social relations model: estimation (indistinguishable) david a. kenny
DESCRIPTION
MLM Strategy Better statistically than the ANOVA approach Allows for missing data One setup for all designs Can estimate non-saturated models (e.g., model with group variances set to zero). Can more easily estimate the effects of multiple fixed variables.TRANSCRIPT
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!