Social Relations Model:Estimation (Indistinguishable)

David A. Kenny

StrategiesMultilevelANOVA

MLM StrategyBetter statistically than the ANOVA

approachAllows for missing dataOne setup for all designsCan estimate non-saturated models (e.g.,

model with group variances set to zero).Can more easily estimate the effects of

multiple fixed variables.

With SPSS, HLM and R’s nlme

Cannot estimate the full SRM.Must assume

zero actor-partner covariancepositive dyadic reciprocity

With SAS and MLwiNA method developed by Tom

SnijdersCan estimate the full SRM.Need to create dummy

variables and force many equality constraints.

ANOVA StrategyOldestUses Expected Mean SquaresTwo Major Programs

TripleR SOREMO

TripleRSchmukle, Schönbrodt, & Backhttp://cran.r-project.org/web/

packages/TripleR/index.htmlhttp://www.academia.edu/

1803794/Round_robin_analyses_in_R_How_to_use_TripleR

TripleRSchmukle, Schönbrodt, & Backhttp://cran.r-project.org/web/

packages/TripleR/index.htmlhttp://www.academia.edu/

1803794/Round_robin_analyses_in_R_How_to_use_TripleR

SOREMOFORTRAN program originally

written in the early 1980s.WINSOREMO makes the

running of SOREMO much easier.

Estimation StrategyComputes estimates of actor,

partner, and relationship effects.Computes their variance.Adjust the variances by irrelevant

components; e.g., variance of actor effects contains relationship variance (Expected Mean Squares)

Getting the Data Ready

One line per each cell of the designOrdered as follows:<1,1>,<1,2>,<1,3>,<1,4>,<2,1> …

<4,3>,<4,4>All variables on that lineFixed formatPersonality variable before dyadic variablesNo missing data

DecisionsSame group sizes?Self data?Personality variables?Constructs?Reverse Variables?

OutputUnivariateMultivariate

Univariate OutputVariance Partitioning RELATIVE VARIANCE PARTITIONING VARIABLE ACTOR PARTNER RELATIONSHIP CONTRIBUTE .335* .345* .320 INFLUENCE .191* .443* .365 EXHIBIT .177* .498* .325 CONTROL .242* .371* .386 PREFER .173* .270* .557

Multivariate Output

Matrix: Actor by Actor

ACTOR BY ACTOR

CORRELATION MATRIX

CONTRIBUTE INFLUENCE EXHIBIT CONTROL PREFER CONTRIBUTE 1.0000 .7091 .7066 .7559 .6260 INFLUENCE .7091 1.0000 .6770 .5842 .1728 EXHIBIT .7066 .6770 1.0000 .6549 .3211 CONTROL .7559 .5842 .6549 1.0000 .4298 PREFER .6260 .1728 .3211 .4298 1.0000

Matrices for Actor, Partner, Actor X Partner, Relationship Intrapersonal, and Relationship Interpersonal

Construct Variance Partitioning

STABLE CONSTRUCT VARIANCE

VARIABLE ACTOR PARTNER RELATIONSHIP LEADERSHIP .122 .363 .132

UNSTABLE CONSTRUCT VARIANCE

VARIABLE ACTOR PARTNER RELATIONSHIP LEADERSHIP .093 .022 .267

Anomalous Results with ANOVA EstimationNegative Variances

Out-of-range Correlations

Negative VariancesOrdinarily impossibleHappens in SRM analysesCan treat the variance as if it

were zero.

Out-of-range Correlations

A correlation greater than +1 or less than -1.

Two possibilitiesCorrelation very near one.Variance due to the component near zero.

Summary of Results Using Different Programs

Term SOREMO SPSS MLM

Mean 3.868 3.868 3.868

Actor Variance 0.233 0.198 0.198

Partner Variance 0.240 0.192 0.204

Group Variance -0.091 0.000 0.000

A-P Covariance 0.059 0.000 0.024

Error Variance 0.222 0.237 0.230

Error Covariance 0.014 0.032 0.022

Suggested Readings

Appendix B in Kenny’s Interpersonal Perception (1994)

Kenny & Livi (2009), pp. 174-183

Thank You!