Statistical Evaluation of Person-Oriented Mediation Using Configural Frequency Analysis

Abstract

Mediation analysis helps explain how and why two variables are related, providing information for investigating causal processes useful for theoretical and applied research (MacKinnon 2008). Inference from mediation analysis typically applies to the population, but researchers and clinicians are often interested in making inference to individual clients or small sub-populations of people. Person-oriented approaches focus on the differences between people, or latent groups of people, to ask how individuals differ across variables. A recently proposed method allows for the analysis of person differences as part of mediation. The method from configural frequency analysis, which we call configural frequency mediation, is based on log-linear modeling of contingency tables. The complexity of configural frequency mediation and its use of a causal steps mediation method, may contribute to the lack of application and study of this promising method since its introduction in the literature a decade ago (von Eye et al. 2009, 2010) In this paper we clarify the steps used for configural frequency mediation and report the results of a large statistical simulation study evaluating the method and comparing it to the variable-oriented traditional method using logistic regression analysis. Overall, configural frequency mediation analysis tended to have excessive type I error rates but we describe an alternative approach to configural mediation analysis based on a joint significance test that had adequate performance. We also clarify the decision rules that define configural mediation analysis and develop a test for configural frequency mediation using a joint significance mediation method.

LOG-LINEAR MODELS USED FOR CFM AND JOINT SIGNIFICANCE TESTS

Appendix equations (17)-(20) are associated with Text equations (6)-(9) while Appendix equations (21)-(26) are associated with Text equations (11)-(16).

$$ \mathrm{Model}\ 1\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y $$

(17)

$$ \mathrm{Model}\ 2\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XM} $$

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$$ \mathrm{Model}\ 3\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XM}+{\lambda}^{XY} $$

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$$ \mathrm{Model}\ 4\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XM}+{\lambda}^{MY} $$

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$$ \mathrm{Model}\ 5\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XY}+{\lambda}^{XM}+{\lambda}^{MY} $$

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$$ \mathrm{Model}\ 6\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XY}+{\lambda}^{MY} $$

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$$ \mathrm{Model}\ 7\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XM}+{\lambda}^{XY}+{\lambda}^{XM Y} $$

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$$ \mathrm{Model}\ 8\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{MY}+{\lambda}^{XY}+{\lambda}^{XMY} $$

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$$ \mathrm{Model}\ 9\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XY} $$

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$$ \mathrm{Saturated}\ \mathrm{Model}\kern0.5em \log \hat{o}=\lambda +{\lambda}^X+{\lambda}^M+{\lambda}^Y+{\lambda}^{XM}+{\lambda}^{XY}+{\lambda}^{MY}+{\lambda}^{XM Y} $$

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