Social Relations Model:Estimation Distinguishable Dyads

David A. Kenny

BackgroundSocial Relations ModelConfirmatory Factor Analysis

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

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.

StrategyCreate a variance-covariance matrix of the 12 variables (MF, MO, MY, FM … YO).

Analyze by Confirmatory Factor Analysis.

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.”

OF: Older Child with Father

Loadings

Actor Factor: Older Child

Partner Factor: Father

Group or Family Factor

Correlations

Generalized reciprocity: Actor-partner correlation, one for role

Dyadic reciprocity: Correlation of errors, one for each pair of roles

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.

Degrees of Freedom

CFA with 4 members: df = 47CFA with 3 members and no

group variance: df = 3

Diagram for 3-Person Family

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.

Separating Error from

RelationshipNeed multiple measures.

xxx

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.

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.

ReferenceReading: Chapter 9 of Dyadic Data Analysis by Kenny, Kashy, and Cook.

Thank You!