Presentation on theme: "Using the Actor-Partner Interdependence Model to Study the Effects of Group Composition David A. Kenny & Randi Garcia University of Connecticut"— Presentation transcript:
Using the Actor-Partner Interdependence Model to Study the Effects of Group Composition David A. Kenny & Randi Garcia University of Connecticut
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 persons 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.
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.
Variables and Notation Y ij = the outcome of person i in group j (How influential is Jill seen?) X ij = gender of person i in group j (Jill is -1 and a male would be +1) M j = the average X scores for group j (if greater than zero, there would be more males in the group)
Traditional Multilevel Modeling of Groups Variables X (level 1) and M j (level 2) to predict Y. Or X – M j (X group mean centered) and M j 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)?
Actor-Partner Interdependence Model The group effect, called Others, is the effect due to OTHER members of the group, denoted as M j. The individuals score is removed from the group mean. Others is a level 1 variable but most of its variance is between groups.
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?
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?
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.
Variance as the Measure of Diversity s 2 = i (X i – M) 2 /(n – 1) s 2 = i j (X i – X j ) 2 /[n(n - 1)] i > j s 2 = 1 - i j (X i X j )/[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.
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 group. Relational Demography of Elfenbein and OReilly Others Similarity Combined with actor similarity becomes diversity If Actor and Others Similarity have the same coefficients, there is a pure diversity effect.
Example Data Set PI: Harmon Hosch Gathered in El Paso, Texas 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).
Results: Main Effects Effect Coefficient SE p Actor >.001 Partners Men seen as persuasive.
Results: Interactions Effect Coefficient SE p Actor Similarity Others Similarity A person is seen as more persuasive if others in the group are similar.
Conclusions Men are seen as more influential than women. If others are similar, a person is seen as influential.
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.
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) Levels or Random Effects
Three Main Effects Actor Partner 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?
Results: Main Effects Effect Coefficient SE p Actor Partner Others Men seen as more influential.
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.
Four Types of Similarity Actor Partner Others
Four Types of Similarity Group similarity equals the sum of these components. Dyadic Similarity Actor Similarity Partner Similarity Others Similarity
The Four APIM Interactions Dyadic: Actor-Partner Actor: Actor-Others Partner: Partner-Others Others: Other-Other
Interaction Results Similarity Effect SE p Dyadic 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.
Partner Seen Relatively Low on Influential Actor Partner Others
Partner Seen Relatively High on Influential Actor Partner Others
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);
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
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.
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.