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**Social Relations Model: Estimation Distinguishable Dyads**

David A. Kenny

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**Background Social Relations Model Confirmatory Factor Analysis**

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

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**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

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Mom Dad Younger Child Older Child

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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.

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

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**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.”

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

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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.

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**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

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**Diagram for 3-Person Family**

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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.

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**Separating Error from Relationship**

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

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Thank You! 4/15/2017

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