Social Relations Model:Estimation Indistinguishable Dyads

David A. Kenny

Strategies

MultilevelANOVA

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 MLwiN

A method developed by Tom Snijders

Can estimate the full SRM.

Snijders Approach:Group Level

Effects can vary at the group level.

Snijders Approach:Dyad Level

At the dyad level there are two scores, one for person A with B and one for person B with A.

Set these two variances to be equal and allow for a correlation to measure dyadic reciprocity.

AdvantagesMore powerful statistical tests.Allows for missing data.Non-saturated models can be

estimated, e.g., a model where generalized reciprocities are set to zero.

Easy to estimate effects of covariates.

ANOVA Strategy

OldestUses Expected Mean SquaresTwo Major Programs

TripleR SOREMO

TripleR

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

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

1803794/Round_robin_analyses_in_R_How_to_use_TripleR

TripleR

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

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

1803794/Round_robin_analyses_in_R_How_to_use_TripleR

SOREMO

FORTRAN 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

Decisions

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

Output

UnivariateMultivariate

Univariate Output

Variance 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 Estimation

Negative VariancesOut-of-range Correlations

Negative Variances

Ordinarily 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!