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One-with-Many Design:Introduction

David A. Kenny

What You Should Know

- Dyad Definitions
- Nonindependence

This Webinar

- Terminology
- Analysis

Definition

- One person is linked to a unique set of many partners, and these partners are not necessarily linked to each other.
- Example: Patients with a physician.
- Sometimes called a nested design.

Examples

- People report how jealous they felt in each of their past relationships (Hindy & Schwarz, 1994).
- A person’s personality is evaluated by several of his or her friends (Vazire & Gosling, 2004).
- Persons describe the drinking behavior of their friends (Mohr, Averna, Kenny, & Del Boca, 2001).
- Persons report on the truthfulness of their everyday interactions with different partners (DePaulo & Kashy, 1998).
- Egocentric networks of friends (O’Malley et al., 2012)

Terminology

- People
- Focal person (the one)
- Partners (the many)
- Source of Data
- Focal persons (1PMT)
- Partners (MP1T)
- Both (reciprocal design: 1PMT & MP1T)

Distinguishability

- Distinguishable: Partners have different role relationships to the focal person (e.g., mother the focal person and partners are father, older child, and younger child).
- Indistinguishable: Partners are interchangeable (e.g., patients with providers)

Distinguishable case: Partners can be distinguished by roles

- e.g., family members (Mother, Father, Sibling)
- Typically assume equal # of partners per focal person

Indistinguishable case: All partners have the same role with the focal person

- e.g., students with teachers or provider with patients
- no need to assume an equal number of partners

Nonindependence in the Nonreciprocal Design: Definition

- Two partners with the same focal person are more similar than two partners with different focal persons.
- Because similarity almost always occurs in this design, nonindependence can be modeled by a variance.

Nonindependence in Nonreciprocal Design

- Different from the standard design
- Meaning depends on data source
- Focal Person
- Focal person sees partners or behaves with partners in the same way.
- Called actor variance
- Partners: Partner Variance
- Partners see or behave with the focal person in the same way.
- Called partner variance

1PMT: Focal person provides data with respect to the partners

Source of nonindependence:

- Actor effect: tendency to see all partners in the same way

MP1T: Partners provide data

Source of nonindependence:

- Partner effect - tendency of all partners to see the focal person in the same way

Analysis Strategies

- Multilevel analysis
- Indistinguishable partners
- Many partners
- Different numbers of partners per focal person
- Confirmatory factor analysis
- Distinguishable partners
- Few partners
- Same number of partners per focal person

Multilevel Analyses

- Each record a partner
- Levels
- Lower level: partner
- Upper level: focal person
- Random intercepts model (nonindependence)
- Lower level effects can be random

Data Analytic Approach for the Non-Reciprocal One-with-Many Design

Estimate a basic multilevel model in which

There are no fixed effects with a random intercept.

Yij = b0j + eij

b0j = a0 + dj

Note the focal person is Level 2 and partners Level 1.

MIXED

outcome

/FIXED =

/PRINT = SOLUTION TESTCOV

/RANDOM INTERCEPT | SUBJECT(focalid) COVTYPE(VC) .

Could add predictors here.

SPSS Output

Fixed Effects

Covariance Parameters

So the actor variance is .791, and ICC is .791/(.791+1.212) = .395

Sources of Nonindependence in the Reciprocal Design

- Individual-level effects for the focal person:
- Actor & Partner variances
- Actor-Partner correlation
- Relationship effects
- Dyadic reciprocity corelation

Data Analytic Approach for Estimating Variances & Covariances: The Reciprocal Design

Data Structure: Two records for each dyad; outcome is the same variable for focal person and partner.

Variables to be created:

role = 1 if data from focal person; -1 if from partner

focalcode = 1 if data from focal person; 0 if from partner

partcode = 1 if data from partner; 0 if from the focal person

Data Analytic Approach for Estimating Variances & Covariances: The Reciprocal Design

A fairly complex multilevel model…

MIXED

outcome BY role WITH focalcodepartcode

/FIXED = focalcodepartcode | NOINT

/PRINT = SOLUTION TESTCOV

/RANDOM focalcodepartcode | SUBJECT(focalid) covtype(UNR)

/REPEATED = role | SUBJECT(focalid*dyadid) COVTYPE(UNR).

Example

- Taken from Chapter 10 of Kenny, Kashy, & Cook (2006).
- Focal person: mothers
- Partners: father and two children
- Outcome: how anxious the person feels with the other
- Distinguishability of partners is ignored.

.

Output: Fixed Effects

The estimates show the intercept is the mean of the ratings made by the mother (focalcode estimate is 1.808). The partcode estimate indicates the average outcome score across partners of the mother which is smaller than mothers’ anxiety. This difference is statistically significant.

The relationship variance for the partners is .549. (Role = -1) and for mothers (Role = 1) is .423.

- The correlation of the two relationship effects is .24: If the mother is particularly anxious with a particular family member, that member is particularly anxious with the mother.
- Var(1) (focalcode is the first listed random variable) is the actor variance of mothers and is .208.
- Var(2) is the partner variance for mothers (how much anxiety she tends to elicit across family members) and is .061. (p = .012; p values for variances in SPSS are cut in half).

Output: Nonindependence

- The ICC for actor is .208/(.208+.423) = .330 and the ICC for partner is .061/(.061+.549) = .100.
- The actor partner correlation is .699, so if mothers are anxious with family members, they are anxious with her.

Conclusion

http://davidakenny.net/doc/onewithmanyrecip.pdf

Thanks to Deborah Kashy

Reading: Chapter 10 in Dyadic Data Analysis by Kenny, Kashy, and Cook

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