1. Dyadic designs to model relations in social interaction data Todd D. Little Yale University

2. Outline Why have such a symposium Dyadic Designs and Analyses Thoughts on Future Directions

3. Some Bad Methods Dyad-level Setups (Ignore individuals) Target-Partner Setups Arbitrary assignment of target vs partner Loss of power Often underestimates relations Ignores dyadic impact Target with multiple-Partner Take average of partners to reduce dyad- level influences Doesn't really do it Ignores dyadic impact

4. Intraclass Setups Represents target with partner & partner with target in same data structure Exchangeable case (target/partner arbitrary) Distinguishable case (something systematic) Keeps dyadic influence Contains dependencies Requires adjustments for accurate statistical inferences (see e.g., Gonzalez & Griffin)

5. Between-Friend Correlations

6. Canonical Correlations Child- Rated Parent- Rated Teacher- Rated Grade

7. Social Relations Model (Kenny et al.) X ijk = m k + a i + b j + g ij + e ijk Where X ijk is the actor i's behavior with partner j at occasion k m k is a grand mean or intercept a i is variance unique to the actor i b j is variance unique to the partner j g ij is variance unique to the ij-dyad e ijk is error variance Round-Robin designs: (n * (n-1) / 2) Sample from all possible interactions Block designs: p persons interact with q persons Checker-board: multiple p's and q's of 2 or more

8. Development Gender Persistence Tenure Relative Ability to Compete Onlooking Directives Imitation.12.39 -25.68.51 -.26 -.27 From Hawley & Little, 1999 SEM of a Block Design

9. Multilevel Approaches Distinguish HLM (a specific program) from hierarchical linear modeling, the technique –A generic term for a type of analysis Probably best to discuss MRC(M) Modeling –Multilevel Random Coefficient Modeling Different program implementations –HLM, MLn, SAS, BMDP, LISREL, and others

10. "Once you know that hierarchies exist, you see them everywhere." "Once you know that hierarchies exist, you see them everywhere." -Kreft and de Leeuw ( 1998 )

11. Logic of MRCM Coefficients describing level 1 phenomena are estimated within each level 2 unit (e.g., individual- level effects) –Intercepts—means –Slopes—covariance/regression coefficients Level 1 coefficients are also analyzed at level 2 (e.g., dyad-level effects) –Intercepts: mean effect of dyad –Slopes: effects of dyad-level predictors

12. Negative Individual, Positive Group

13. Positive Individual, Negative Group

14. No Individual, Positive Group

15. No Group, Mixed Individual

16. A Contrived Example Y ij = Friendship Closeness ratings of each individual i within each dyad j. Level 1 Measures: Age & Social Skill of the individual participants Level 2 Measures: Length of Friendship & Gender Composition of Friendship

17. The Equations y ij =  0j +  1j Age +  2j SocSkill +  3j Age*Skill + r ij The Level 1 Equation:  0j =  00 +  01 (Time) +  02 (Gnd) +  03 (Time*Gnd) + u 0j  1j =  10 +  11 (Time) +  12 (Gnd) +  13 (Time*Gnd) + u 1j  2j =  20 +  21 (Time) +  22 (Gnd) +  23 (Time*Gnd) + u 2j  3j =  30 +  31 (Time) +  32 (Gnd) +  33 (Time*Gnd) + u 3j The Level 2 Equations:

18. Future Directions OLS vs. ML estimator and bias Individual-oriented data vs. dyad-oriented data Thoughts on Future Directions

19. Level 1 Equations: Meaning of Intercepts Y = Friendship Closeness Ratings –i individuals –across j dyads –r ij individual level error Intercept (Dyad-mean Closeness) –Y ij =  0j + r ij

20. Level 2 Equations: Meaning of Intercepts Do Dyad Means Differ? Mean Closeness across Dyads –  0j =  00 + u 0j Mean Closeness and dyad-level variables (time together and gender composition) –  0j =  00 +  01 (TIME) +  02 (Gen) + u 0j

21. Level 1 Equations: Meaning of Slope E.g., Relationship between Closeness and Social Skill within each dyad –Y ij =  0j +  2j (SocSkil) + r ij Intercept for each dyad:  0j Social Skill slope for each dyad:  2j

22. Level 2 Equations: Meaning of Slopes Mean Social Skill-Closeness relationship across all dyads –   j =  10 + u 1j Does SocSkill-Closeness relationship vary as a function of how long the dyad has been together? –  1j =  10 +  11 (TIME) + u 1j