Kenneth A. Frank
Michigan State University
Chandra Muller
University of Texas
Anna Strassmann Mueller
University of Memphis
Presented at Academia Sinica Taipei Aug 2014

This research uses data from the AHAA study, which was funded by a grant (R01
HD040428-02, Chandra Muller, PI) from the National Institute of Child Health and
Human Development , and a grant (REC-0126167, Chandra Muller, PI, and Pedro
Reyes, Co-PI) from the National Science Foundation . This research was also supported by grant, 5 R24 HD042849, Population Research Center , awarded to the
Population Research Center at The University of Texas at Austin by the Eunice
Kennedy Shriver National Institute of Health and Child Development. This research also uses data from Add Health, a program project directed by Kathleen Mullan
Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan
Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-
HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and
Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara
Entwisle for assistance in the original design. Information on how to obtain the Add
Health data files is available on the Add Health website
(http://www.cpc.unc.edu/addhealth). No direct support was received from grant P01-
HD31921 for this analysis. Copies of this paper were presented at workshops at
Notre Dame’s Center for Research on Educational Opportunity and at the University of Texas Population Center. We thank our audiences at those presentations for their thoughtful comments. Opinions reflect those of the author and do not necessarily reflect those of the granting agencies.

Together, theories of social embeddedness and social capital have contributed to a rational analysis of the value of resources that inhere in social relations, but little is known about how those relationships form and are structured by social institutions. Using the Adolescent Health and Academic Achievement
(AHAA) and the National Longitudinal Study of Adolescent Health (Add Health) studies, the odds of a new friendship nomination were 1.77 greater within clusters of high school students who take courses together than between them.
The estimated effect cannot be attributed to exposure to peers in similar grade levels, indirect friendship links or through pair level course overlap, and the finding is robust to alternative model specifications. The authors also show how tendencies associated with status hierarchy inhering in triadic friendship nominations are neutralized within the clusters. These results have implications for the production and distribution of social capital within social systems such as schools, giving the clusters social salience as “local positions.”
Keywords: adolescence; social capital; emergent structure; social reproduction, social Keywords: adolescence; social capital; emergent structure; social reproduction

• Social embeddedness
– People give preference to those with whom they share social relations
• Social capital
– Many benefits (and some constraints) of resources embedded in social relations

B
C
A
Adolescent Friendships as Academic Resources: The Intersection of Friendship, Race, and
School Disadvantage
Robert Crosnoe , Shannon Cavanagh , Glen H. Elder Jr.
Sociological Perspectives , Vol. 46, No. 3 (Autumn, 2003), pp. 331-352
D

– Eder 1985
– Crosnoe et al. 2003; Alfassi 1998; Fuchs,
Fuchs, and Kazdan 1999; Riegle-Crumb et al
2006
– McFarland, 2001

– Not how is it cultivated in a system (that’s another paper, or Putnam)
– But how do the underlying social relations form?
– How is the process shaped by social institutions such as the school?
– Rational analysis of relationship formation

• Adolescents: Individual preference for homophily within organizational constraint of grade level (Zhen and Xie
2008)
• Young adults: choice homophily within homophily induced by structural constraints in email lists and courses (Kossinets and Watts 2009)
• Treat individual agency and constraint as separate, independent factors.
• We will look at how the confluence of individual agency and organizational constraint creates emergent social structures that then shape friendship formation

Macro constraint (course offerings, grades)
Friendship choices
Individual agency (course choices)

Extension:
Emergent Structures Defined by Multiple Shared Activities
• Sports based on extra curriculum
– much of student social experience is during the regular curriculum
– 1,000 hours/year in social experiences called “courses”
• Consider common participation in multiple activities
• Basketball and drama
• Latin Club and internetkids
– Combination of experiences defines new shared experience
• Tired going from practice to rehearsal
– Common transitions
• Observe one another
• Time and opportunity to initiate contact
– Common sets of interests
– Differentiation from others

Crosnoe (2011, page 25)
The morning is a grind for Chris, with all of his pre-AP classes lined up in a row. He is pulling As, but it is tough work. Most of his closest friends - a group of nine guys and five girls he has known since elementary school take the same classes . Because they all need to be on (or their parents keep them on) the AP track and because there are only so many pre-AP and AP classes at Lamar, they typically get to move from class to class more or less en masse . This is a good thing because they help each other get by - talking to each other about homework, translating what teachers say for each other . Perhaps more importantly, they harass each other when one of them gets a bad grade , their taunts of being ACC bound (short for
Austin Community College) providing enough motivation to ensure that the next grade will be better.
common courses and transitions lead to an emergent group
Support: “help each other get by” normative sanctions: harassment associated with a bad grade
Emergent group “en masse”, not just a particular course or shared courses between pairs of adolescents, becomes a salient context.

Organization of Opportunities for Interaction in the
School: Local Positions
• Clusters of students who take courses together
• Preserves duality of data (students and courses)
• Apply cluster analysis to the set of transcripts in each school
– Transcripts represent people and experiences
• See
– Field, Samuel H., Kenneth A. Frank, Kathryn Schiller, Catherine Riegle-Crumb, and Chandra Muller. 2006. "Identifying Social Positions From Affiliation
Networks: Preserving the Duality of People and Events." Social Networks 28(2):
97-186. Field and Frank equal coauthors
–
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.

Conceptualization of Clustering in 2-Mode data
From Skvoretz and Faust’s adaptation of p* models
Actor 2-stars
Event 2-stars

E
F
Genetics
Analysis
40
41
39
20th Cent American Lit
43 42
Organic Chem
38
45
44
English 3
Woodworking 2
Desktop Computer
46
47
48
22
28
21
27 US Hist 2
English 4
23
26
24
25
C
1
4
10
Global Ed
Am Lit
9
2
PE 10
8 7
Health 10
3
5
6
58 57
Advanced Biology
Calculus 56
Music Theory
US Hist, Honors
55
Physical Chem
H
18
16
19
17
15
14
Computer Appreciation
20
PE 11 Brit Lit
Algebra II
US Hist 1
11
Chem I
12
13
G
50
49
51 52
Basic Math
Resource Social Studies
Technical English 54
Resource Math
Resource Science
B
A
I
D
Algebra I
Typing 2
Spanish I
Health 9 30
32 Science, Unified
Early Western Civilizations
37
29 31
PE/Health 9
34
English 1
35
33 36
61
Geometry Informal
62
English 2
59
60
Typing 3
Accounting 2

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

Advantages of Local Positions as Pools of
Potential Friends
• Focused around curricular experiences – courses
– Common sets of interests
– In- vs Out- group distinctions
– Third parties present for norms
– Opportunities to observe and initiate interactions
– Common transitions between events
• Based on combinations of experiences
• Unique and emergent in each school
– Algorithm applied uniformly to transcript data in each
Add Health school, clusters differ by school

Macro constraint (course offerings, grades)
Local Positions
Individual agency (course choices)
Friendship choices

• Primary hypothesis (H
1
):
• Adolescents will be more likely to nominate members of their local positions as new friends than to nominate others in their school as new friends.
• Research questions
– What are the effects of local positions on new friendship nominations among adolescents?
– How large are the effects relative to standard homophily?
• How much of the effects can be attributed to dyadic components?
– Overlap in coursetaking
• Represent preexisting preferences (Kossinets and Watts)
– Mutual friends

Hypothesis for Status Difference
Ashley
Completion of cycle Sue
Completion of transitivity
Lisa
Existing friendship
Nomination to
Complete Pattern
Completion of transitivity and resisting cycles  hierarchy status difference
Lisa,Ashley
= transitivity completed –cycles completed.
H
2
:The greater the potential to complete transitivity versus cycles the more likely one adolescent will nominate another as a friend.
Model of directed, includes other triadic terms

Completion of
Transitivity
Hypothesis for Status Difference
Ashley
Sue
Lisa
Completion of
Cycle
Existing friendship
Nomination to
Complete Pattern
Completion of transitivity and resisting cycles  hierarchy status difference
Lisa,Ashley
= transitivity completed –cycles completed.
H
2
:The greater the potential to complete transitivity versus cycles the more likely one adolescent will nominate another as a friend.
Model of directed, includes other triadic terms

3

• Add Health data, nationally representative
• Longitudinal: control for prior behavior
• Original data in Frank et al (2008) Three Levels:
– students (n=4,000)
– within local positions (n=770)
– within schools (n=78)
• Dependent Variable: existence of new friendship nomination between two adolescents at Time 2 (Wave II , reported spring 1996)
– Counted if either nominated the other as a friend (but results apply for most other specifications);
– Up to 10 friendship nominations (probably covers most friends – Moody
2001)
• Network:
– Exposure through course taking (also have exposure through friends, but sample size reduced)
– Local positions
– Friendship nominations

Independent Variables
• Local Positions
– identified by applying Field et al.’s adaptation of Frank’s algorithm to transcript data from 1995-1996, weighted for sizes of courses. See Frank et al., 2008
.
• Homophily:
– Same race (for whites, and for others (Zhen and Xie, 2008)
– Same gender
– Similarity of parental education level
– Similarity of age
– Similarity of GPA
• Structural constraint: formal
– Similarity of grade level (Zhen and Xie, 2008)
• Structural constraint: informal
– Number of mutual friendship links
• Shared activities
– common sports played
– Common academic activities
– Common art clubs
• Pair-Level Course overlap
– Number of courses shared, adjusting for size

Model of Friendship Formation (Non-directed)

Time-line Relating Academic Experiences to
Friendship Nominations

Comments on Model
• Controlled for dependencies within dyad
– Only one observation for each dyad: outcome is whether there was any nomination (demonstrated transaction costs overcome)
– Most dyads are single nomination (300 reciprocated). Results primarily for unreciprocated ties
• Controlled for dependencies associated with each member with fixed effects
– # friendships involving each adolescent
• Treated as categorical: dummy for each value: Quillian and Campbell.
2003
• Comparable using alternating signed k-stars (Sinijders’ et al 2006) geometrically weighted degree count (GWDC).
• May only need mutual friends and race/gender homophily
(Goodreau 2006)
– Not interested in modeling at individual level
• Controlled for schools with fixed effects (dummy for each school)
• Controlled for prior friendship by selecting only those dyads for which there were no friendship nominations at Time 1 (Wave I or In-School in Add
Health)
• Removed those who were members of same friendship clique (roughly size
3-4) at time 1
• Subjects were in high school in the 94-95 and 95-96 school years (same as in Frank et al., 2008). Final n ~ 3,000.
• weighted
– Product of the weights for each actor
– Log of weights because they were skewed

• Hypothesis 1

• Odds of a friendship forming between members of the same local position are 1.77 greater than the odds of friendship forming between members of different local positions (controlling for other factors in the model).
– Odds ratio was 2.5 without other controls in the model
• Coefficient for membership in the same local position was larger than the coefficients for
– Same gender
– Both adolescents being white
– One standard deviation increase in most of the covariates.
– Exceptions
• Same race (not white): oppositional culture
• grade level
• Local positions one of the strongest factors affecting the formation of new friendships among adolescents in the 10 th and 11 th grades.
– Cuts across other bases of friendship

Generating the Ensemble Estimate
• Use SAS to write out commands, looping through each possible combination.
• Generate estimates in each case
• Save to file
• Combine by analyzing with HLM V-known.

Hypothesis 2
Hypothesis 3

– Multiple sources of influence
• friends, coursemates, local position members, schools

State of the Art: No?
Alternative Selection Model of Friendship Formation
• SIENA (Snijders: http://www.stats.ox.ac.uk/~snijders/siena/ )
– Advantages
• simulation based
• Friendship formation + dissolution
• Includes influence (e.g., changes in coursetaking)
– Concerns
• No case weights until very recently
• Difficult to run on full Add Health
• More complex model includes
• Exponential Random Graph Models (Robins et al., 2007)
– Advantages
• Controls for dependencies among observations (dyads, triads and quatrads …_
– Concerns
• Multicollinearity, possible degenerate solutions
• Structural competes with substantive explanations
• I did control for these terms, with a time lag. What happens at a nomination? Do I know others?
• P2: Van Duijn
– Advantages
• Random effects for degree distribution
• Markov chain Monte Carlo
– Concerns
• Parametric assumption about degree distribution
• No case weights

Discussion: Emergence and Salience of Local Positions
• Dynamic interplay
– Adolescents choose courses which determine emergent local positions within constraints of offerings
– creates opportunities for friendships
– The potential friends tie back to motivations for coursetaking – you take courses to comply with local position norm
– Confluence of agency and constraint to create meso-level structures
• Reduce Transaction Costs
– Within opportunities structured by the school
– Contain others with similar interests
– Provide opportunities for interaction
– Shared transitions
• Reduce status differences
– Status differences among triads are building blocks of status differences among groups
– Status differences neutralized within local positions

Discussion: Systemic Implications Local Positions
• Local positions contain weak ties
• Beyond the range of the friendship circle. Convey new and salient information.
• bring outer circle of potential friends into the friendship circle
(Call and Mortimer 2001; Cronsoe et al., forthcoming;
Giordano 2003; Harter and Fischer 1999; Haynie 2001).
• Social capital emerges from school:
– Not uniform
– Or pressed in neat grade level sheets
– but in local position clumps
• Implications for other forms of social organization in other institutions (e.g., work or religious).
• Also helps us understand the structural underpinnings of motivation to cultivate potential friends –
– Especially for girls – girls good at using local positions to identify potential friends

• Schools create venues for friendship formation.
Venues can be modified
– Choose venues (courses and extracurriculars: Quiroz et al, 1997)
– Direct participation (Moody 2001)
• Effects of previous institutions penetrate new friendships via local positions
– Homophily
– Prior segregation (Orfield)
– Reducing immediate homophily may not eliminate trend based on previous tendency

• Endogeneity of local positions?
• Friendships outside the school?
• Other forms of interaction
– e.g., BookFace (sp intentional)
• School unique because it is well bounded

• Even given these limitations, our results point to the powerful role of the American high school in organizing the everyday life of its youth. While the social world of adolescence has often been cast as a domain of youth’s indiscretion where adult sensibilities are lacking, our results illustrate the tight linkage between academic and social opportunities structured by schools —in this case local positions that emerge through coursetaking commonalities —and the informal world adolescents must negotiate.

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.

• Members of the wide network of peers “…are more apt to encompass elements of distance and difference, in effect constituting a ‘tougher audience’ for the developing adolescent…Movement into such relations of contrast requires a developmental ‘stretch’ that is not as pronounced in the more comfortable world of close friendship”
– (page 277 Giordano, Peggy C. 2003. "Relationships in Adolescence." Annual Review of
Sociology 29: 257-81).
• Critique of Friendship Influence
– Friends accept adolescents for who they are
(Harter and Fischer 1999;
Lightfoot 1997; Bearman and Bruckner 2001)
– Adolescents more likely to select friends with similar interests than to be influenced by existing friends
(Dornbusch 1989; Matsueda and
Anderson 1998)

Tangent: Influence of Potential Friends
?

Tangent: Influence of Potential Friends
?

Tangent: Influence of Potential Friends
?

Identifying Potential Friends: Minimizing Transaction Costs
Minimize Exposure/vulnerability when seeking friendship.
– Leifer, E. M. 1988
Friendship by mutual negotiation
1) Formal structural constraints (Zhen and Xie, 2008; Kossinets and Watts,
2009)
Difficult to initiate friendship if you do not have contact
2) Informal structural constraint: Micro friendship structure
Friends of friends: broker introductions, enforce norms
3) Shared activities
Sports, academics, arts
Can retreat into the common shared activity if friendship overture fails
4) Course overlap structured opportunities to interact with others with shared interests applies to all students, whole school day

Baseline Hypotheses for Friendship Formation
• 1) 2) Structural constraint
– The more similar the grade level of two adolescents the more likely a friendship will form between them.
• 2) Micro friendship structure
– The more mutual friends two adolescents have, the more likely a friendship will form between them.
• 3) Shared activities
– The more two adolescents participate in similar extracurricular activities, (e.g., sports) the more likely a friendship will form between them.
• 4) Course overlap
– The more courses two adolescents share the more likely a friendship will form between them.