1 Social Relations Model: Estimation Distinguishable Dyads David A. Kenny
2 Background Social Relations Model Confirmatory Factor Analysis 4/15/2017BackgroundSocial Relations ModelConfirmatory Factor Analysis
3 Data Structure Members of the groups are distinguishable. 4/15/2017Data StructureMembers of the groups are distinguishable.Each member has a different role.Prototypical examplea familymother, father, & childOther exampleswork teamslaboratory teams with roles or types
5 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.
6 4/15/2017StrategyCreate a variance-covariance matrix of the 12 variables (MF, MO, MY, FM … YO).Analyze by Confirmatory Factor Analysis.
7 Factors Each measure loads on a group, actor, and partner factor. 4/15/2017FactorsEach 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.”
8 OF: Older Child with Father Loadings Actor Factor: Older Child Partner Factor: Father Group or Family Factor
9 4/15/2017CorrelationsGeneralized reciprocity: Actor-partner correlation, one for roleDyadic reciprocity: Correlation of errors, one for each pair of roles
10 4/15/2017IdentificationNeed 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.
11 Degrees of Freedom CFA with 4 members: df = 47 4/15/2017Degrees of FreedomCFA with 4 members: df = 47CFA with 3 members and no group variance: df = 3
13 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.
14 Separating Error from Relationship Need multiple measures. xxx
15 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.
16 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.
17 ReferenceReading: Chapter 9 of Dyadic Data Analysis by Kenny, Kashy, and Cook.