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Dyadic designs to model relations in social interaction data

Dyadic designs to model relations in social interaction data. Todd D. Little Yale University. Outline. Why have such a symposium Dyadic Designs and Analyses Thoughts on Future Directions. Some Bad Methods. Dyad-level Setups (Ignore individuals) Target-Partner Setups

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Dyadic designs to model relations in social interaction data

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  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 Grade Child-Rated Parent-Rated Teacher-Rated

  7. Social Relations Model (Kenny et al.) • Xijk= mk + ai + bj + gij + eijk • Where Xijkis the actor i's behavior with partner j at occasion k • mk is a grand mean or intercept • ai is variance unique to the actor i • bj is variance unique to the partner j • gij is variance unique to the ij-dyad • eijk 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 .68 -.26 Onlooking -25 Relative Ability to Compete Gender .51 Directives .39 Persistence -.27 .12 Imitation Tenure 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."-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 • Yij = 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 Level 1 Equation: yij = 0j + 1jAge + 2jSocSkill + 3jAge*Skill + rij The Level 2 Equations: 0j = 00 + 01(Time) + 02(Gnd) + 03(Time*Gnd) + u0j 1j = 10 + 11(Time) + 12(Gnd) + 13(Time*Gnd) + u1j 2j = 20 + 21(Time) + 22(Gnd) + 23(Time*Gnd) + u2j 3j = 30 + 31(Time) + 32(Gnd) + 33(Time*Gnd) + u3j The 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 • rij individual level error • Intercept (Dyad-mean Closeness) • Yij= 0j + rij

  20. Level 2 Equations:Meaning of Intercepts • Do Dyad Means Differ? • Mean Closeness across Dyads • 0j=00+ u0j • Mean Closeness and dyad-level variables (time together and gender composition) • 0j=00+01(TIME)+02(Gen)+ u0j

  21. Level 1 Equations: Meaning of Slope • E.g., Relationship between Closeness and Social Skill within each dyad • Yij = 0j + 2j (SocSkil) + rij • 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 • 1j=10+ u1j • Does SocSkill-Closeness relationship vary as a function of how long the dyad has been together? • 1j = 10 + 11(TIME) + u1j

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