One-with-Many Design: Estimation David A. Kenny June 22, 2013

2 What You Should Know Introduction to the One-with-Many Design

3 The One-with-Many Provider-Patient Data

4 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)

5 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

6 Multilevel Analyses: Nonreciprocal Design 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 FocalIDPartIDDV 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.

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

Fixed Effects: Nonreciprocal Design Can add to the model Focal person characteristics Would be actor if 1PMT design Would be partner if MP1T design Partner characteristics Would be partner if 1PMT design Would be actor if MP1T design Can be random: The coefficient may vary by focal person Important to make zero interpretable 9

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

11 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

12 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

13 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).

14 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..

15 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 focalcode partcode a. Dependent Variable: outcome.

16 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) Var(2) Corr(2,1) focalcode + partcode [subject = focalid] Var(1) Var(2) Corr(2,1) a. Dependent Variable: outcome.

17 Output: Nonindependence The ICC for actor is.208/( ) =.330 and the ICC for partner is.061/( ) =.100. The actor partner correlation is.699, so if mothers are anxious with family members, they are anxious with her.

Fixed Effects: Reciprocal Design Two ways to think about fixed effects Standard way Focal person characteristics (fx) Partner characteristics (px) APIM way (the same variable must be measured for the focal person and partners) Actor characteristics (ax) Partner characteristics (ptx) 18

Fixed Effects: Reciprocal Design /FIXED = focalcode partcode fX*focalcode fX*partcode pX*focalcode pX* partcode| NOINT or /FIXED = focalcode partcode aX*focalcode aX*partcode ptX*focalcode ptX*partcode| NOINT Note: fX*focalcode = aX*focalcode fX*partcode = ptX*partcode pX*focalcode = ptX*focalcode pX*partcode = aX*partcode 19

Conclusion Thanks to Deborah Kashy Reading: Chapter 10 in Dyadic Data Analysis by Kenny, Kashy, and Cook 29