Dyadic Analysis: Using HLM

David A. Kenny

University of Connecticut

http://davidakenny.net/kenny.htm

http://davidakenny.net/hlmdyad

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Types of DyadsDefinitions

Distinguishable

Dyads with a categorical within-dyads variables that makes a difference

e. g., parent-child

Indistinguishable

Ordering of the two members is arbitrary

e.g. roommates

Whether dyads are distinguishable or not is matter of theoretical and statistical considerations.

Nonindependence:Definition

Degree of greater similarity (or dissimilarity) between linked observations versus unlinked observations

Nonindependence as the correlation between linked observations.

Negative Nonindependence

Two scores from the same dyad are more dissimilar than two scores from different groups.

How?

Compensation: If one person has a large score, the other person lowers his or her score. For example, if one person acts very friendly, the partner may distance him or herself,

Social comparison: The members of the dyad use the relative difference on some measure to determine some other variable. For instance, satisfaction after a tennis match is determined by the score of that match.

Zero-sum: The sum of two scores is the same for each dyad. For instance, the two members divide a reward that is the same for all dyads.

Division of labor: Dyad members assign one member to do one task and the other member to do another. For instance, the amount of housework done in the household may be negatively correlated.

Dyadic Designs Standard

Each person has one partner Social Relations Model (SRM) Designs

Each person has many partners, and each partner paired with many persons

One-with-Many Each person has many partners, but each

partner is paired with only one person

Standard Design

One-with-Many Design

SRM Designs

Remaining part of the presentation focuses on the

standard design which is used in most dyadic studies.

Dyadic Data Organization Individual

One record for each individual Only that individual’s data on the record

Dyad (useful for distinguishable dyads) Each record one dyad Different variables for each person

Pairwise (useful for distinguishable dyads) One record for each person The person’s data and partner data included

(each data point included twice)

Pairwise Data Organization

Dyad Number Member Number The Person’s Data Partner’s Data Acitelli Example

Types of Variables

Between Dyads – Level TwoBoth members have the same score

X = X′

Within DyadsSum of two scores a constant

X + X′ = c for all dyads

Mixed Variables Variables that vary within and

between groups Examples

• Most outcomes (and mediators)

• Individual differences (e.g., personality)

Gender and the Three TypesBetween

Gay and Lesbian Couples

Within

Heterosexual Married Couples

Mixed

Friends

Actor-Partner Interdependence Model

Types of APIM Modelsactor only

a > 0; p = 0partner only

p > 0; a = 0couple model

a = psocial comparison model

a + p = 0

Actor-Partner Interaction

•Partner effect depends on the level of the actor effect•More than one way to test•A Level 2 Variable

Measurement of the Actor-Partner Interaction

•Standard Product Approach (XX’) – make sure variables centered•Discrepancy Score (│X – X′│) (Absolute Difference)

•Similarity – Negative Coefficient•Dissimilarity – Positive Coefficient

•Higher Score of the Two [Max(X,X′)] – “It Takes Two” •Lower Score [Min(X,X′)] – “One of Us Can Drag Us Both Down”

EstimationIndistinguishable Members

Multilevel ModelingPairwise Data FileIllustrate with HLM

Distinguishable MembersStructural Equation ModelingDyad Data File

Approaches Illustrated

Conventional Multilevel Model with Random InterceptsTwo-Intercept Model

Briefly DiscussedOne-with-many designStandard design studied longitudinally