Social Relations Model: Estimation Distinguishable Dyads David A. Kenny

Background Social Relations Model Confirmatory Factor Analysis 4/15/2017 Background Social Relations Model Confirmatory Factor Analysis

Data Structure Members of the groups are distinguishable. 4/15/2017 Data Structure Members of the groups are distinguishable. Each member has a different role. Prototypical example a family mother, father, & child Other examples work teams laboratory teams with roles or types

Mom Dad Younger Child Older Child

Four-Person Family In 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.

4/15/2017 Strategy Create a variance-covariance matrix of the 12 variables (MF, MO, MY, FM … YO). Analyze by Confirmatory Factor Analysis.

Factors Each measure loads on a group, actor, and partner factor. 4/15/2017 Factors Each 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

4/15/2017 Correlations Generalized reciprocity: Actor-partner correlation, one for role Dyadic reciprocity: Correlation of errors, one for each pair of roles

4/15/2017 Identification Need 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 = 47 4/15/2017 Degrees of Freedom CFA with 4 members: df = 47 CFA with 3 members and no group variance: df = 3

Diagram for 3-Person Family

Model the Means We 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 Relationship Need 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.

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

Thank You! 4/15/2017