Download - Dyadic designs to model relations in social interaction data Todd D. Little Yale University
Dyadic designs to model Dyadic designs to model relations in social interaction relations in social interaction
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Todd D. Little
Yale University
OutlineOutline
•Why have such a symposium
•Dyadic Designs and Analyses
•Thoughts on Future Directions
Some Bad MethodsSome 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
Intraclass SetupsIntraclass 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)
Between-Friend Correlations
NN EE OO AA CC
Child-Rated
.05 .10 .06 .06 .06
Parent-Rated
.07 .02 .06 -.04 .17
Teacher-Rated
.35 .21 .29 .36 .30
Canonical Correlations
All .16 .26 .485 .31 .59 .536 .34 .66 .637 .17 .42 .738 .16 .34 .739 .28 .44 .65
10 .26 .40 .61
Child-Rated
Parent-Rated
Teacher-Rated
Grade
Social Relations Model (Kenny et al.)Social Relations Model (Kenny et al.)
•Xijk = mk + ai + bj + gij + eijk
Where Xijk is the actor i's behavior with partner j at occasion kmk is a grand mean or intercept ai is variance unique to the actor ibj is variance unique to the partner jgij is variance unique to the ij-dyadeijk 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
Development
Gender
Persistence
Tenure
RelativeAbility to Compete
Onlooking
Directives
Imitation.12
.39
-25
.68
.51
-.26
-.27
From Hawley & Little, 1999
SEM of a Block Design SEM of a Block Design
Multilevel ApproachesMultilevel 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
"Once you know that "Once you know that hierarchies exist, hierarchies exist,
you see them you see them everywhere."everywhere."
-Kreft and de Leeuw (1998)
Logic of MRCMLogic 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
Negative Individual, Positive GroupNegative Individual, Positive Group
Positive Individual, Negative GroupPositive Individual, Negative Group
No Individual, Positive GroupNo Individual, Positive Group
No Group, Mixed IndividualNo Group, Mixed Individual
A Contrived ExampleA 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
The EquationsThe Equations
yij = 0j + 1jAge + 2jSocSkill + 3jAge*Skill + rij
The Level 1 Equation:
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 Level 2 Equations:
Future DirectionsFuture Directions
•OLS vs. ML estimator and bias
•Individual-oriented data vs. dyad-oriented data
•Thoughts on Future Directions
Level 1 Equations: Level 1 Equations: Meaning of Intercepts Meaning of Intercepts
• Y = Friendship Closeness Ratings– i individuals– across j dyads– rij individual level error
• Intercept (Dyad-mean Closeness)– Yij = 0j + rij
Level 2 Equations:Level 2 Equations:Meaning of Intercepts 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
Level 1 Equations: Level 1 Equations: Meaning of SlopeMeaning 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
Level 2 Equations: Level 2 Equations: Meaning of SlopesMeaning of Slopes
• Mean Social Skill-Closeness relationship across all dyads
– j = 10 + u1j
• Does SocSkill-Closeness relationship vary as a function of how long the dyad has been together?– 1j = 10 + 11(TIME) + u1j