Introduction to the Models and Tools
for Social Networks
Kenneth Frank, College of Education and
Fisheries and Wildlife
Help from: Ann Krause, Ben Michael
Pogodzinski, Bo Yan, Min Sun, I-Chen,
Chong Min Kim
1
Abstract

Many quantitative analyses in the social sciences are applied to data
regarding characteristics of people, but not to data describing interactions
among people. But interactions play an important role in affecting people’s
behavior and beliefs that cannot be explained purely in terms of individual
attributes or organizational context. In this workshop we will focus on
analyzing social network data (who interacts with whom) so that we can relate
people's interactions with what they think and do. We draw on statistical
concepts that account for the unusual nature of network data as well as
substantive theories across the social sciences to specify and interpret social
network models.

Topics include models of influence through a social network, choices in a
social network, clustering and graphical representations; ethical issues and
IRB, and software. Throughout examples are given using simple toy data and
analyses in published papers.

Students taking this workshop should have roughly one year of applied
statistics so that they are extremely comfortable with the general linear model
(regression and ANOVA), and analysis of 2x2 tables.
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
Introduction
Overview
 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...
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Mine Frank: Integrating Social Networks into Models and G...
Personal
Two Fundamental Processes Involving Human Social Networks
Selection and Influence
Causality
Scramble Exercise
Influence
Selection
Graphical representations
Centrality
Ethics
Resources
9
What Are Social Networks?
 A set of actors and the ties (resource flows) or relations
(stable states) among them.

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close colleagues (relation) among teachers (actors)
help (tie) one teacher (actor) provides to another
communication (tie) between people (actors) in an organization
friendships (relation) among politicians (actors)
links (relation) among web sites (actors)
referrals (tie) among social service agencies (actors)
 For me: actors must
 have agency
 Able to take deliberate action
 Actor network theory ? Can artifacts have agency and take
deliberate action?
 More than BookFace
10
Format of Network Data (W)
Your name: Lisa Jones (person 1)
Please indicate who helped you with computers at xxx and the frequency with which you interact with each person.
Name
Yearly
Monthly
Weekly
Daily
Bob Jones_(2)________
1
2
3
4
Sue Meyer_(3)________
1
2
3
4
____________________
1
2
3
4
____________________
1
2
3
4
Data entered (nominator, nominee, frequency)
1 22
1 34
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, frequency)
212
243
11
Representations of Social Networks
Friendships among the French financial elite
Matrix
1
25
14
Edgelist
15
4
26
1
1
25
1
14
1
15
1
1
1
1
4
26
1
1
13
1
17
1
1
1
1
1
1
19
1
1
1
1
1
1
20
13
17
19
20
1 21112
1
211
1545463790
1
1
1|......111.|
1
1
25|..1....11.|
1
1
14|.1.1.1.11.|
1
1
15|..1..1.11.|
4|.......11.|
1
1
26|..11...11.|
1
1
13|1......11.|
1
1
1
17|1111111.11|
19|11111111..|
1
1
20|.......1..|
1
1 13
1 17
1 19
25 14
25 19
14 25
14 15
14 26
14 17
14 19
15 14
15 26
15 17
15 19
4 17
4 19
12
Representations: Notation
 xij, takes a value of 1 if i nominates j , 0
otherwise: x1 25=0, x1 13=1
 Ken uses:
wii’, takes a value of 1 if i nominates i’, 0
otherwise: w1 25=0, w1 13=1
13
Representations: Sociogram
Lines indicate
friendships:
solid within
subgroups,
dotted between
subgroups.
numbers
represent actors
Rgt,Cen,Soc,Non
= political parties;
B=Banker,
T=treasury;
E=Ecole National
D’administration
Frank, K.A. & Yasumoto, J. (1998). "Linking Action to Social Structure within a System: Social Capital
Within and Between Subgroups." American Journal of Sociology, Volume 104, No 3, pages 642-686
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Characteristics of Social Network Data
 Directionality
 If A nominates B as a bully, B may not nominate A as a bully
 Valued relations
 How frequently does teacher A interact with teacher B?
 Multiple relations
 Are students friends, romantic partners, coursemates?
 Centricity
 Sociocentric: whole social network
 Egocentric: each person and their own network
 Modes
 One mode: actor to actor
 Friendship, bullying
 Two mode: actors and events
 Students and the courses they attend
 Ceo’s and the boards they are members of
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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
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rank, K.A., Muller, C., Schiller, K., Rieglerumb, C., Strassman-Muller, A., Crosnoe,
., Pearson J. 2008. “The Social Dynamics
Mathematics CourseTaking in high
chool.” American Journal of Sociology, Vol
13 (6): 1645-1696.
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Two mode: actors
and events
21
Favorites:
Barry Wellman on Misconceptions
22
Favorites:
Doreian: Social Network Effects added to
other Effects
 Inner causes: psychological motivation
 Ascriptive effects: gender
 Social network effects: centrality in group
 Doreian, Patrick (2001). “Causality in
Social network Analysis.” Sociological
Methods and Research, Vol 30, No. 1, 81114.
23
Favorites:
Breiger: Tracking Network Analysis from
Metaphor to Application
 Great review of theoretical motivations for
network analysis dating back to Marx,
Durkheim, Cooley
 Includes emphasis on cognition
 Breiger, R.L. “The Analysis of Social
Networks.” Pp. 505–526 in Handbook of
Data Analysis, edited by Melissa Hardy
and Alan Bryman. London: Sage
Publications, 2004.
http://www.u.arizona.edu/~breiger/NetworkAnalysis.pdf
24
Mine
Frank: Integrating Social Networks into Models and
Graphical Representations
 Multilevel models
 Accounts for nesting of people within groups (e.g., students within
schools)
 Effects of groups modeled at the group level (e.g., effect of school
restructuring on achievement
 Assumptions
 Groups independent of each other
 People within groups independent of each other. Hmmmmmmmm.
 People within schools influence each other
 Student to student
 Teacher to teacher
 Teacher to student
 People within schools select interaction partners
 Adolescents’ friends and peers
 Teachers’ close colleagues

Frank, K. A. 1998. "The Social Context of Schooling: Quantitative Methods". Review
of Research in Education 23, chapter 5: 171-216.
25
Social Processes in Schools
26
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
27
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.
28
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 |
Relations |
Change in Relations
0
1
2
Time
3
29
Causality
 Is it selection or influence?
 Do people choose to interact with others like themselves (selection) or
do they change
 Birds of a feather flock together
 Beliefs/behaviors based on interactions with others (influence)?
 She’s hanging out with the wrong crowd!
 Need longitudinal data!!!!!!!
 Influence
 With whom did you talk over the last week: asked at week 2 (12)
 What are your beliefs? (asked at week 1)
 What are your beliefs (asked at week 2)
 Selection
 With whom did you talk over the last week: asked at week 1 (0 1)
 With whom did you talk over the last week: asked at week 2 (1 2)
 What are your beliefs? (asked at week 1, or asked at weeks 1 and 2 and
take the average)
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Scramble Exercise
 Think: Identify a network
 Actors
 Relations
 Directionality, Valued relations, Multiple relations, Modality,
Centricity
 Process and bases of Influence
 why would one person be influenced by another?
 Process and bases of Selection
 why would one person choose to interact with a specific other?
 Form: Meet and share in groups of 3-4
 Others: Question bases for making inferences
 Scramble: Form new group of 3-4 people
 Matchmaker (at lunch): Identify matches of interest
between members of first and second group
31
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
32
Overview
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
Introduction
Influence

Influence: How Interactions Affect Beliefs and Behaviors
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Model and Equation: Toy Data

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Influence Model with Toy Data Software
Questions about W: Timing
Studies of Teachers’ Implementation of Innovation
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For Actor 3:
Influence Exercise
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The Formal Model of Influence -- the Network Effect
Influence in Words (for teachers’ use of computers)
Exposure: Graphical Representation
Measures of Y: Use of Computers
Format of Network Data (W)
General Influence Model in Empirical Example
Definitions of Social Capital (Individual Level)
Social Capital and the Network Effect
Modification: Capacity to Convey Resource
Longitudinal Model
Effects of Social Capital on Implementation of Computers ...
Importance of Controlling for the Prior: Longitudinal Data
Selection
Graphical Representations
Centrality
Ethics
Resources
33
Influence: How Interactions Affect Beliefs and Behaviors
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547 (0-7:52)
Research questions
How does a teacher’s interactions affect her implementation of
innovations?
How does a banker’s interactions affect her profitability?
How does an adolescent’s interactions affect her delinquency,
alcohol use or engagement in school?
Theoretical Mechanisms (see Frank and Fahrbach, 1999)
Frank, K.A., & Fahrbach, K. (1999). "Organizational Culture as a Complex System:
balance and Information in Models of Influence and Selection." Special issue of
Organization Science on Chaos and Complexity, Vol 10, No. 3, pp. 253-277.
Normative/conformity : change to conform to others around
Information: change based on new information
Dual processes: both apply
Friedkin, Noah (2002). Social Influence Network Theory: Toward a Science of Strategic
Modification of Interpersonal Influence Systems. In National Academy Press:
Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers
(2003). http://www.nap.edu/books/0309089522/html/
Overview
34
The Formal Model of Influence -- the
Network Effect
 wii’
Network. Extent of relation between i and i’, as perceived by i.
 yit
 Outcome. An attitude or behavior of actor i at time t
 ∑i’wii’yi’t-1..
 Exposure. Sum of attributes of others to whom actor i is
related at t-1.
 yit = ρ∑i’wii’t-1tyi’t-1 +γ yit-1 +eit
 Model. Errors are assumed iid normal, with mean zero and
variance (σ2).
yit   i '1 wii ' yi 't 1   yit 1  ei
n
35
Influence in Words
(for technology use)
Use of technology time 2i=
ρ[use of first colleague time 1] +
ρ[use of second colleague time 1] +
ρ[use of third colleague time 1] +
γ(use time 1)i +
error time 2i
36
Exposure: Graphical Representation
Exposure to Expertise of Others
for Computer Use
B
C
C
A
D
37
Model and Equation: Toy Data
Y2
2
2
1
-.5
-2
-.5
= intercept+
=.116+(.125)
ρWY1
0 1 1 000x0
1 0 1 010x0
0
01
10
01
100
0x1
1
0 0 0 011x1
0 0 0 100x0
0 0 1 110x0
+
2.4
2.6
1.1
-.5
-3
-1
γY1
+
E2
0 x 2.4=0
2.4
.029
1 x 2.6=2.6
2.6
-.093
1.1
.094
= 0 x 1.1=0
+ (.67)
+ -.027
1 x 6-.5=-.5
-.5
0 x -3 =0
-3
-.025
1 x – 1=-1
-1
.022
Total =(1.1)/3 =.37
38
For Actor 3:
y3 time 2= intercept+ ρ(y2 time 1+ y4 time 1+y6 time 1)/3 + γ y3 time 1
+ e3 time 2
1=.116+.125*(2.6-.5-1)/3 + .67(1.1) + .094
39
Influence Exercise
Assume Bob talks to Sue with frequency 1, to Lisa with frequency 3
and not at all to Jane. Last year (at time 1), Sue’s organic farming
implementation behavior was a 9, Lisa’s was a 5 and Jane’s was 2.
What is the mean of the exposure of Bob to his peers regarding
organic farming?
Hint ( Mean=sum/n, but what should n be?)
Specify a model with two sources of exposure (e.g., within versus
between subgroups)
Influence answers
40
Influence Model with Toy Data Software
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation
/7de39417-3bb2-493a-bda2-e338666d0547
(7:52-32:51)
 http://www.msu.edu/~kenfrank/software.htm#Influence_Models_
 Influence program using means and merges in spss
 (7:52-21:20)
 Spss tutorials


http://www.stanford.edu/group/ssds/cgi-bin/drupal/files/Guides/software_docs_reading_raw_data_SPSS.pdf
http://www.hmdc.harvard.edu/projects/SPSS_Tutorial/spsstut.shtml
 influence program using proc means and merges in sas

 (21:20-32:51)
 Sas tutorial: http://www.ats.ucla.edu/stat/sas/
Influence program using means and merges in stata [save and uncompress]
 Stata tutorial: http://www.ats.ucla.edu/stat/stata/
41
Exercise: Modifications to the Influence
Model (SPSS)





Is influence increased if we weight exposure by the in-degree (number of
times nominated) of the person influencing (i’)?
 Change: COMPUTE exposure=relate * yvar1
 To: COMPUTE exposure=relate * yvar1*(indeg+1)
Is influence stronger of we take the sum instead of the mean?
 Change: /exposure_mean_1=MEAN(exposure)
 To: /exposure_sum_1=SUM(exposure)
 Use exposure_sum_1 in the regression
What if you didn’t control for the prior?
 Change: /METHOD=ENTER exposure_mean_1 yvar1.
 To /METHOD=ENTER exposure_mean_1.
Does coefficient for exposure term depend on prior (interaction term)?
run influence for technology
42
Exercise: Modifications to the Influence
Model (SAS)
 Is influence increased if we weight exposure by
the in-degree (number of times nominated) of
the person influencing (i’)?
 Set useattr=1;
 Is influence stronger of we take the sum instead of the mean?
 Change: mean=totinfl
 To: sum=totinfl
 What if you didn’t control for the prior?
 Change: model yvar2=totinfl yvar1;
 To: model yvar2=totinfl ;
 Does coefficient for exposure term depend on prior
(interaction term)
 run influence for technology
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Questions about W: Timing
 Should we use simultaneous or staggered behavior?
 Yt=ρWYt
 accounts for all direct and indirect (or primary, secondary, tertiary,
etc) effects
 hard to estimate (Y on both sides)
 Christakis and Fowler
 http://www.nytimes.com/2009/09/13/magazine/13contagiont.html?_r=1&pagewanted=1&ref=magazine
 Yt=ρWYt-1
 easier to estimate
 Only direct effects
 et=ρWet
 Autocorrelated disturbances – exposed to the same effects
 Charles Manski’s reflection problem
44
Observational studies with controls for
pretests work better than you think
Shadish et al (JASA 2008)
 Quantify how much biased removed by statistical control using
pretests in a given setting
 Sample: Volunteer undergraduates
 Outcome: Math and vocabulary tests
 Treatment:
 basic didactic,
 showing transparencies
 defining math concepts
OLS Regression with pretests removes 84% to 94% of bias relative to RCT!!
Propensity by strata not quite as good
See also Concato et al., 2000 for a comparable example in medical research
OLS might not work
 So what would it take to change an
inference?
 How strong must a confound be to reduce
estimated effect below a threshold for making
an inference?
 https://www.msu.edu/~kenfrank/research.htm#causal
 Related to: how bad would your sample have to be to
invalidate your inference?
46
Questions about W:
Cohesion versus Structural Equivalence
 Cohesion -- direct connections/communication
Examples:
Students’ educational and aspirations decisions are influenced through
direct discussions
Adolescents’ delinquency is influenced by the delinquency of their
friends
 Structural Equivalence -- common roles/comparison & comparison
Examples
Students who occupy similar positions defined by curricular tracks may
develop similar educational aspirations
Businesses who sell to similar others may adopt similar practices
 Direct Influence versus Indirect Influence (Leenders)
 Are you influenced by those who you do not talk to, but with whom
you share intermediaries?
47
Redundant Effects through A Network
48
Questions about W: Row Normalization
and Interpretation of Influence
 Divide values by row marginal
 Different transformation for each subject
 Changes metric to “influence units”
 Access of one unit of expertise of one influence unit
increases number of uses of computers by xx per
year.
 Theoretical meaning of “influence units” versus
frequency of interaction
 Could you model “influence unit” with a selection
model?
49
Articles on Causality
50
Critique of
Christakis
and Fowler
“influence”
model
pages 5-6
Lyons, Russell
The spread of evidence-poor medicine via flawed social-network analysis, Stat., Politics, Policy 2, 1
(2011), Article 2. DOI: 10.2202/2151-7509.1024
See Andrew Gelman: http://themonkeycage.org/blog/2011/06/10/1-lyonss-statistical-critiques-seemreasonable-to-me-there-could-well-be-something-important-that-im-missing-but-until-i-hear-otherwisefor-example-in-a-convincing-reply-by-christakis-and-f/
Articles on Causality
52
Articles on Causality
53
Studies of Teachers’ Implementation of Innovation
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/7de39417-3bb2-493a-bda2-e338666d0547
(32:51)40:00)
 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 (20052006)
54
Measures of Y: Use of Computers
Teacher’s Use of Technology at Time 2 (α=.94)
I use computers to help me...
Never Yearly Monthly Weekly Daily
1
2
|3
4
1
2
|3
4
1
2
|3
4
1
2
|3
4
1
2
3|
4
1
2
3 | 4
| indicates mean response
5
5
5
5
5
5
introduce new material into the curriculum.
guide student communication.
model an idea or activity.
connect the curriculum to real world tasks.
teach the required curriculum.
motivate students.
Expertise (α=.76):
Use at time 1 for teacher and student purposes (e.g., to help students communicate)
Total number of applications with which the teacher was familiar at time 2
extent to which the teacher reported being able to operate computers at time 2
How confident the teacher felt with computers at time 2
55
Format of Network Data (W)
Your name: Lisa Jones (person 1)
Please indicate who helped you with computers at xxx and the frequency with which you interact with each person.
Name
Yearly
Monthly
Weekly
Daily
Bob Jones_(2)________
1
2
3
4
Sue Meyer_(3)________
1
2
3
4
____________________
1
2
3
4
____________________
1
2
3
4
Data entered (nominator, nominee, frequency)
1 22
1 34
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, frequency)
212
243
56
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=ρWY
 Y: Teacher’s use of computers in
classroom (in times used per year)
 W: help or talk about technology (in days
per year)
 ρ: network effect of interaction on use of
computers
57
Exposure to Expertise of Others
B
m
fro
B
lp
He
Help from C
Hel
pf
A
rom
C
C
D
D
58
Questions regarding W




Take sum or Mean?
Timing?
Cohesion versus structural equivalence
Social capital as a guide
59
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)
60
Social Capital and the Network
Effect
Social Capital=
potential to access resources through social
relations
Resource =Expertise
Social relation=help from teacher i’ to teacher i.

n
help
expertise
ii
'
i ' t 1
i '1
61
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

n
i '1
helpii 'expertisei 't 1x total help provided by i'
62
Longitudinal Model
 yi t=intercept+ρ∑i’wii’ t-1→tyi’ t-1 x ∑iwii’
+γyit-1
 Take sum (resources accessed)
 Partial control for selection of similar
or valuable others by including yit-1
 Continuity through γ.
63
Effects of Social Capital on Implementation of Computers in the
Classroom
64
Importance of Controlling for the Prior: Longitudinal Data
65
Metric Based on Expertise/Day
 WY is an interaction:
 units = days per year x expertise
 Solution 1: interpret standardized coefficients
 Network effect as strong as perceptions
 Solution 2:
 Divide by number of days in a year: WY/365,
 new metric is access to expertise per day
 .23WY =.23HelpxExpertise=84HelpxExpertise/365
 Access of one unit of expertise per day increases
number of uses of computers by 84 per year.
66
Your own Influence Model
A) Identify a network in which you are interested
B) Characterize the theoretical processes of influence that occur in the network. Through
what mechanisms due actors influence each other? What is conveyed through a tie or relation that
could change an actor’s belief or behavior?
C) write down a model of influence
1) How should W be specified -- what is the relation?
2) What is the time interval during which interaction occurs With a partner
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 be
added or modified?
B) Does the time interval seem reasonable?
C) Is the process based on cohesion or structural equivalence?
D) How would you measure the variables, w and y in your model?
67
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) 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 Data
Selection Application Transition from Social Exchange to quasi ties ...
Alternatives for Running p2
Graphical Representations
Centrality
Ethics
Resources
68
Selection: How Actors Choose Others with whom to Interact
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd-491e-bf300b2377f332a6: (0:00-19:40)
Examples of Research Questions
How do farmers decide to whom to provide help?
How do bankers decide to whom to loan money?
How do social service agencies choose other agents to refer clients to?
Theoretical Mechanisms (see Frank and Fahrbach, 1999)
Frank, K.A., & Fahrbach, K. (1999). "Organizational Culture as a Complex System:
balance and Information in Models of Influence and Selection." Special issue of
Organization Science on Chaos and Complexity, Vol 10, No. 3, pp. 253-277.
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
Adolescents select friends who are like themselves
Teachers who want to be innovative interact with other innovators
Overview
69
Selection Model
 p( wii ' ) 
log 
  0  1 yi  yi '
1  p( wii ' ) 
Absolute value of difference
in attributes
Represents the effect of difference in attribute
70
The Logistic Regression Model
The "logit" model solves these problems:
ln[p/(1-p)] = 0 + 1X
 p is the probability that the event Y occurs, p(Y=1)
 [range=0 to 1]
 p/(1-p) is the "odds ratio"
 [range=0 to ∞]
 ln[p/(1-p)]: log odds ratio, or "logit“
 [range=-∞ to +∞]
71
e     x
P( y x) 
1  e    x
72
Interpretation of Ogive
 The logistic distribution constrains the
estimated probabilities to lie between 0 and
1.
 The estimated probability is:
p = 1/[1 + e(0 + 1X )]
 if you let 0 + 1X =0, then p = .50
 as 0 + 1X gets really big, p approaches 1
 as 0 + 1X gets really small, p approaches 0
73
74
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)
(You’ll need one term for effects associated with
gender, and another for race)
75
Selection Exercise
B) Assume that Bob and Lisa are African
American and that Jane and Bill are white. Bill
and Bob are Male and Lisa and Jane are
female.
Calculate the independent variables based on
difference of race and gender for Bob with each
of his interaction partners:
(Bob, Lisa): different gender = _______;
(Bob, Jane): different gender =_______;
(Bob, Bill): different gender = _______;
different race = _________
different race = _________
different race =__________
76
Selection Exercise
C) Assuming the values of the θ’s are
negative and that the effect of race is
stronger than that of gender, who is Bob
most likely to talk to?
D) Include a term capturing the interaction of
similarity of race and gender
Selection answers
77
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” !
78
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.
Wi’i =0
Wi’i =1
Wii’ =0
Cell A
Cell B
(reciprocity)
Wii’ =1
Cell C
Cell D
(reciprocity)
Model as 4 cells, A,B,C,D instead of just Wii’ =0
79
Estimation via p*
80
Visual representations of p2 model
control for dependencies associated with nominator and nominee
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd491e-bf30-0b2377f332a6: (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 375397.
81
Reciprocity: Wii’ (as yij) Wi’i (as yji) Modeled Simultaneously
(Lazega and Van Duijn 1997)
82
Selection Model (p2)
Pair Level (i,i’)
Difference
In attribute
reciprocity
 p(wii ' ) 
log 
  0i  0i '  1 yi  yi '   wi 'i
1  p( wii ' ) 
Sender Level (i) or nominator
Sender
attribute
 0i   00   y  ui
i
01 i
Receiver Level (i’) or nominee
Receiver
i 'attribute
0i '   00   01 yi '  vi '
Sender
variance
ui ~N(0,τu)
Receiver
variance
Vi’ ~N(0,τv)
83
Boots and Shoes:
aligning my notation with Marijtje’s
Pair Level (i,i’)
Level 1 Difference
In attribute
reciprocity
 p(wii ' ) 
log 
  0i  0i '  1 yi  yi '   wi 'i
1  p( wii ' ) 
Pair Level (j,i)
 p( yij ) 
log 
   i   j   yzi  y j   y ji
1  p( yij ) 
Modeling density
84
Boots and Shoes:
aligning my notation with Marijtje’s
Level 2
Nominator (i)
 0i   00   y  ui
 i   1 xi  Ai
attribute
i
01 i
variance
ui ~N(0,τu)
Sender (i)
nominee (i’)
attribute
0i '   00   y  vi '
i'
01 i '
Receiver (j)
covariance
variance
Vi’ ~N(0,τv)
 j   2 x j  Bj
85
Setting up p2
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd491e-bf30-0b2377f332a6: (19:40-42:25)
0) make square network data file out of list using makemat.sas will put
file called
c:\stocnet\network\matrix.dat
1) Using Van Duijn’s p2:
go to: http://stat.gamma.rug.nl/stocnet/
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 @
http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf
Skip running p2
86
87
Toy data
Outcome network data at time t
Save in c:\stocnet\networks\toyw.dat
011000
101000
010100
000011
000100
001100
Attributes (1 & 2)
Save in c:\stocnet\actfiles\toyatt.dat
2.4 2
2.6 2
1.1 1
-.5 -.5
-3 -2
-1 -.5
Optional: network data at t-1
Save in c:\stocnet\networks\pretoyw.dat
000100
100000
010001
000011
010000
001000
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
88
Running p2

Start a new session by
1. Click on “Start with new session”
2. Then hit the “Apply” button
89
Running p2

Click on the “Data” icon to add data.
90
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
91
Running p2
Once you finish
adding data, click
on the “Apply”
button first.
Then, you can
click on the “View”
button to view
data.
92
Running p2
 Click on the “Model” icon
93
Running p2
 Select the p2 model
94
Running p2
 Click on the “Data specification” button
95
Running p2
put network1 (toydata) into digraph
put file1 (indiv) into selected attributes
96
Running p2
 Specify model with actor attributes on
network parameters
Density is pair
level for us
97
Visual Representations of Selection
Models
98
Selection Model (p2)
Pair Level (i,i’)
Difference
In attribute
reciprocity
 p(wii ' ) 
log 
  0i  0i '  1 yi  yi '   wi 'i
1  p( wii ' ) 
Sender Level (i)
Sender
attribute
 0i   00   y  ui
i
01 i
Receiver Level (i’)
Receiver
i 'attribute
0i '   00   01 yi '  vi '
Sender
variance
ui ~N(0,τu)
Receiver
variance
Vi’ ~N(0,τv)
99
Toy Data
Network (w)
Attribute
y1 y2
total
2
2
3
2
1
2
Total
1
2
3
3
1
2
100
|Yi-Yi’ |
W
101
Example Output for p2 for Toy Data
see also http://stat.gamma.rug.nl/stocnet/downloads/manualp2.pdf
P2MCMC RW ml mv
testtoy.out
October 13, 2009,
11:36:25 AM
@1
General Information:
Digraph: C:\stocnet\temp\~toyw.dat
@1
General Information:
Digraph: C:\stocnet\temp\~toyw.dat
October 13, 2009, 11:36:25 AM
Number of valid tie indicator observations: 45
@1
Descriptives:
Group
Observed Initial
Tie variables
ties
Exchange ties
Size
Size
Present
Missing
Digraph
Number of ties
Reciprocal ties
Mutliplex
1
6
6
30
0
~toyw.dat
12
10
-
-
102
Variances
@1
Random effects:
parameter
estimate
(τu) sender variance :
(τv) receiver variance:
(τuv) covariance
standard
error
quantiles from sample
0.5
2.5
25
50
75
97.5
1.69
99.5
0.4323
0.4288
0.05
0.08
0.18
0.29
0.51
4.9249
7.4311
0.05
0.08
0.24
2.37
6.76 25.69 37.16
-0.3081
1.7522
-6.96 -5.24 -0.52
0.01
0.29
2.58
2.67
5.21
103
Selection model (p2): Toy Data
Pair level (i,i’)
 p(wii ' ) 
log 
  0i  0i ' -2.38 yi  yi '  3.76wi 'i
1  p(wii ' ) 
Sender Level (i)
0i  3.79  .308yi  ui
ui ~N(0,.43)
Receiver Level (i’)
vi ~N(0,4.9)
0i '  3.79  [not modeled]  vi '
104
Regression Coefficients
@1
Fixed effects:
0 is contained within the
95% interval of the posterior distribution
@2
Overall effects:
Density
Reciprocity
parameter
estimate
~toyw.dat:
3.7863
~toyw.dat:
3.7586
standard
error
2.6904
2.3022
quantiles from sample
0.5
2.5
25
50
-1.71 -1.10 1.76 3.46
-1.35 -0.30 2.16 3.67
75
97.5 99.5
5.36 11.46 11.85
4.99 9.24 10.33
parameter
estimate
0.3084
standard
error
0.6322
quantiles from sample
0.5
2.5
25
50
-0.74 -0.67 -0.21 0.29
75
0.77
parameter
estimate
-2.3816
standard
error
1.0525
quantiles from sample
0.5
2.5
25
50
75
97.5 99.5
-5.60 -5.28 -3.03 -2.41 -1.55 -0.68 -0.32
@2
Specific covariate effects:
@3
Sender covariates:
Attribute2
97.5
1.55
99.5
1.62
@3
Density covariates:
abs_diff_Attribute1
This last term models wither difference in attribute 1 predicts density.
105
Selection model (p2): Toy Data
Pair level (i,i’)
 p(wii ' ) 
log 
  0i +0i ' -2.38 yi  yi '  3.76wi 'i
1  p(wii ' ) 
Bigger difference
 more interaction
Sender Level (i)
High Reciprocity
Big y2
 more interaction
0i  3.79  .308yi  ui
ui ~N(0,.43)
Receiver Level (i’)
vi ~N(0,4.9)
0i '  3.79  [not modeled]  vi '
106
Combined Selection model (p2): Toy Data
Pair level (i,i’)
 p(wii ' ) 
log 
  3.79  .308yi +ui -2.38 yi  yi '  3.76wi 'i
1  p(wii ' ) 
Θ0i’
Sender Level (i)
0i  3.79  .308yi  ui
ui ~N(0,.43)
107
Add Dyadic Covariate
108
Specify P2 Model
109
P2 Data Specification
110
P2 Model Specification
111
Modify Parameters for Quick Estimation
112
Prediction for Pair (2,5) Selection Model
(p2): Toy Data
Pair level (2,5)
 p(w 2,5 ) 
log 
 =3.79+.308×22 -2.38 22 --25 +3.7605,2
1-p(w 2,5 ) 
=3.79+.308×2-2.38×4+3.760(0)=-5.1,
p(w 2,5 )=
e
-5.1
1+e
-5.1
=.006
Actual value: W2,5=0
113
Keeping Terms Straight in p2
Q: Who helps you with math?
Sender
Receiver
=person who nominates others
=person who receives help
=expansiveness
= person who is nominated by others
= person who provides help
=attractiveness
Keeping Terms Straight in p2
Q: Who gave you cigarettes?
Sender
=person who nominates others
=person who receives cigarettes
=expansiveness
Receiver
= person who is nominated by others
= person who provides cigarettes
=attractiveness
Exercise for P2
 How can you make an inference about the
effect of similarity of an attribute
 What happens to the similarity of attribute
when you control for time 1?
 Try putting in the model:
 Difference in attribute1+attribute1 on
sender+attribute1 on receiver
 Did it work?
 What is the difference between putting in
difference in attribute instead of absolute
value of the difference?
Marijtje Van Duijn’s P2 in her own words
 http://www.gmw.rug.nl/~steglich/dynamics/
workshop/sienap2ergm.pdf
 Data sets:
http://www.stats.ox.ac.uk/~snijders/siena/s
50_data.htm
 Try s50: 50 teenage girls, friendships at 3
time points:
http://www.stats.ox.ac.uk/~snijders/siena/s50_
data.htm

Look at full report
variances
Alternatives for Running p2
In sas:
download Sam Field’s p2 via sas from my web site:
http://www.msu.edu/~kenfrank/software.htm#Selection_Mo
dels:_p2
download glimmix from my web site and save to c:\
run glimmix.sas in sas
run Sam’s program (p2_explore.sas)
Note it generates its own ego and alter files (see data i and
data j) and network data (a5), but these could be read in.
Can also do using Peter Hoff’s R routine
http://www.stat.washington.edu/hoff/Code/GBME/. For
R, go to http://cran.cnr.berkeley.edu/
122
Selection Application
Transition from Social Exchange to Systemic Exchange Via Quasi-Ties
http://edcc1a.cvm.msu.edu:8080/ess/echo/presentation/3aaca18c-edcd491e-bf30-0b2377f332a6: (42:25-48:00)
Frank, K.A. 2009 Quasi-Ties: Directing Resources to Members of a Collective
American Behavioral Scientist. 52: 1613-1645
123
p2 extended model
Quasi-tie
124
Interaction of Close Colleagues and Identification of the Potential
Provider on the Provision of Help: Evidence of a Quasi-Tie
125
Cross Nested Multilevel Poisson Regression (i.e., p2 social network model)
of Extent (# of days per year) to which i’ Helped i
Quasi-tie
126
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
127
KliqueFinder:
Identifying Clusters in Network Data
Go to:
https://www.msu.edu/user/k/e/kenfrank/web/resources.
htm#KliqueFinder
Based on:




Frank, K. 1996. “Mapping interactions within and between cohesive
subgroups.” Social Networks 18: 93-119.
Frank. K.A. 1995. “Identifying Cohesive Subgroups.” Social Networks (17):
27-56.
*Field, S. *Frank, K.A., Schiller, K, Riegle-Crumb, C, and Muller, C. 2006.
“Identifying Social Contexts in Affiliation Networks: Preserving the Duality of
People and Events. Social Networks 28:97-123. * co first authors.
https://www.msu.edu/user/k/e/kenfrank/web/research.htm#representation
128
129
Scenarios for the Network analyst
For each of the scenarios below,
identify the theoretical processes at work
write down what model or tool you would employ to evaluate the theory.
describe what data you would collect to apply the model or tool to
describe what estimation procedure/tool you would use.
Sally is concerned that her daughter is experimenting with alcohol and thinks it is because her
daughter’s friends are experimenting. Sally wonders generally if adolescents tend to drink
more if their friends drink alcohol.
Michael wants to understand the social structure of his synagogue. 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?
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/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
ei  i '1 wii 'ei ' e  We
n
ei is the centrality of actor i. wii is the network data. λ 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: Still not sure how this
works?
EIGEN
FACTOR
VALUE
------- ------1: 13.238
2: -1.000
3: -12.238
======= =======
26.475
WARP=175/(175-1-149)=175/25=7
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
Overview







Introduction
Influence
Selection
Graphical Representations
Centrality
Ethics
Resources
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
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


Logistics of Data Collection
Organizing data entry
Resources for Networks: Books
Resources for Networks: Web
Resources: Clearinghouses
Resources: Individual web Pages
138
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)


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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.
139
Organizing data entry
check out:
http://www.classroomsociometrics.com/
140
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.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
Video: >rich media >vodcast>podcast>Course Portal (1:23:41-1:28)
141
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.
142
143
Scenarios for the Network Analyst:
Ethical Considerations
For your previous answer to each of the scenarios below, identify
who would benefit from the analysis,
who bears the costs
how confidentiality of subjects could be protected
Sally is concerned that her daughter is experimenting with alcohol and thinks it is because her
daughter’s friends are experimenting. Sally wonders generally if adolescents tend to drink
more if their friends drink alcohol.
Michael wants to understand the social structure of his synagogue. He has an idea that there are
certain sets of people who interact with each other, and, if he could understand what those
sets of people are, he might better be able to tailor programs of the synagogue to be more
effective.
How could Michael use the information above track the diffusion of new beliefs or behaviors in his
synagogue?
Pennie wants to know under what conditions one social service agency would allocate resources to
another. Is it because they have a history of doing so, they share clients, they deal with
similar issues, etc.
What clustering among social service agencies might emerge as a result of the processes above?
144
Resources for Networks: Books
•
Kadushin, Charles. (2012). Understanding Social Networks: Theories,
Concepts, and Findings. Oxford: Oxford University Press.
•
Peter J. Carrington, John Scott, Stanley Wasserman “Models and Methods
in Social Network Analysis” Cambridge, order from Amazon on-line.
•
Wasserman, S., & Faust, K. (2005). Social networks analysis: Methods and
applications. New York: Cambridge University. Go to Amazon to order
electronically.
•
•
Freeman, Linton (2004). The Development of Social Network Analysis: A
Study in the Sociology of Science. Empirical Press of Vancouver, BC,
Canada
http//www.booksurge.com/product.php3?bookID=GPUB01133-00001
•
Scott, J., 1992, Social Network Analysis. Newbury Park CA: Sage.
•
Wellman, Barry and S.D. Berkowitz, 1997. Social Structures: A Network
Approach.(updated edition) Greenwich, CT: JAI Press.
145
Resources for Networks: Courses
and Introductions
Introductory On the Web
Borgatti’s slide show:
http://www.analytictech.com/networks/intro/index.html
Kadushin’s intro
http://www.charleskadushin.com/
Barry Wellman’s intro:Social Network Analysis: An Introduction
http://www.chass.utoronto.ca/~wellman/publications/index.html
David Knoke’s intro to social network methods:
http://www.soc.umn.edu/%7Eknoke/pages/SOC8412.htm
Wasserman, S., & Faust, K. (1994). Social networks analysis: Methods and applications.
New York: Cambridge University.
Jim Moody’s course: http://www.soc.duke.edu/~jmoody77/s884/syllabus_09.htm
146
General Resources
 International social network analysis web page:
http://www.insna.org/
 Syllabi::
http://www.ksg.harvard.edu/netgov/html/sna_courses_ev
ents.htm
147
Resources: Individual Web Pages

Individual Web Pages :

Phil Bonacich http://www.soc.ucla.edu/professors/PHILLIP%20BONACICH/?id=4

Ron 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/

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/
148
Resources data

http://snap.stanford.edu/index.html


http://datamob.org/datasets/tag/social-networks


Barabasi
http://www.icpsr.umich.edu/icpsrweb/NACDA/studies/20541


UCINET
http://www.nd.edu/~networks/resources.htm


Mark newman
http://vlado.fmf.uni-lj.si/pub/networks/data/UciNet/UciData.htm


Multiple potential sources (including Enron)
http://www-personal.umich.edu/~mejn/netdata/


Stanford, large data sets
National Social Life, Health, and Aging Project (NSHAP)
http://www.insna.org/software/data.html

INSNA page
149
Resources Exercise
 Find 2 web resources not listed above and
post them on angel
150
Influence Exercise: Answers
Assume Bob talks to Sue with frequency 1, to Lisa with frequency 3 and not at all to
Jane. Last year (at time 1), Sue’s organic farming implementation was a 9, Lisa’s was
a 5 and Jane’s was 2.
What is the mean exposure of Bob’s to his peers regarding delinquency?
Sum=1x9+3x5+0x2=24
N= 2 (number Bob talks to) or 3 (number of people) or 4 (number of
interactions)? Hmmmmmm.
Mean = 24/2=12 or 24/3=8 or 24/4=6.
Or, use the sum?
Specify a model with two sources of exposure (e.g., within versus between subgroups
Let sii’ =1 if i and i’ are in the same subgroup, 0 otherwise
n
yit ρwithin
s w
i  1,
i i
ii  ii yi  t1 ρbetween
Return to influence
n
(1
i  1,
i i
sii )wii yi  t1 γyi t1

eit .
151
Selection Answers
 p( wii ' ) 
log 
  0  1 yi  yi '  2 zi  zi '
1  p( wii ' ) 
152
Selection Answers
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 race and gender for Bob
with 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
Note: variable is 1 if different gender, 0 if same gender.
Could also make it: 1 if same gender, 0 if different gender
153
Selection answers
C
For Bob and Jane: .4-.2(1)-.5(1)= -.3
D
Return to
selection
154
Resources Exercise
 Find 2 web resources not listed above and
post them on angel
155
Bounds on ρ
(Based in part on dissertation by Jiqiang
Xu)
 Ord says 1/λmin < ρ < 1/λmax , λ is an eigen value
 likelihood =G[OLS, ∑aln(1-ρλa)]
 Alternative: eigen values and eigen vectors (V):
 λV =WV → V =(1/ λ)WV
 Perfect fit if ρ=1/ λ,
 eigen value λa
 with Y = corresponding eigen vector, Va
156
0234 | 00 
.46 
 2044 | 00
.50 


 
Y=
.50 
W= 3403 | 00 


 
4430
|
10


.54 
    
 


 
0000
|
04


.06 
0000 | 40
.03 


 
W=
0234 | 00 
 2044 | 00


3403 | 00 


4430
|
10


    


0000 | 04 
0000 | 40


Y=
  .1 
  .01 


.01 


.
1


  


9999 
9999 


OLS estimate of ρ = .5, R2=.99
OLS estimate of ρ = 1.21, R2=.97
157
Substantive Restriction on Y
 1/λmin < ρ < 1/λmax to confine to largest
component
 What if there are multiple components?
 Separate estimate of ρ in each component,
average over components?
 Standardize: z(ρ)= p/(1/λmax -1/λmin)
158
Find the network model
Try to relate this
regression to one of
our network models.
How does her
analysis take
into account ties
among people?
How could you
extend?
159
Measure of Bridging Capital
160
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?
161
162
Prior to workshop
1)Standard statistical software package
Sas, 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.16531020
0/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,
163
assumptions
Plan of Activities Day 1 of 2 day
workshop
9-10:15: Introduction to social network analysis
10:15-10:45 scramble exercise (introductions)
10:45-11 break
11-12 introduction to influence model
Includes exercise
12-1 Lunch
make introductions from scramble exercise!
1-1:45 application of the influence model
1:45-2:30 introduction to selection model
Includes exercise
2:30-2:45 Break
2:45-3:30 application of the selection model
3:30-3:4:30 Clustering an graphical representations
includes interactive exercise
4:30-5 set up for second day [download videos]
164
Plan of Activities Day 2: Software
 9-9:15: Break into groups to focus on
 Influence, selection, graphical representations
 9:15-10:15 Watch video demonstration
and try basics
 10:15-12 supported experimentation and
exploration
 12-1: lunch
 1-2: example demonstration of theoretical
models
 2-3:30 supported experimentation with
models
165
Research on networks in education

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on teachers:
Jim Spillane
Peter Youngs
Cynthia Coburn
Alan Daly
Min Sun
Chong Min Kim
Nienke Moolenaar
Ben Pogodzinski
Bill Penuel
Russell Cole
Jonathan Supovitz
Kara Finnigan
Kara Jackson
Paul Cobb
Tom Smith
 On adolescent networks
on schools

 Bill Carbonaro
 Jim Moody
 Yu Xie
 Chandra Mueller
 Ann Strassman Muller
 Derek Kreiger
166