A New Approach to the Study of Teams: The GAPIM David A. Kenny http://davidakenny.net/doc/gapim.ppt http://davidakenny.net/doc/gapim.pdf

My Collaborator Randi Garcia

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?

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.

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.

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.

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

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.

n-1 paths from each other to the score

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

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.

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?

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?

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.

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.

Group Diversity as the Sum of All Possible Relationships

Group Diversity = Actor Similarity + Others Similarity

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.

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.

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.

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)?

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)

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).

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

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

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.

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?”

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).

(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)

Three Main Effects Partner Actor Others

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?

Men seen as more influential. 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.

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.

Four Types of Similarity Partner Actor Others

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

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* -0.102+ 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

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)

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.

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.

“It’s not over until its over.” http://davidakenny.net/doc/gapim.ppt http://davidakenny.net/doc/gapim.pdf