1. One-with-Many Design: Introduction David A. Kenny June 11, 2013

2. 2 What You Should Know Dyad Definitions Nonindependence

3. 3 This Webinar Terminology Analysis

4. 4 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.

5. 5 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)

6. 6 The One-with-Many Provider-Patient Data

7. 7 Terminology  People l Focal person (the one) l Partners (the many) Source of Data l Focal persons (1PMT) l Partners (MP1T) l Both (reciprocal design: 1PMT & MP1T)

8. 8 Distinguishability l 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). l Indistinguishable: Partners are interchangeable (e.g., patients with providers)

9. 9 Distinguishable case: Partners can be distinguished by roles e.g., family members (Mother, Father, Sibling) Typically assume equal # of partners per focal person

10. 10 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

11. 11 Nonindependence in the Nonreciprocal Design: Definition l Two partners with the same focal person are more similar than two partners with different focal persons. l Because similarity almost always occurs in this design, nonindependence can be modeled by a variance.

12. 12 Nonindependence in Nonreciprocal Design l Different from the standard design l Meaning depends on data source l Focal Person l Focal person sees partners or behaves with partners in the same way. l Called actor variance l Partners: Partner Variance l Partners see or behave with the focal person in the same way. l Called partner variance

13. 13 1PMT: Focal person provides data with respect to the partners Source of nonindependence: Actor effect: tendency to see all partners in the same way

14. 14 MP1T: Partners provide data Source of nonindependence: Partner effect - tendency of all partners to see the focal person in the same way

15. 15 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

16. 16 Multilevel Analyses Each record a partner Levels Lower level: partner Upper level: focal person Random intercepts model (nonindependence) Lower level effects can be random

17. Data Analytic Approach for the Non- Reciprocal One-with-Many Design FocalIDPartIDDV 116 125 135 213 222 234 243 317 328 Estimate a basic multilevel model in which There are no fixed effects with a random intercept. Y ij = b 0j + e ij b 0j = a 0 + d j 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.

18. 18 SPSS Output Covariance Parameters Fixed Effects So the actor variance is.791, and ICC is.791/(.791+1.212) =.395

19. 19 Reciprocal One-with-Many Design Sources of nonindependence More complex…

20. 20 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

21. 21 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

22. 22 Data Analytic Approach for Estimating Variances & Covariances: The Reciprocal Design A fairly complex multilevel model… MIXED outcome BY role WITH focalcode partcode /FIXED = focalcode partcode | NOINT /PRINT = SOLUTION TESTCOV /RANDOM focalcode partcode | SUBJECT(focalid) covtype(UNR) /REPEATED = role | SUBJECT(focalid*dyadid) COVTYPE(UNR).

23. 23 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..

24. 24 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. Estimates of Fixed Effects a Parameter EstimateStd. ErrordftSig. 95% Confidence Interval Lower BoundUpper Bound focalcode1.807695.040989207.00044.102.0001.7268861.888505 partcode1.698269.034249207.00049.587.0001.6307481.765790 a. Dependent Variable: outcome.

25. 25 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). Estimates of Covariance Parameters a Parameter EstimateStd. ErrorWald ZSig. 95% Confidence Interval Lower BoundUpper Bound Repeated MeasuresVar(1).549234.03808314.422.000.479444.629184 Var(2).423155.02934114.422.000.369385.484753 Corr(2,1).239029.0462285.171.000.146585.327334 focalcode + partcode [subject = focalid] Var(1).208409.0357155.835.000.148952.291601 Var(2).060898.0271342.244.025.025430.145838 Corr(2,1).698818.1709964.087.000.206931.908699 a. Dependent Variable: outcome.

26. 26 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.

27. Conclusion http://davidakenny.net/doc/onewithmanyrecip.pdf Thanks to Deborah Kashy Reading: Chapter 10 in Dyadic Data Analysis by Kenny, Kashy, and Cook 29