Test of DistinguishabilityDavid A. Kenny

March 24, 2013

You Need to Know

• Estimation method

–SEM

–MLM

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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

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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.

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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.5

Specifically how does it matter?

• Actor and partner effects differ.

• Means, intercepts, and variances differ.

• If multiple variables, correlations differ.

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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

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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)

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Using SEM

Tests

Complete indistinguishability: 2(6) = 9.192, p = .163

Y Indistinguishability: 2(4) = 7.228, p = .124

Effect Indistinguishability: 2(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.

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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.

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Using MLM

• SPSS: For the deviance use -2 Log Likelihood from “Information Criteria.”

• Indistinguishable– Deviance: 282.884– Number of parameters: 5

• Distinguishable– Deviance: 275.607– Number of parameters: 9

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MLM Result

 2(9 – 5) = 282.884 - 275.607

= 7.277, 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.

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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.

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