social relations model: estimation indistinguishable dyads david a. kenny
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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!
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