1. A New Approach to the Study of Teams: The GAPIM
David A. Kenny

2. My Collaborator
Randi Garcia

3. Example Question Jill is a member of a six-member work team.
We measure how much Jill likes being on the team.
The research question: How does a person’s gender and the genders of the other team members affect how a person likes being on the team?

4. The Many Effects of Gender
Women may not like being in these work teams.
People may like being in teams when there are more women.
People may like being groups that is diverse in terms of gender.
People may like being in groups in which the other team members' gender is similar to them.
A woman may not like being the only woman in the group.

5. Modeling All the Effects
Most often these effects are studied individually which can be problematic.
Why? Consider the effect of gender and the effect of diversity of gender.
Those two effects are highly correlated when there are relatively few females on teams: One is more likely to be female in a gender diverse group.

6. Modeling Approach Model is based on dyadic relationships.
That model is the Actor-Partner Interdependence Model (APIM).
Though based on a dyadic model, the new model contains extra-dyadic (i.e., team) effects.

7. APIM for Dyads Person 1’s Gender Person 1’s Satisfaction
Actor Person 1
Person 1’s Satisfaction
Partner
Person 1
Partner
Person 2
Person 2’s Gender
Person 2’s Satisfaction
Use the case of coworker dyads
Actor Person 2

8. Extending the APIM to Groups: GAPIM
The “group effect,” called “Others,” is the effect due to OTHER members of the group, denoted as Mjʹ.
So the individual’s score is removed from the group mean.
Others is a level 1 variable, but most of its variance is between groups.

9. n-1 paths from each other to the score

10. An Equivalent and Simpler(?) Version of the Model
M1ʹ is the mean
of person 1’s others

11. GAPIM
The “team effect,” called “Others,” is the effect due to OTHER members of the group, denoted as Mj’.
The individual’s score is removed from the team mean.
Others is a level 1 variable but most of its variance is between teams.

12. Main Effects
Actor: Do men (or women) more likely to like being on the team?
Others: If most of the partners are men (or women), do people like being on the team?

13. Interactions
Actor x Others: If the person is similar to others on the term, does the person like being on the team?
Other x Other: If the other members of the team are similar to each other, does the person like the team?

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

15. 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 team.

16. Group Diversity as the Sum of All Possible Relationships

17. Group Diversity = Actor Similarity + Others Similarity

18. The Two Types of Similarity
Actor Similarity
How well the person fits into the team.
“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.

19. 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: Team
To have unbiased estimates of standard errors, we must allow for nonindependence due to teams.

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

21. 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)?

22. GAPIM Example of Garcia
52 groups of 4 or 5 University of Connecticut students
154 women and 87 men
Gender composition was allowed to vary
Procedure
Were asked to write an individual short story about a picture
Group discussed “strengths” and “weaknesses” of each group member’s story
The group wrote a group story
Leadership was not assigned
Small group identification measure (adapted from Leach et al., 2008)

23. SPSS Syntax
MIXED
influential WITH gender other_gender actor_sim others_sim
/FIXED = gender other_gender actor_sim others_sim
/PRINT = SOLUTION TESTCOV
/RANDOM INTERCEPT SUBJECT(team_id).

24. Results of Gender on Individual Satisfaction with Being in the Group
Model
Main Effects
Interactions
Gender
Others Gender
Actor Similarity
Others Similarity
Main Effects Only
-0.071
0.234+ 0a
Complete
-0.026
0.227+
0.295*
-0.21
Others Only
-0.034
0.198
.256*
-0.256*
Female = -1, Male = 1
aFixed to zero.
+ p < .10 * p < .05

26. DataToText Project
Have the researcher tell DataToText what is the research question.
DataToText performs the requisite analyses.
DataToText gives the results from those analyses:
computer output
a written description

27. DataToText Statement
GAPIM_I x = gend/y=GIDSCALE/ groupid = teamnum xn = 'Gender' yn = 'Group Identification' groupn="team" upper_lab="Women" lower_lab="Men" xmiss=1.

28. Three Types of Team Outcomes
Individual: “How much do you like being a member of your team?”
Group: “How productive is the team?”
Dyad: “How influential do you think each team member is?”

29. Second 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).

30. (The Social Relations Model)
Random Effects
Group: How much influence in the jury?
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)

31. Three Main Effects
Partner
Actor
Others

32. 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?

33. Men seen as more influential.
Results: Main Effects
Effect Coefficient SE p
Actor
Partner
Others
Men seen as more influential.

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

35. Four Types of Similarity
Partner
Actor
Others

36. Four Types of Similarity
Team similarity (or diversity) equals the sum of these components.
Partner Similarity
Dyadic Similarity
Actor Similarity
Others Similarity

37. Main Effects Interactions Model aFixed to zero.
Actor Gender
Partner Gender
Others’ Gender
Dyad
Similarity
Actor
Partner
Others’
-0.023
0.102*
-0.098 0a
Complete Model
-0.007
0.086*
-0.092
0.018
0.148*
0.076
Contrast:
Actor vs. Partner
-0.097
0.125*b
-0.125*b
aFixed to zero.
bFixed to be equal, but opposite sign.
+ p < .10 * p < .05

39. 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 (faultlines)

40. Limitations
Requires
Interval outcomes
At least four-person teams
A large number of teams
Considerable variation in diversity; does not work well when:
Few members of one type (e.g., few males)
All groups relatively heterogeneous (e.g., most groups have 3 men and 3 women)
Does not provide an account of the dynamic factors of group interaction.

41. Conclusions
The model is able to model much of the complexity of group composition.
Ability to model team (not presented), individual, and dyadic outcomes.
Approach combines state-of-the-art statistical methods with theories of teams.

42. “It’s not over until its over.”