  • Influence Model with Toy Data Software
  • Questions about W Timing
  • Studies of Teachers Implementation of Innovation
  • Measures of Y Use of Computers
  • Format of Network Data (W)
  • General Influence Model in Empirical Example
  • Definitions of Social Capital (Individual Level)
  • Social Capital and the Network Effect
  • Modification Capacity to Convey Resource
  • Longitudinal Model

23
Influence How Interactions Affect Beliefs and
Behaviors
  • Research questions
  • How does a teachers interactions affect her
    implementation of innovations?
  • How does a bankers interactions affect her
    profitability?
  • How does an adolescents interactions affect her
    delinquency, alcohol use or engagement in school?
  • Theoretical Mechanisms
  • Normative/conformity change to conform to
    others around
  • Information change base don new information
  • Dual processes both apply

Overview
24
The Formal Model of Influence -- the Network
Effect
  • wii
  • Network. Extent of relation between i and i, as
    perceived by i.
  • yit
  • Outcome. An attitude or behavior of actor i at
    time t
  • ?iwiiyit-1..
  • Exposure. Sum of attributes of others to whom
    actor i is related at t-1.
  • yit ??iwiiyit-1 ? yit-1 eit
  • Model. Errors are assumed iid normal, with mean
    zero and variance (s2).

25
Influence in Words (for teachers use of
computers)
use of computers time 2i ?use of first
colleague time 1 ?use of second colleague
time 1 ?use of last colleague time 1 ?(use
time 1)i error time 2i
26
Exposure Graphical Representation
27
Model and Equation Toy Data
?WY1
?Y1
Y2

E2

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
2.4 2.6 1.1 -.5 -3 - 1
2 2 1 -.5 -2 -.5
2.4 2.6 1.1 -.5 -3 - 1
.11 -.01 .21 .13 .09 .13
0 1 0 1 0 1
x x x x x x
0 x 2.40 1 x 2.62.6 0 x 1.10 1 x -.5-.5 0
x -3 0 1 x 1-1 Total (1.1)/3 .36
0 1 0 1 0 1
(.15)


(.67)

28
For Actor 3
  • y3 time 2 ?(y2 time 1 y4 time 1y6 time 1)/3
    ? y3 time 1 e3 time 1
  • 1.15(2.6-.5-1)/3 .67(1.1) .21

29
Influence Exercise
  • Assume Bob talks to Sue with frequency 1, to Lisa
    with frequency 2 and not at all to Jane. Last
    year (at time 1), Sues delinquency behavior was
    a 9, Lisas was a 5 and Janes was 2.
  • What is the mean of the influence of Bobs peers
    regarding delinquency?
  • Hint ( Meansum/n, but what should n be?)
  • Specify a model with two sources of influence
    (e.g., within versus between subgroups

Influence answers
30
Influence Model with Toy Data Software
  • http//www.msu.edu/kenfrank/software.htmInfluenc
    e_Models_
  • Influence program using means and merges in spss
  • influence program using proc means and merges in
    sas

31
Exercise Modifications to the Influence Model
  • Is influence increased if we weight exposure by
    the in degree (number of times nominated) of the
    person influencing (i)?
  • Change COMPUTE exposurerelate yvar1
  • To COMPUTE exposurerelate yvar1(indeg1)
  • Is influence stronger of we take the sum instead
    of the mean?
  • Change /exposure_mean_1MEAN(exposure)
  • To /exposure_sum_1SUM(exposure)
  • What if you didnt control for the prior?
  • Change /METHODENTER exposure_mean_1 yvar1.
  • To /METHODENTER exposure_mean_1.

32
Questions about W Timing
  • Should we use simultaneous or staggered behavior?
  • Yt?WYt
  • 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/13conta
    gion-t.html?_r1pagewanted1refmagazine
  • Yt?WYt-1
  • easier to estimate
  • Only direct effects
  • et?Wet
  • Autocorrelated disturbances exposed to the same
    effects
  • Charles Manskis reflection problem

33
Studies of Teachers Implementation of Innovation
  • 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)

34
Measures of Y Use of Computers
  • Teachers Use of Technology at Time 2 (a.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 (a.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

35
Format of Network Data (W)
Your name Lisa Jones (person 1) Please indicate
who helped you with computers at xxx and the
frequency with which you interact with each
person. Name Yearly Monthly Weekly
Daily Bob Jones_(2)________ 1 2 3 4 Sue
Meyer_(3)________ 1 2 3 4 ____________________
1 2 3 4 ____________________ 1 2 3 4 Data
entered (nominator, nominee, relate) 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)________ 1 2 3 4 2.
Lin Freeman (4)_______ 1 2 3 4 3.
____________________ 1 2 3 4 4.
____________________ 1 2 3 4 Data entered
(nominator, nominee, relate) 2 1 2 2 4 4
36
General Influence Model in Empirical Example
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.
  • Y?WY
  • Y Teachers use of computers in classroom (in
    times used per year)
  • W help or talk about technology (in days per
    year)
  • ? network effect of interaction on use of
    computers

37
Exposure to Expertise of Others
38
Questions regarding W
  • Take sum or Mean?
  • Timing?
  • Cohesion versus structural equivalence
  • Social capital as a guide

39
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)

40
Social Capital and the Network Effect
  • Social Capital
  • potential to access resources through social
    relations
  • Resource Expertise
  • Social relationhelp from teacher i to teacher i.

41
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

42
Longitudinal Model
  • yi t??iwii t-1?tyi t-1 x ?iwii ?yit-1
  • Take sum (resources accessed)
  • Partial control for selection of similar or
    valuable others by including yit-1
  • Continuity through ?.

43
Effects of Social Capital on Implementation of
Computers in the Classroom
44
Importance of Controlling for the Prior
Longitudinal Data
45
Overview
  • 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) Wii (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 Data
  • Selection Application Transition from Social
    Exchange to quasi ties ...
  • Alternatives for Running p2
  • Graphical Representations

46
Selection How Actors Choose Others with whom to
Interact
  • Examples of Research Questions
  • How do teachers 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 (references from Frank
    Fahrbach 1999)
  • Balance seeking/homophily -- seeking to interact
    with others like yourself
  • Information seeking Goal oriented
  • Reduce uncertainty
  • Power oriented
  • Better understanding
  • Curiosity
  • Inoculate
  • Evidence of Effects

Overview
47
Selection Model
Absolute value of difference in attributes
Represents the effect of difference in attribute
48
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.
  • wii represents whether i and i talked,
  • yi represents the gender of i (0 if male, 1 if
    female), and
  • zi represents the race of i (0 if white, 1 if
    African American)
  • (Youll need one term for effects associated with
    gender, and another for race)

49
Selection Exercise
  • B) Assume Bob that 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 __________

50
Selection Exercise
  • C) Assuming the values of the ?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
51
Estimation of Selection Model
  • Use the example of wii being whether one teacher
    helped another
  • Naive logistic regression
  • Similarity of attributes captured by -yi t-h -
    yi t-h .
  • Likelihood function p(A and B) p(A)p(B) if A
    and B are independent. NO!
  • Helpii is not independent of Helpii !

52
The p1 Approach
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.
Model as 4 cells, A,B,C,D instead of just Wii 0
53
Visual representations of p2 modelcontrol for
dependencies associated with nominator and nominee
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/stocne
t/ 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.
54
Reciprocity Wii (as yij) Wii (as yji) Modeled
Simultaneously (Lazega and Van Duijn 1997)
55
Basic Selection Model (p2)
Pair Level (i,i)
Difference In attribute
reciprocity
Sender Level (i)
Sender variance
Sender attribute
ui N(0,tu)
Receiver Level (i)
Receiver attribute
Receiver variance
Vi N(0,tv)
56
Toy Data
Network (w)
Attribute y1 y2
total
2 2 3 2 1 2
57
Yi-Yi
W
58
Setting up p2
Skip running p2
  • 0) make square network data file out of list
    using makemat.sas will put file called
    c\stocnet\network\matrix.dat
  • sas program for formatting toy data for p2
  • 1) Using Van Duijns p2
  • go to http//stat.gamma.rug.nl/stocnet/
  • go to downloads and save stocnet in c\stocnet
    (follow directions if you install somewhere
    else).
  • Unzip into c\stocnet
  • run stocnet.exe
  • Manual available _at_ http//stat.gamma.rug.nl/stocne
    t/downloads/manualp2.pdf

59
Running p2
  • Start a new session by
  • Click on Start with new session
  • Then hit the Apply button

60
Running p2
  • Click on the Data icon to add data.

61
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

62
Running p2
  • Once you finish adding data, click on the Apply
    button first.
  • Then, you can click on the View button to view
    data.

63
Running p2
  • Click on the Model icon

64
Running p2
  • Select the p2 model

65
Running p2
  • Click on the Data specification button

66
Running p2
  • put network1 (toydata) into digraph
  • put file1 (indiv) into selected attributes

67
Running p2
  • Specify model with actor attributes on network
    parameters

68
Add Dyadic Covariate
69
Specify P2 Model
70
P2 Data Specification
71
P2 Model Specification
72
Example Output for p2 for Toy Datasee also
http//stat.gamma.rug.nl/stocnet/downloads/manualp
2.pdf
  • P2MCMC RW ml mv
  • testtoy.out
  • October 13, 2009, 113625 AM
  • _at_1
  • General Information
  • Digraph C\stocnet\temp\toyw.dat
  • _at_1
  • General Information
  • Digraph C\stocnet\temp\toyw.dat
  • October 13, 2009, 113625 AM
  • Number of valid tie indicator observations 45
  • _at_1
  • Descriptives

73
Variances
  • _at_1
  • Random effects
  • parameter standard
    quantiles from sample
  • estimate error
    0.5 2.5 25 50 75 97.5 99.5
  • (tu) sender variance 0.4323 0.4288
    0.05 0.08 0.18 0.29 0.51 1.69 2.67
  • (tv) receiver variance 4.9249 7.4311
    0.05 0.08 0.24 2.37 6.76 25.69 37.16
  • (tuv) covariance -0.3081 1.7522
    -6.96 -5.24 -0.52 0.01 0.29 2.58 5.21

74
Selection model (p2) Toy Data
Pair level (i,i)
Sender Level (i)
ui N(0,.43)
Receiver Level (i)
vi N(0,4.9)
75
Regression Coefficients
  • _at_1
  • Fixed effects
  • _at_2
  • Overall effects
  • parameter standard
    quantiles from sample
  • 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
  • Reciprocity toyw.dat 3.7586 2.3022
    -1.35 -0.30 2.16 3.67 4.99 9.24 10.33
  • _at_2
  • Specific covariate effects
  • _at_3
  • Sender covariates
  • parameter standard
    quantiles from sample
  • estimate error
    0.5 2.5 25 50 75 97.5 99.5

76
Selection model (p2) Toy Data
Pair level (i,i)
Bigger difference ? more interaction
High Reciprocity
Sender Level (i)
Big y2 ? more interaction
ui N(0,.43)
Receiver Level (i)
vi N(0,4.9)
77
Combined Selection model (p2) Toy Data
Pair level (i,i)
?0
Sender Level (i)
ui N(0,.43)
78
Prediction for Pair (2,5) Selection Model (p2)
Toy Data
Pair level (2,5)
Actual value W2,50
79
Selection ApplicationTransition from Social
Exchange to Systemic Exchange Via Quasi-Ties
Frank, K.A. 2009 Quasi-Ties Directing Resources
to Members of a Collective American Behavioral
Scientist.  52 1613-1645
80
p2 extended model
Quasi-tie
81
Interaction of Close Colleagues and
Identification of the Potential Provider on the
Provision of Help Evidence of a Quasi-Tie
82
Cross Nested Multilevel Poisson Regression (i.e.,
p2 social network model)of Extent ( of days per
year) to which i Helped i
Quasi-tie
83
Alternatives for Running p2
  • In sas
  • download Sam Fields p2 via sas from my web site
  • http//www.msu.edu/kenfrank/software.htmSelectio
    n_Models_p2
  • download glimmix from my web site and save to c\
  • run glimmix.sas in sas
  • run Sams 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.
  • Tom Snijders SIENA (dynamic models, includes
    influence model)
  • http//stat.gamma.rug.nl/siena.html
  • Can also do using Peter Hoffs R routine
    http//www.stat.washington.edu/hoff/Code/GBME/.
    For R, go to http//cran.cnr.berkeley.edu/
  • Statnet exponential random graph models
  • http//csde.washington.edu/statnet/

84
Overview
  • 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
  • Ethics
  • Resources

85
KliqueFinder
  • Finds subgroups and embeds in sociogram
  • 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.
  • For full details, see
  • file///C/Documents20and20Settings/kenfrank/My
    20Documents/MyFiles/my20web20page/research.htmr
    epresentation

86
Clustering and Graphical Representations of
Networks
  • Goal to identify patterns in the network
  • Rearrange rows and columns of social network
    matrix to reveal clustering
  • Plot actors and ties in two dimensions to reveal
    clustering
  • Theory for defining cluster membership
  • cohesion (clusters are called subgroups) an
    actor should be in a cluster if the actor has
    demonstrated a preference for engaging in ties
    with members of the cluster. Result ties are
    concentrated within subgroups
  • structural equivalence (blocks) an actor should
    be in a cluster if the actor engages in a similar
    pattern of ties as members of that cluster.
  • Result blocks represent positions, but ties not
    necessarily concentrated within blocks.

87
Steps for finding clusters
  • 1) determine criterion for defining clusters
  • 2) maximize criterion
  • 3) Examine evidence of clusters
  • 4) evaluate performance of the algorithm
  • 5) interpret clusters
  • commonality of attributes
  • focal experiences
  • subsequent behavior

88
Step 1) Criteria for Determining defining
  • Structural Equivalence
  • Factor analyze sociomatrix (Katz Kahn)
  • iteratively rearrange and revalue rows and
    columns (CONCORR -- White el al., 1976)
  • Cohesion
  • utilize fixed criteria (e.g., must be connected
    to at least k others in clusters, or must be
    minimal path length from k others, etc).
  • use flexible criterion -- preference relative
    to group sizes and number of ties

89
Model Based Cohesion
  • samegroupii 1 if actors i and i are members
    of the same subgroup,
  • 0 otherwise.
  • Then ?1 represents subgroups salience
  • So ...... Maximize ?1 (odds ratio)

90
Odds Ratio for Association Between Common
Subgroup Membership and The Occurrence of Ties
Between Actors
91
Finding number of subgroups
  • 1) find a subgroup seed (3 actors who interact
    with each other, and with similar others)
  • 2) add to the cluster to maximize ?1 until you
    cannot do any more
  • 3) start new subgroup with new seed
  • 4) shuffle between existing subgroups
  • 5) make new subgroups as necessary, dissolve old
    ones as necessary.

92
Step 2) Maximizing Criterion
N Group And Actor Id 24
AAAABBBBBBCCCCCCCCDDDDDD
2 1221
1 11 2111122 Group ID7445612214981335
60796037 -----------------------------------
- 1 A 7A213.................1.. 1
A 244A3........4............ 1 A
433A..................... 1 A
15433A.................... ----------------
-------------------- 2 B
26.2..B443................ 2 B
21.1..4B.......4........2. 2 B
12....4.B................. 2 B
2....33.B.............1.. 2 B
1..3.3..3B..........3..2. 2 B
14........1B.............. ----------------
-------------------- 3 C
9..........C...3.33.3.... 3 C
8.4....4....C.4..4.4..... 3 C
11..........33C.4.3...4... 3 C
13.4...4....444C.......... 3 C
33....4....4.44C......... 3 C
5.1.......43.2.3C........ 3 C
6..........444..4C4...... 3 C
20..........3..3.44C...... ----------------
-------------------- 4 D
17.1.........1......D.1... 4 D
19..........4.3.....3D4... 4 D
16..........4..4...444D... 4 D
10..3....1.............D3. 4 D
23.....3.............343D. 4 D
27.1...1.............3..3D
?1 1.1738
93
Step 3) Examine evidence of clusters
  • 1) randomly redistribute ties
  • 2) apply algorithm
  • 3) record value of odds ratio
  • 4) repeat 1000 times to generate distribution
  • 5) use mean of distribution as baseline for
    comparison

94
Distribution of ?1base From Application of the
Algorithm to Data Simulated Without Regard for
Subgroup Membership
Observed value 1.1738
95
Output for Sampling Distribution
  • PREDICTED THETA (1 base) BASED ON SIMULATIONS.
  • VALUE BASED ON UNWEIGHTED DATA.
  • 0.76985
  • ESTIMATE OF THETA (1 subgroup processes)
  • 0.40397 (total-predictedevidence of
    groups) 1.1738-.76985.40397
  • THE TOTAL THETA1 IS
  • 1.1738
  • APPROXIMATE TEST OF CONCENTRATION OF TIES
  • WITHIN SUBGROUPS BASED ON
  • SIZE OF THETA1 subgroup processes
  • THETA1
  • SUBGROUP APPROX APPROX
  • PROCESSES LRT P-VALUE
  • 0.40 34.82 0.00

96
Step 4) Evaluating the performance of the
algorithm Did the Algorithm Recover the Correct
Subgroups?
  • Many algorithms search for optimal subgroups.
    KliqueFinder does not, but how different are the
    subgroups it finds from the optimal or known
    subgroups?

97
Output for Recovery of Subgroups
PREDICTED ACCURACY LOG ODDS OF COMMON
SUBGROUP MEMBERSHIP, OR - .5734 (FOR A 95
CI) 1.4989 The Log odds applies to the
following table OBSERVED
SUBGROUP DIFFERENT SAME
___________________
DIFFERENT A B
KNOWN
SUBGROUP ----------------
SAME C
D
------------------- THE
LOGODDS TRANSLATES TO AN ODDS RATIO OF
4.4766 WHICH INDICATES THE INCREASE IN THE
ODDS THAT KLIQUEFINDER WILL ASSIGN TWO ACTORS
TO THE SAME SUBGROUP IF THEY ARE TRULY IN THE IN
THE SAME SUBGROUP.
98
Crystalized sociogram of Close Collegial Ties
Step 5 Interpret
99
Sociogram of Our Hamilton High
100
(No Transcript)
101
Representations Sociogram
Lines indicate friendships solid within
subgroups, dotted between subgroups. numbers
represent actors Rgt,Cen,Soc,Non political
parties BBanker, Ttreasury EEcole National
Dadministration
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
102
Clusters in Foodwebs
Krause, A., Frank, K.A., Mason, D.M., Ulanowicz,
R.E. and Taylor, W.M. (2003). "Compartments
exposed in food-web structure." Nature
426282-285
103
Cryslaized SociogramClose Colleagues among
Teachers
G indicates grade level taught
104
Ripple Plot
  • Overlay talk about technology on geography of
    crystallized sociogram
  • Lines indicate talk about technology
  • Size of dot indicates teachers use of technology
    at time 1
  • Ripples indicate increase in use from time 1 to
    time 2

105
(No Transcript)
106
Running KliqueFinder
  • Download KliqueFinder at
  • http//www.msu.edu/kenfrank/software.htmKliqueFi
    nder_
  • Follow instructions to install
  • Replace c\kliqfind\kliqfind.exe with alternate
    kliquefinder from Angel, using right click

SKIP TO NEXT SECTION
107
KliqueFinder
  • Click Run Analysis.
  • Once the analysis is finished, click Clusters
    output button to view the evidence of subgroups
    and performance of algorithm.
  • Close clusters output
  • Go to netdraw and open data file as file/open/vna
    textfile/complete

108
KliqueFinder
  • Click on Browse button to specify the
    directory where the data file is located.

109
KliqueFinder
  • Choose Basic setup and then click Run setup
    file button.

110
KliqueFinder
  • Click on the Browse button to choose a data
    file.

111
Run Analysis
112
View Clusters Output
113
Sociomatrix for Stanne.list
AFTER ASCENT N Group And Actor Id
24 AAAABBBBBBCCCCCCCCDDDDDD

2 1221 1 11 2111122 Group
ID744561221498133560796037 ----------------
-------------------- 1 A
7A213.................1.. 1 A
244A3........4............ 1 A
433A..................... 1 A
15433A.................... ----------------
-------------------- 2 B
26.2..B443................ 2 B
21.1..4B.......4........2. 2 B
12....4.B................. 2 B
2....33.B.............1.. 2 B
1..3.3..3B..........3..2. 2 B
14........1B.............. ----------------
-------------------- 3 C
9..........C...3.33.3.... 3 C
8.4....4....C.4..4.4..... 3 C
11..........33C.4.3...4... 3 C
13.4...4....444C.......... 3 C
33....4....4.44C......... 3 C
5.1.......43.2.3C........ 3 C
6..........444..4C4...... 3 C
20..........3..3.44C...... ----------------
-------------------- 4 D
17.1.........1......D.1... 4 D
19..........4.3.....3D4... 4 D
16..........4..4...444D... 4 D
10..3....1.............D3. 4 D
23.....3.............343D. 4 D
27.1...1.............3..3D
114
PREDICTED THETA (1 base) BASED ON
SIMULATIONS. VALUE BASED ON UNWEIGHTED DATA.
0.76985 ESTIMATE OF THETA (1 subgroup
processes) 0.40397 THE TOTAL THETA1
IS 1.1738 THETA1 ALSO CAN BE
INTERPRETED AS HALF THE LOG-ODDS OF THE
FOLLOWING TABLE, INCLUDING OBSERVED AND
(EXPECTED) VALUES TIE
NO YES
___________________
NO 1604. 92.
(1560.) ( 136.) IN SAME
SUBGROUP ----------------
YES 320.
192. ( 364.) ( 148.)

------------------- ODDS RATIO, LOG
ODDS, (LOG ODDS/2) -------------------------------
------------ Observed 10.46087 2.34764
1.17382 Expected 4.66315 1.53969 0.76985
115
APPROXIMATE TEST OF CONCENTRATION OF TIES WITHIN
SUBGROUPS BASED ON SIZE OF THETA1 subgroup
processes THETA1 SUBGROUP APPROX
APPROX PROCESSES LRT P-VALUE
0.40 34.82 0.00 APPROXIMATE TEST OF
CONCENTRATION OF TIES WITHIN SUBGROUPS BASED ON
CONSERVATIVE PREDICTED VALUE FOR THETA1
THETA1 SUBGROUP APPROX APPROX
PROCESSES LRT P-VALUE 0.37 29.42
0.00 These p-values are based on a
likelihood ratio test between the models LOG
P(Xii'xii')theta0theta1base(samegroup) LOG
P(Xii'xii')theta0theta1base(samegroup)
theta1 subgroup processes(samegroup) A SMALL
P-VALUE INDICATES THAT ONE CAN REJECT THE NULL
HYPOTHESIS THAT theta1 subgroup processes IS
ZERO. AND WE TAKE THIS AS EVIDENCE THAT
ACTORS ENGAGE IN EXCHANGES WITHIN SUBGROUPS AT A
RATE THAT IS UNLIKELY TO HAVE OCCURRED BY CHANCE
ALONE.
116
Make Sociogram in Netdraw
117
Sociogram of Our Hamilton High
118
KliqueFinder ApplicationsAdding Individual
Attributes
  • run KliqueFinder
  • data file collt1.list
  • make graph
  • use ID from other file? Yes
  • sas file name c\kliqfind\indiv
  • be sure to include full path
  • id variable nominator
  • string variable gradelev
  • Save
  • In sas, run socgramz in the working directory

119
KliqueFinder ApplicationsAdding Individual
Attributes
  • Select Yes for User ID (character) from other
    SAS file?

120
KliqueFinder ApplicationsAdding Individual
Attributes
  • Type the following information in the
    corresponding boxes
  • Then Click Save

121
Choosing an ID Variable
122
With ID based on Grade
123
KliqueFinder ApplicationsReplacing Lines
  • run KliqueFinder
  • data file collt1.list
  • make graph
  • save
  • retrieve socgramz.sas in the working directory
  • replace all occurrences of collt1.list with
    collt2.list
  • run

124
Opening socgramz.sas
125
Changing lines
126
Change lines to different source
127
New Lines based on Collt2
128
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 daughters 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?

129
Overview
  • Introduction
  • Influence
  • Selection
  • Graphical Representations
  • Centrality
  • Centrality The strength of the Connection
    between an Ac...
  • Bonacich Centrality Revised
  • Critique of Centrality
  • Centralization -- the Centrality of the System
  • Barnett G., Rice, R. warp. (1985,
    Longitudinal Non-...
  • Ethics
  • Resources

130
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/syllabu
    s_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 (wii1 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

ei is the centrality of actor i. wii is the
network data. ? is a constant
131
Bonacich Centrality Revised
132
Critique of Centrality
  • Individualistic, not view of network
  • Does not explicitly account for resources flowing
    through ties
  • structural

133
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?

134
Barnett G., Rice, R. warp. (1985,
Longitudinal Non-Euclidean Networks Applying
Galileo, Social Networks, pages 287-322)
135
Calculating Warp
EIGEN FACTOR VALUE -------
------- 1 13.238 2 -1.000
3 -12.238 26.475
WARP175/(175-1-149)175/257
136
Overview
  • Introduction
  • Influence
  • Selection
  • Graphical Representations
  • Centrality
  • Ethics
  • Confidentiality/Ethical issues in Collecting
    Network Data
  • The SRI/KliqueFinder Solution to confidentiality.
  • Actual relations not revealed
  • Resources

137
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/2005BreigerIntro
    Ethics.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.
  • 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/social20network/irb
    20with20network20data.htm

138
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.

139
Actual relations not revealed
140
Overview
  • Introduction
  • Influence
  • Selection
  • Graphical Representations
  • Centrality
  • Ethics
  • Resources
  • Logistics of Data Collection
  • Organizing data entry
  • Resources for Networks Books
  • Resources for Networks Web
  • Resources Clearinghouses
  • Resources Individual web Pages

141
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

142
Organizing data entrycheck out
http//www.classroomsociometrics.com/
143
Resources for Networks Books
  • Kadushin, Charles (2010) Making Connections An
    introduction to social network theory, concepts
    and findings
  • 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?bookIDGPUB01
    133-00001
  • 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.

144
Resources for Networks Web
  • Introductory On the Web
  • Borgattis slide show
  • http//www.analytictech.com/networks/intro/index.h
    tml
  • Kadushins intro
  • http//home.earthlink.net/ckadushin/Texts/Basic2
    0Network20Concepts.pdf
  • Barry Wellmans introSocial Network Analysis An
    Introduction
  • http//www.chass.utoronto.ca/wellman/publication
    s/index.html
  • David Knokes intro to social network methods
  • http//www.soc.umn.edu/7Eknoke/pages/SOC8412.ht
    m
  • Wasserman, S., Faust, K. (1994). Social
    networks analysis Methods and applications. New
    York Cambridge University.
  • Jim Moodys course http//www.soc.duke.edu/jmood
    y77/s884/syllabus_09.htm

145
General Resources
  • International social network analysis web page
    http//www.insna.org/
  • Syllabi http//www.ksg.harvard.edu/netgov/html/s
    na_courses_events.htm

146
Resources Individual Web Pages
  • Individual Web Pages
  • Phil Bonacich http//www.sscnet.ucla.edu/soc/facul
    ty/bonacich/home.htm
  • Ron Breiger (http//www.u.arizona.edu/breiger/)
  • Ronald Burt (google Ron Burt)
  • http//portal.chicagogsb.edu/portal//server.pt/gat
    eway/PTARGS_0_2_332_207_0_43/http3B/portal.chicag
    ogsb.edu/Facultycourse/Portlet/FacultyDetail.aspx?
    min_year20044max_year20063person_id30400
  • Ken Frank 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.santafe.edu/mark/
  • Tom Snijders http//stat.gamma.rug.nl/snijders/

147
Resources Exercise
  • Find 2 web resources not listed above and post
    them on angel

148
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), Sues delinquency behavior was
    a 9, Lisas was a 5 and Janes was 2.
  • What is the mean of the influence of Bobs peers
    regarding delinquency?
  • Sum1x93x50x224
  • N 2 (number Bob talks to) or 3 (number of
    people) or 4 (number of interactions)? Hmmmmmm.
  • Mean 24/212 or 24/38 or 24/64.
  • Or, use the sum?
  • Specify a model with two sources of influence
    (e.g., within versus between subgroups
  • Let sii 1 if i and i are in the same subgroup,
    0 otherwise

Return to influence
149
Selection Answers
150
Selection Answers
151
Selection answers
C
D
Return to selection
About PowerShow.com