Using the Actor-Partner Interdependence Model to Study the Effects of Group Composition

1. Using the Actor-Partner Interdependence Model to Study the Effects of Group Composition David A. Kenny & Randi Garcia University of Connecticut http://davidakenny.net/doc/gapim.ppt http://davidakenny.net/doc/gapim.doc

2. Example Question • Jill is a member of a six-person group. Jill is female. • We measure how influential Jill is in the group. • The research question: How does a person’s gender and the genders of the other group members affect how influential a person is seen? • Denote gender as X and presume X is a dichotomy.

3. Multilevel Data • The answer to the research question requires a multilevel data set. • Two levels • The lower level or level 1: Person • The upper level or level 2: Group • To have unbiased estimates of standard errors, we must allow for nonindependence due to groups.

4. Variables and Notation • Yij = the outcome of person i in group j (How influential is Jill seen?) • Xij = gender of person i in group j (Jill is -1 and a male would be +1) • Mj = the average X scores for group j (if greater than zero, there would be more males in the group)

5. Traditional Multilevel Modeling of Groups • Variables X (level 1) and Mj (level 2) to predict Y. • Or X – Mj(X “group mean centered”) and Mj to predict Y.

6. Problems with the Traditional MLM Formulation • Part-whole problem. • Can be difficult to interpret. • Linkage to theory unclear. • What about other effects of X, especially diversity in the Xs (or the similarity of the Xs)?

7. Actor-Partner Interdependence Model • The “group effect,” called “Others,” is the effect due to OTHER members of the group, denoted as Mj’. • The individual’s score is removed from the group mean. • Others is a level 1 variable but most of its variance is between groups.

10. Main Effects for the Example Actor: Are men (or women) more likely to be seen as influential? Others: If most of the partners are men (or women), is the person seen as influential?

11. Interactions Actor x Others: If the person is similar to others, is the person seen as influential? Other x Other: If the other members of the group are similar to each other, is the person seen as influential?

12. Re-conceptualization of Diversity Instead of thinking about diversity as a property of the group (i.e., a variance), we can view diversity as the set of relationships.

13. Variance as the Measure of Diversity s2 = Si(Xi – M)2/(n – 1) s2 = SiSj(Xi – Xj)2/[n(n - 1)] i > j s2 = 1 - SiSj(XiXj)/[n(n - 1)/2] i > j Thus, diversity can be viewed as a summary of the similarity of all the possible relationships in the group.

14. Group Diversity as the Sum of All Possible Relationships

15. Group Diversity = Actor Similarity + Others Similarity

16. The Two Types of Similarity • Actor Similarity • How well the person fits into the group. • “Relational Demography” of Elfenbein and O’Reilly • Others Similarity • Combined with actor similarity becomes diversity • If Actor and Others Similarity have the same coefficients, there is a pure diversity effect.

17. Example Data Set • PI: Harmon Hosch • Gathered in El Paso, Texas • 134 6-person juries from the jury pool • The sample was 54.7% Female, 58.7% Hispanic, 31.5% White, 3.9% Black, and 2.2% Asian American or Native American. • Mock jury case: theft • We have a measure of influence (1 to 5; to be discussed later).

18. SPSS Syntax MIXED influential WITH gender other_gender actor_sim others_sim /FIXED = gender other_gender actor_sim others_sim /PRINT = SOLUTION TESTCOV /REPEATED = memnum | SUBJECT(group) COVTYPE(CSR) .

19. Results: Main Effects Effect Coefficient SE p Actor 0.093 0.025 >.001 Partners-0.077 0.073 .291 Men seen as persuasive.

20. Results: Interactions Effect Coefficient SE p Actor Similarity -0.050 0.062 .422 Others Similarity 0.257 0.106 .016 A person is seen as more persuasive if others in the group are similar.

21. Conclusions • Men are seen as more influential than women. • If others are similar, a person is seen as influential.

22. What was the measure of “Influential”? • Based on a relational measure. • Each person asked (round-robin design): “How persuasive is each other person in the group.” • We need to extend the model, both fixed and random, to a dyadic outcome.

23. Levels or Random Effects Group: How much influence in the group? Individual • Actor: How much influence Jill sees others? • Partner: How influential is Jill seen by others (may be correlated with Actor)? Dyad: If Jill sees Sally as influential, does Sally see Jill as influential? (The Social Relations Model)

24. Three Main Effects Partner Actor Others

25. Main Effects Actor: Are men (or women) more likely to see others as influential? Partner: Are men (or women) more likely to be seen by others as influential? Others: If the most of the partners are men (or women), is the person seen as influential?

26. Results: Main Effects Effect Coefficient SE p Actor -0.007 0.024 .776 Partner 0.086 0.026 .001 Others -0.092 0.062 .142 Men seen as more influential.

27. Interactions Instead of thinking about diversity (or homogeneity) as a property of the group (i.e., a variance), we can view diversity as the set of relationships.

28. Four Types of Similarity Partner Actor Others

29. Four Types of Similarity • Group similarity equals the sum of these components. Partner Similarity Dyadic Similarity Actor Similarity Others Similarity

30. The Four APIM Interactions Dyadic: Actor-Partner Actor: Actor-Others Partner: Partner-Others Others: Other-Other

31. Interaction Results Similarity Effect SE p Dyadic 0.018 0.200 .368 Actor 0.148 0.056 .009 Partner -0.102 0.058 .080 Others 0.076 0.074 .306 If the partner is different from others (partner similarity) and you are similar to others (actor similarity), you see the partner as influential.

32. Partner Seen Relatively Low on Influential Partner Actor Others

33. Partner Seen Relatively High on Influential Partner Actor Others

34. SAS Syntax PROC MIXED COVTEST; CLASS dyad group; MODEL influential = actor partner other dsim asim psim osim / S DDFM=SATTERTH; RANDOM a1 a2 a3 a4 a5 a6 p1 p2 p3 p4 p5 p6 INTERCEPT / G SUB=group TYPE = LIN(4) LDATA=g; REPEATED /TYPE=CS SUB=dyad (group);

35. Extensions • Some people may have a bigger partner effect (e.g., leaders). • Non-dichotomous X variables: • Interval variables • Nominal variables with more than two levels • Multiple X variables • Solo effects

36. Limitations • Requires • Interval outcomes • At least four-person groups • a large number of groups • considerable variation in diversity • Does not provide an account dynamic factors of group interaction.

37. Conclusions • The model presented offers some unique opportunities for the study of groups. • Approach combines state-of-the-art statistical methods with theories of groups.

38. Thank You! http://davidakenny.net/doc/gapim.ppt http://davidakenny.net/doc/gapim.doc

39. data g;input parm row col value;datalines; 1 1 1 1 1 2 2 1 1 3 3 1 1 4 4 1 1 5 5 1 1 6 6 1 2 7 7 1 2 8 8 1 2 9 9 1 2 10 10 1 2 11 11 1 2 12 12 1 3 1 7 1 3 2 8 1 3 3 9 1 3 4 10 1 3 5 11 1 3 6 12 1 4 13 13 1