3Example Dataset: Acitelli dyad dataset 148 married couples Outcome Satisfaction (Wife and Husband)Predictor VariableOther-Positivity (Wife and Husband)How positive the Wife views her Husband, and how positive the Husband views his Wife
4Distinguishability It is assumed that distinguishing variable matters. How does it matter?Different results for the two members.Test of distinguishability determines whether distinguishability empirically matters.
5Should You Even Perform a Test of Distinguishability? YesCould simplify the model and parsimony is valued.Could dramatically increase power.NoThe literature may expect separate analyses for the two types of members.Can present separate results but say they do not differ.
6Specifically how does it matter? Actor and partner effects differ.Means, intercepts, and variances differ.If multiple variables, correlations differ.
7Constraints Pairs of six parameters set equal to each other Two actor effectsTwo partner effectsTwo error variancesTwo Y interceptsTwo X variancesTwo X means
9Types of Distinguishability Complete IndistinguishabilityAll parameters equal (6)Y IndistinguishabilityMean and variance of X not set equal (4)What is done in Multilevel ModelingEffect IndistinguishabilityOnly actor and partner effects set equal (2)
10Using SEM Tests Complete indistinguishability: c2(6) = 9.192, p = .163 Y Indistinguishability: c2(4) = 7.228, p = .124Effect Indistinguishability: c2(2) = 0.328, p = .849All tests indicate that we cannot conclude members are distinguishable in terms of their gender.If significant: Distinguishability empirically matters.If not: No evidence distinguishability matters.
11Using MLM Estimate two models One in which members are distinguishable.One in which members are indistinguishable.Use ML not REML estimation.Subtract deviance of the more complex model (distinguishable) from the deviance of the simpler model.That difference is distributed as chi square under the null hypothesis with 4 degrees of freedom.
13Using MLMSPSS: For the deviance use -2 Log Likelihood from “Information Criteria.”IndistinguishableDeviance:Number of parameters: 5DistinguishableDeviance:Number of parameters: 9
14MLM Result c2(9 – 5) == , p = .122The null hypothesis is that the dyads are indistinguishable. We cannot reject the null hypothesis, so we conclude that there is no empirical evidence that dyad members should be differentiated by their gender.
15Additional ReadingsMLM: davidakenny.net/doc/indistinguishability_mlm.pdfSEM: page 108 in Kenny, D. A., Kashy, D. A., & Cook, W. L. Dyadic data analysis. New York: Guilford Press.