1. University of Connecticut
Using the Actor-Partner Interdependence Model to Study the Effects of Group Composition
David A. Kenny &
Randi Garcia
University of Connecticut

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]
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 >.001
Partners
Men seen as persuasive.

20. Results: Interactions
Effect Coefficient SE p
Actor Similarity
Others Similarity
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 (The Social Relations Model)
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. Men seen as more influential.
Results: Main Effects
Effect Coefficient SE p
Actor
Partner
Others
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
Partner
Others
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
Actor
Others

33. Partner Seen Relatively High on Influential
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

39. data g;input parm row col value;datalines;