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Grappling with Grouping IIISocial Network Analysis
David HenryDavid HenryUniversity of Illinois at Chicago
Allison DymnickiAmerican Institutes for Research
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Families and Communities Social Network and N ti I fl P j t
Acknowledgments
Research GroupPatrick TolanDeborah Gorman-Smith
Normative Influence ProjectsFern ChertokDaneen DeptulaAllison Dymnicki
Michael Schoenyy
Jane JegerskiChristopher KeysKimberly KobusJennifer Watling NealJennifer Watling NealZachary NealMichael Schoeny
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Acknowledgments • This work was supported by grants from the
Centers for Disease Control and Prevention and the National Institute of Justice. The content of this presentation is solely the responsibility of the p y p yauthors and does not necessarily represent the official views of the funders.
• For more information visit www ihrp uic eduFor more information, visit www.ihrp.uic.edu.
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I. Cluster Analysis
Grappling with Grouping
II. Clustering methods for binary variablesIII. Social Network Analysis
Central theme: Clustering approximates uniqueness in the same way that a sample mean approximates athe same way that a sample mean approximates a population.
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N k A l i• Widely used in community psychology research
Network Analysis
• 28 studies since 2000 in just two journals (AJCP, JCP)j j ( , )
– Search terms: “Network Analysis”
• Similar search using the term “cluster analysis” returned 14 studies.
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Community Studies Employing Network Analysisy p y g yStudy Variables Type of Analysis
Swindle et al., 2000Positive and negative social transactions in networks of HIV+ persons Rating scales
Hirsch et al., 2002 Differences in strength of ties by race Ego network
Ying, 2002 Social network composition of Taiwanese graduate students Rating scales
Langhout, 2003 A single case study using ego networks Ego network
Fleisher & Krienert, 2004Violence among female gang members increases before pregnancy and decreases afterward Qualitative InterviewsCriticism practical support were significant predictors of
Levendosky et al., 2004Criticism, practical support were significant predictors of mental health for battered women. Rating scales
Toohey et al., 2004Differences between nearly homeless and housed women on beliefs about netweok members as housing resources Rating scales
Zea et al., 2004Target‐specific factors were related to the probability of disclosure. Rating scales
Chia, 2006 Sociometric nominations in a work organization Sociometric
Knowlton & Latkin, 2007 Ego networks Ego network
Dominguez & Maya‐Lariego, 2008 Ego network support characteristics Ego network
Pernice Duca 2008 Social Support in clubhouse mental health programs Rating scales
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Pernice‐Duca, 2008 Social Support in clubhouse mental health programs Rating scales
Community Studies Employing Network Analysisy p y g y
Study Variables Type of Analysisy
Toro et al., 2008 Social Support in homeless adults ‐ ego networks Ego network
Campo et al., 2009 Convergent and discriminant validity with other measures Rating scales
Latkin et al., 2009Network drug use contributed to perceptions of neighborhood disorder. Ego network
Neal, 2009 Density, centrality, and relational aggression Informant
Trotter & Allen, 2009 Ego networks, qualitative analysis Ego network
Crowe, 2010 Personal and Organizational Community Networks Sociometric
L t l 2010 C it C N t k S i t iLugue et al., 2010 Community Cancer Network Sociometric
Prelow et al., 2010Social Support buffered ecological risk effects on psychological distress Rating scales
Haines et al., 2011Network characteristics of an interdisciplinary collaboration based on multiple types of relationships Sociometric
Neal et al (2011) Cohesion vs structural similarity in teacher advice networks Sociometric
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Neal et al. (2011) Cohesion vs. structural similarity in teacher advice networks Sociometric
V i t f N t k M th dVariety of Network Methods in Community Psychology Studies
Type NumberSociometric nominations 5Informant-based Methods 1Ego-networks 7Rating Scales 8Rating Scales 8Qualitative 1
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Outline• Overview of methods
Sociometrics
Outline
– Sociometrics– Informants– Ego-networksEgo networks– Dynamic
• For each (-1)– Theory/method/measures– Software
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– Strengths and limitations
• Data source: Relationships
Network Analysis with Sociometrics• Data source: Relationships
– “Who are your friends?” (Kobus & Henry, 2009)– “What organizations do you belong to?” (Crowe, a o ga a o s do you be o g o (C o e,
2010)• Analysis: Matrix and Graph Representations
A B C D E F GA 0 1 0 1 0 0 0
B 1 0 0 1 0 0 0 BEC 0 0 0 0 1 1 0
D 1 1 0 0 0 0 0
E 0 0 1 0 0 1 0
A
C D
EF
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F 1 0 0 0 0 0 0
G 0 0 0 0 0 1 0G
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Sociometrics: Network Measures
28.042/12)1(
gg
XDENSITY
where X = relationships (ties) = 12
)(gg
g = network size (# of potential relationships) = 42A B C D E F G Σ
A 0 1 0 1 0 0 0 2A 0 1 0 1 0 0 0 2
B 1 0 0 1 0 0 0 2
C 0 0 0 0 1 1 0 2
D 1 1 0 0 0 0 0 2 A
BE
FD 1 1 0 0 0 0 0 2
E 0 0 1 0 0 1 0 2
F 1 0 0 0 0 0 0 1
G 0 0 0 0 0 1 0 1
A
C D
F
G
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Σ 3 2 1 2 1 3 0 12
G
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Sociometrics: Networks Measures
• Mutuality Index 77.0)1(
)1(2
222
222
2
LLgLLLMg
M = number of mutual relationships = 5g = network size = 7L f th td f th t t l t k 12
)( 2g
L = sum of the outdegree of the total network = 12L2 = sum of squares of the outdegree of the total network =22
A B C D E F G Σ
A
BE
F
A 0 1 0 1 0 0 0 2
B 1 0 0 1 0 0 0 2
C 0 0 0 0 1 1 0 2A
C D
F
G
D 1 1 0 0 0 0 0 2
E 0 0 1 0 0 1 0 2
F 1 0 0 0 0 0 0 1
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GG 0 0 0 0 0 1 0 1
Σ 3 2 1 2 1 3 0 12
Sociometrics: Network Measures
• Boundary Density (Hirsch, 1980)T
Tactual = number of actual ties across subgroups = 2
083.0 possible
actual
TT
BD
Tpossible = number of possible ties across subgroups = 24
A B C D E F G Σ
A 0 1 0 1 0 0 0 2
BE
A 0 1 0 1 0 0 0 2
B 1 0 0 1 0 0 0 2
C 0 0 0 0 1 1 0 2
D 1 1 0 0 0 0 0 2A
C D
F
G
D 1 1 0 0 0 0 0 2
E 0 0 1 0 0 1 0 2
F 1 0 0 0 0 0 0 1
G 0 0 0 0 0 1 0 1
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GΣ 3 2 1 2 1 3 0 12
Sociometrics: Measures of Individuals
Mean Geodesic Distance
jji
jij D
orD
where D = Distance and B = Reachability
j
ijj
ij Bo
B
In: 1.33 for F, 2.0 for D and 2.16 for GA B C D E F G Σ
A
B
C
EF
A 0 1 0 1 0 0 0 2
B 1 0 0 1 0 0 0 2
C 0 0 0 0 1 1 0 2
C D
G
D 1 1 0 0 0 0 0 2
E 0 0 1 0 0 1 0 2
F 1 0 0 0 0 0 0 1
G 0 0 0 0 0 1 0 1
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G 0 0 0 0 0 1 0 1
Σ 3 2 1 2 1 3 0 12
Sociometrics: Measures of IndividualsSociometrics: Measures of Individuals
• Position A
BE
F
– Member– Liaison– Isolate
C D
G
• Liaisons > Members or Isolates on tobacco and alcohol use (2 studies)(2 studies)
• Members and Isolates more influenced by peer substance use than Liaisons.
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Sociometrics: Statistical Models Example
D d h t d t b t i dDyads have a tendency to become triads:
“birds of a feather? or “friends of friends?”We can model the likelihood of triad closure, but the
chance models are complexRandom graph models and double permutation tests
provide alternatives suitable for predicting network
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provide alternatives suitable for predicting network structures or individual ties.
N k A l i i h S i iNetwork Analysis with Sociometrics
• Strengths– Unbiased assessment of social influence– Patterns of diffusion and communication– Rich measurement and theory
Li it ti• Limitations– Missing nominators compromise accuracy– Costly assessmentCostly assessment– Complex coding and analysis– Requires bounded social space
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q p
Network Analysis with SociometricsSoftware
• Stand-alone ProgramsStand alone Programs– UCINET (http://www.analytictech.com/ucinet/)– Krackplot (Freeware – visualization software)
(http://www andrew cmu edu/user/krack/krackplot sh(http://www.andrew.cmu.edu/user/krack/krackplot.shtml)
• R (http://www.r-project.org/)– iGraph– snasna
• ExcelN d XL F htt // d l d l /
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– NodeXL: Freeware http://nodexl.codeplex.com/
Network Analysis from Informants• Data Source: “Who hangs out together?”
Informants CompilationInformant Port Kit Tunner Port Kit TunnerInformant1
Port Kit Tunner Port Kit Tunner
Port 1 0 1 .5Kit 0 5Kit 0 .5Informant2Port 1 1
• Variations
Port 1 1Kit 1
– Cognitive Social Structures (Krakhardt, 1987)– Social Cognitive Mapping (Cairns et al., 1985)
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Informants: Examples
• Cairns, Leung, Buchannan, and Cairns (1995) used social cognitive mapping to study the fluidity, reliability, and interrelations of social networks of 4th and 7th
graders over a 3-week period.
• Neal (2009) used Cognitive Social Structures to study the influence of centrality and density on relational aggression in a sample of 3rd through 8th grade children.
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Informants: Software
• Cognitive Social Structures• Cognitive Social Structures– consensus aggregation across k informant matrices
k
ji,ij RRac oss o a a cescan be done in Excel or R.– See Krackhardt (1987) for specific instructions.
• Social Cognitive Mapping– Contact Man-Chi Leung, Ph.D. at UNC (man-
[email protected] ) for a copy of the SCM 4.0 program and manual.
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p g
Network Analysis from Informants
• Strengths:– Provides valid estimates of network ties with
comparatively few informants.– Missing data does not decrease accuracy– Economical to administer
• LimitationsDifficult to assess directed relations– Difficult to assess directed relations
– Requires bounded social space (e.g., classrooms, schools, organizations)
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, g )
Ego Network AnalysisEgo Network Analysis
• Theory: Best for unbounded networks where• Theory: Best for unbounded networks where saturation is not possible
• Data Source:– Prompts for different social functions– Demographics, relationships, frequency– Behavior of network members
• Analysis:Net ork si e densit di ersit bo ndar densit– Network size, density, diversity, boundary density, heterogeneity, position, behavior of network members
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Ego Networks: MeasuresEgo Networks: Measures
• Heterogeneity• Heterogeneity
e
A
ityHeterogene
nk
iA1
2
1
nityHeterogene iA 1
where A = a categorical attribute (e.g., gender, race)Ak = number of individuals with the attributee = number of individuals with valid data on An = total number of traits of A in the ego network
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Ego Networks: Examplesg p
• Dominguez & Maya-Lariego, 2008 Ego networks of host individuals and immigrants in– Ego networks of host individuals and immigrants in the U.S. and Spain
– Host individuals had lower centrality than did yimmigrants according to multiple measures.
T l G S ith & H 2003• Tolan, Gorman-Smith, & Henry, 2003– Ego network assessments of delinquent involvement
in adolescent malesin adolescent males– Network violence predicted future individual violence.
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E N kEgo Networks• Strengths
– Does not require assessment of entire network– Can provide social network and social support
i f tiinformation– Does not require bounded social space.
• Limitations• Limitations– Possible bias in the direction of the individual’s
behavior– Ego is central by definition, so meaning of position
and centrality are problematic.
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E N k S fEgo Networks: Software• Like informant-based network data, ego networks
populate matrices and graphs of the type we have been discussing.
• Ego network data can be visualized in Krackplot and• Ego network data can be visualized in Krackplot and other programs and analyzed using any software program you would use to analyze sociometric data.
• Because ego networks tend to be smaller than networks derived from sociometric studies, analyses can often be conducted by hand or using Excel orcan often be conducted by hand or using Excel or SPSS.
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Dynamic Social Network AnalysisDynamic Social Network Analysis
• Theory– Social relationships are dynamic– Most SNA is static– Static analysis may miss important characteristics of
the social world.• Examples• Examples
– Is “liaison” a position or a transition state?– Changes in parent groups over the course of g p g p
intervention.
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Group 212: Prep
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Group 212: Session 4p
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Group 212: Session 9p
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Group 212: Session 14p
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SAFE-E Group 212
0 80.91
2 53
0 40.50.60.70.8
1.52
2.5
00.10.20.30.4
00.5
1
# of contactsDensity
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Dynamic SNADynamic SNA
• Methods– Berger-Wolf method
• α (Persistence)• β (turnover)• γ (membership)
Software– Software• tnet package in R does analysis of time-stamped
ties - http://toreopsahl.com/tnet/p p• DNA (Discourse Network Analyzer)
http://www.philipleifeld.de/
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Summary
Saturation Possible?
Absentees or non-participants?
Multiple Time
Pointsparticipants? PointsN Y N Y N Y
Sociometrics - + + - + -Informants - + + + + -Ego-Networks + ? + - + -Dynamic SNA ? ? ? ? - +
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y