social relations model: estimation distinguishable dyads david a. kenny
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Social Relations Model:Estimation Distinguishable Dyads
David A. Kenny
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BackgroundSocial Relations ModelConfirmatory Factor Analysis
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Data StructureMembers of the groups are
distinguishable.Each member has a different role.Prototypical example
a familymother, father, & child
Other exampleswork teamslaboratory teams with roles or types
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Four-Person FamilyIn the four-person family, there are twelve possible relationships:
mother-father (MF) father-mother (FM)
mother-older child (MO) father-older child (FO)
mother-younger child (MY) father-younger child (FY)
older child-mother (OM) younger child-mother (YM)
older child-father (OF) younger child-father (YF)
older child-younger c. (OY) younger child-older c. (YO)
The first letter corresponds to the actor and the second letter corresponds to the partner.
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StrategyCreate a variance-covariance matrix of the 12 variables (MF, MO, MY, FM … YO).
Analyze by Confirmatory Factor Analysis.
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FactorsEach measure loads on a group,
actor, and partner factor.Separate actor and partner
variances can be estimated for each member of the group.
All loading fixed at 1.Relationship effects are treated as
“errors.”
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OF: Older Child with Father
Loadings
Actor Factor: Older Child
Partner Factor: Father
Group or Family Factor
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Correlations
Generalized reciprocity: Actor-partner correlation, one for role
Dyadic reciprocity: Correlation of errors, one for each pair of roles
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IdentificationNeed at least 4 members of the
group to estimate all the SRM variances and correlations.
With 3 members, an identifying assumptions must be made, e.g., no group variance.
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Degrees of Freedom
CFA with 4 members: df = 47CFA with 3 members and no
group variance: df = 3
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Diagram for 3-Person Family
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Model the MeansWe can estimate factor means for each of
the factors.
To be identified, we nee to make constraints.
One idea is ANOVA constraints: actor and partner effects sum to zero; relationship effects sum to zero by row and column.
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Separating Error from
RelationshipNeed multiple measures.
xxx
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What To Do If the Model Does Not
Fit?Generally the model does fit.
For families, if it does not, can estimate correlations for intra-generational effects. See Kenny et al. (2006) for details.
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Variance Partitioning
For a four-person, each of 12 scores has four different sources of variance.
Except for the family variance, the other three sources explain a different amount.
Different profile of proportion of variance explained for each score.
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ReferenceReading: Chapter 9 of Dyadic Data Analysis by Kenny, Kashy, and Cook.
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Thank You!