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**University of Connecticut**

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

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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.

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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.

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**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)

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**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.

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**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)?

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**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.

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**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?

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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?

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**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.

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**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.

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**Group Diversity as the Sum of All Possible Relationships**

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**Group Diversity = Actor Similarity + Others Similarity**

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**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.

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**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).

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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) .

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**Results: Main Effects Effect Coefficient SE p**

Actor >.001 Partners Men seen as persuasive.

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**Results: Interactions**

Effect Coefficient SE p Actor Similarity Others Similarity A person is seen as more persuasive if others in the group are similar.

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**Conclusions Men are seen as more influential than women.**

If others are similar, a person is seen as influential.

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**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.

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**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)

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Three Main Effects Partner Actor Others

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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?

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**Men seen as more influential.**

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

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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.

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**Four Types of Similarity**

Partner Actor Others

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**Four Types of Similarity**

Group similarity equals the sum of these components. Partner Similarity Dyadic Similarity Actor Similarity Others Similarity

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**The Four APIM Interactions**

Dyadic: Actor-Partner Actor: Actor-Others Partner: Partner-Others Others: Other-Other

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**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.

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**Partner Seen Relatively Low on Influential**

Actor Others

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**Partner Seen Relatively High on Influential**

Actor Others

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**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);

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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

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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.

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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.

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

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**data g;input parm row col value;datalines;**

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