Triad Trajectories and Mental Health Transitions in Adolescents A Working Paper

1. Triad Trajectories and Mental Health Transitions in AdolescentsA Working Paper G. Robin Gauthier and James Moody Department of Sociology Duke University Durham, North Carolina Thanks to Jeffery Smith, Duke Sociology

2. Outline • Past Findings and Literatures • Social Network and Mental Health literature Triads • Balance Theory (Heider) • Davis and Leinhardt, 1972; Hallinan, 1976; Bearman and Moody, 2004 Add Health data Triad transition model

3. Social Networks and Mental Health • Network Characteristics • Density • Size • Multiplexy • Strength of tie • Social Support (Pearlin,1999) • Chronic stressors • Acute stressors • Social Support; instrumental and emotional • Coping strategies • Mastery

4. Triads • Advantages of studying triads • Characterize macro structure from the distribution of triads (Tau Statistic, Holland and Leinhardt) • smallest unit with a group structure independent of the individuals within it (Simmel) • competition, alliances, or mediation • Hierarchy (Mayhew, Chase) • The triad can be used to study both local and global structure • Granovetter, 1973

5. Balance theory:A Friend of a friend...Heider

6. Transitivity in Directed Graphs • Holland and Leinhardt (1971) • MAN labelling system • Tau Statistic Ranked Cluster Model • Davis and Leinhardt (1972)

7. Triples within triads: Strength of (In)transitivity • Any triad can be decomposed into its 6 triples • Constituent triples, like triads can be characterized as vacuous, transitive or intransitive • The order of these triples matter for the level of in(transitivity) experienced by each node

8. Triads are characterized by more or less intransitivity, rather than intransitivity or transitivity Triad type 120c and constituent triples a-b-c; a-c Transitive b a-c-b; a-b Vacuous b-a-c; b-c Vacuous b-c-a; b-a Intransitive c-a-b; c-b Intransitive a c c-b-a; c-a Vacuous 021C 111D 111U 030T 030C 201 120D 120U 120C 210 300 Transitive 0 0 0 1 0 0 2 2 1 3 6 Intransitive 1 1 1 0 3 2 0 0 2 1 0 Reproduced from Wasserman and Faust (1994), pp. 572

9. Triad Transitivity Levels 003 012 102 021D 021U 030T 120D 120U 300 Legend Vacuous Transitive Intransitive Mixed 021C 111D 111U 030C 201 120C 210

10. Research: Triad trajectories, intransitivity and mental health Sorenson and Hallinan (1976) Model of dynamic triadic change using a Markov chain approach Bearman and Moody (2004) Adolescent girls in intransitive relationships are more likely to experience suicidal thoughts

11. Transition Model • Triads can be characterized by trajectories • Depressive symptoms change over time • People are embedded in multiple triad trajectories • A given triad can have more or less transitivity • There is a change in intransitivity associated with each unique triad path • Individuals within a triad can experience different levels of transitivity • Individuals can experience different levels of intransitivity in different triads • Research Question: how do the paths by which triads become more or less transitive matter (or not) in determining how depressive symptoms change over time-given that individuals are embedded in multiple complicated trajectories simultaneously.

12. Add Health data • Nationally representative longitudinal study of adolescents in grades 7-12 during the 1994-’95 school year • 80 high schools and two of their feeders, yielding in total 132 schools • One in-school survey, four detailed in-home follow-ups, the most recent in 2008 • Longitudinal network data has been collected on 12 of the schools, this paper uses 9 of these • In two of these, nominations were restricted to one male and one female friend per student • Two schools are (provisionally) dropped from the analysis due to their size

13. Working Measures Depression transition measure Wave I to II 4 question CES-D subset Wave II to III 19 question CES-D subset Explanatory Variable Trajectory level summary score of intransitivity Controls Grade, gender, race, school, parental SES, gpa, in-degree, out-degree, social isolation, attachment to school

14. Empirical Distribution of Triad Types Legend Null Transitive Intransitive Mixed

15. 030C 120C 102 111U 021C 201 300 111D 210 012 003 021D 120U Vacuous triad 030T Transitive triad Intransitive triad 120D 021U Increases # intransitive Decreases # intransitive One-Step Trajectory Model Mixed triad

16. Choosing a Model Absolute distance matrix -the transitions are made up of the one-step transitions which minimize the length of the path Observed probability matrix -transitions are determined by weighting the probability of transition by the observed probabilities of the adjacent triad type

17. Assumptions • Triads transition one edge at a time • At each transition point, triads move into the most empirically probable adjacent type • An edge once cut or added is not re-cut or re-added at the next transition point, but may be at subsequent transition points

18. Divergent Paths: An Example 111D 102 201 012 300 210 120C 021C 030C Vacuous triad Transitive triad Vacuous triad Mixed triad Distance weight Observed Probability Weight Both models

19. Directions for Analysis • Model transition dependence • Moody and Smith, forthcoming • Block models • Ties within and across blocks-role structure • Clique analysis • Group affiliations • How do the effects of in(transitivity) differ by context