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.
With SPSS, HLM and R’s nlme Cannot estimate the full SRM. Must assume zero actor-partner covariance positive 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.
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.
ANOVA Strategy Oldest Uses Expected Mean Squares Two Major Programs TripleR SOREMO
SOREMO FORTRAN program originally written in the early 1980s. WINSOREMO makes the running of SOREMO much easier.
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)
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
Decisions Same group sizes? Self data? Personality variables? Constructs? Reverse Variables?
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 Variances Out-of-range Correlations
Negative Variances Ordinarily impossible Happens in SRM analyses Can treat the variance as if it were zero.
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.
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
Suggested Readings Appendix B in Kenny’s Interpersonal Perception (1994) Kenny & Livi (2009), pp. 174-183