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Social Relations Model: Estimation Indistinguishable Dyads David A. Kenny

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Strategies Multilevel ANOVA

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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.

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With SPSS, HLM and R’s nlme Cannot estimate the full SRM. Must assume zero actor-partner covariance positive dyadic reciprocity

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With SAS and MLwiN A method developed by Tom Snijders Can estimate the full SRM.

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Snijders Approach: Group Level Effects can vary at the group level.

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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.

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Advantages More 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.

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ANOVA Strategy Oldest Uses Expected Mean Squares Two Major Programs TripleR SOREMO

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TripleR Schmukle, Schönbrodt, & Back http://cran.r- project.org/web/packages/Tripl eR/index.html http://www.academia.edu/18037 94/Round_robin_analyses_in_R _How_to_use_TripleR

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TripleR Schmukle, Schönbrodt, & Back http://cran.r- project.org/web/packages/Tripl eR/index.html http://www.academia.edu/18037 94/Round_robin_analyses_in_R _How_to_use_TripleR

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SOREMO FORTRAN program originally written in the early 1980s. WINSOREMO makes the running of SOREMO much easier.

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Estimation Strategy Computes 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)

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Getting the Data Ready One line per each cell of the design Ordered as follows:,,,, …, All variables on that line Fixed format Personality variable before dyadic variables No missing data

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

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Output Univariate Multivariate

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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

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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

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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

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Anomalous Results with ANOVA Estimation Negative Variances Out-of-range Correlations

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Negative Variances Ordinarily impossible Happens in SRM analyses Can treat the variance as if it were zero.

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Out-of-range Correlations A correlation greater than +1 or less than -1. Two possibilities Correlation very near one. Variance due to the component near zero.

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Summary of Results Using Different Programs TermSOREMOSPSS MLM Mean3.868 Actor Variance0.2330.198 Partner Variance0.2400.1920.204 Group Variance-0.0910.000 A-P Covariance0.0590.0000.024 Error Variance0.2220.2370.230 Error Covariance0.0140.0320.022

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Suggested Readings Appendix B in Kenny’s Interpersonal Perception (1994) Kenny & Livi (2009), pp. 174-183

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Thank You!

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