# Test of Distinguishability

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Test of Distinguishability
David A. Kenny March 24, 2013

You Need to Know Estimation method SEM MLM

Example Dataset: Acitelli dyad dataset 148 married couples Outcome
Satisfaction (Wife and Husband) Predictor Variable Other-Positivity (Wife and Husband) How positive the Wife views her Husband, and how positive the Husband views his Wife

Distinguishability 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.

Should You Even Perform a Test of Distinguishability?
Yes Could simplify the model and parsimony is valued. Could dramatically increase power. No The literature may expect separate analyses for the two types of members. Can present separate results but say they do not differ.

Specifically how does it matter?
Actor and partner effects differ. Means, intercepts, and variances differ. If multiple variables, correlations differ.

Constraints Pairs of six parameters set equal to each other
Two actor effects Two partner effects Two error variances Two Y intercepts Two X variances Two X means

Types of Distinguishability
Complete Indistinguishability All parameters equal (6) Y Indistinguishability Mean and variance of X not set equal (4) What is done in Multilevel Modeling Effect Indistinguishability Only actor and partner effects set equal (2)

Using SEM Tests Complete indistinguishability: c2(6) = 9.192, p = .163
Y Indistinguishability: c2(4) = 7.228, p = .124 Effect Indistinguishability: c2(2) = 0.328, p = .849 All 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.

Using 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.

Using MLM SPSS: For the deviance use -2 Log Likelihood from “Information Criteria.” Indistinguishable Deviance: Number of parameters: 5 Distinguishable Deviance: Number of parameters: 9

MLM Result  c2(9 – 5) = = , p = .122 The 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.

Additional Readings MLM: davidakenny.net/doc/indistinguishability_mlm.pdf SEM: page 108 in Kenny, D. A., Kashy, D. A., & Cook, W. L. Dyadic data analysis. New York: Guilford Press.