dyadic designs to model relations in social interaction data todd d. little yale university
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Dyadic designs to model Dyadic designs to model relations in social interaction relations in social interaction
datadata
Todd D. Little
Yale University
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OutlineOutline
•Why have such a symposium
•Dyadic Designs and Analyses
•Thoughts on Future Directions
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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
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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)
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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
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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
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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
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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
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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
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"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)
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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
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Negative Individual, Positive GroupNegative Individual, Positive Group
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Positive Individual, Negative GroupPositive Individual, Negative Group
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No Individual, Positive GroupNo Individual, Positive Group
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No Group, Mixed IndividualNo Group, Mixed Individual
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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
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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:
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Future DirectionsFuture Directions
•OLS vs. ML estimator and bias
•Individual-oriented data vs. dyad-oriented data
•Thoughts on Future Directions
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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
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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
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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
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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