grappling with grouping iii social network analysis - institute for

Grappling with Grouping IIISocial Network Analysis

David HenryDavid HenryUniversity of Illinois at Chicago

Allison DymnickiAmerican Institutes for Research

Advancing Health Practice and Policy through Collaborative Research

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


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.


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.


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.


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


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


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


Outline• Overview of methods

Sociometrics

Outline

– Sociometrics– Informants– Ego-networksEgo networks– Dynamic

• For each (-1)– Theory/method/measures– Software


– 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


F 1 0 0 0 0 0 0

G 0 0 0 0 0 1 0G

Advancing Health Practice and Policy Through Collaborative Research

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


Σ 3 2 1 2 1 3 0 12

G

Advancing Health Practice and Policy Through Collaborative Research

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


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


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


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.


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


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


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 /


– 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)


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.


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.


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)


, 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


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


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.


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.


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.


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.


Group 212: Prep


Group 212: Session 4p


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


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/


Summary

Saturation Possible?

Absentees or non-participants?

Multiple Time

Pointsparticipants? PointsN Y N Y N Y

Sociometrics - + + - + -Informants - + + + + -Ego-Networks + ? + - + -Dynamic SNA ? ? ? ? - +


y

grappling with grouping iii social network analysis - institute for

Documents