ISSN 2043-8087
Journal of Experimental Psychopathology
 Volume 2, Issue 2, 210-251, 2011
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An SEM Perspective on Evaluating Mediation: What Every Clinical Researcher Needs to Know

Erik Woody
University of Waterloo

Volume 2, Issue 2, 2011, Pages 210-251

After a brief consideration of the definition and importance of mediation, statistical tests for mediation are reviewed, including the joint significance of the two effects involved in the mediation, the Sobel test and its variants, resampling with the bootstrap, Bayesian estimation using MCMC simulation, and the effect ratio. A structural-equation-modeling (SEM) perspective on mediation then introduces the alternative scenarios that could yield a false-positive mediation finding. Design-based, partial solutions are advanced for problems of measurement, uncontrolled common causes, and temporal ordering that can confound mediation analysis. Next, the issue of heterogeneity of effects and statistical interactions in mediation analyses are addressed, including a discussion of moderated mediation and mediated moderation. Finally, the relation of mediation analysis to experimentation is discussed, with attention to the possibility of creatively integrating SEM-based mediation analysis and experimental design.

Table of Contents
  Some Definitions
  Statistical Tests of Mediation
    Joint significance of the two paths involving the mediator.
    Sobel test and its variants.
    Resampling with the bootstrap.
    Bayesian estimation using MCMC simulation techniques.
    "Partial" versus "full" mediation and the effect ratio.
    Recommendations and power.
  How Hard is It to Pass a Statistical Test of Mediation?
  The Need for Explicit Models
An SEM-Based Perspective on Mediation
  Alternative Models Having to do with Measurement Issues
  Alternative Models Having to do with Uncontrolled (Omitted) Common Causes
  Alternative Models Having to do with Temporal Ordering
  Implications of Alternative Models
    Multiple indicators.
    Correlated errors.
    Measuring and controlling for third variables.
    Measuring and controlling for earlier levels of the same variables as in the model.
Heterogeneity and Interactions in the Evaluation of Mediation
  Heterogeneity of Partial Slopes
  Moderated Mediation and Mediated Moderation
The Relation between Mediation Analysis and Experimental Design
  Integrating Mediation Analysis and Experimental Design
Concluding Recommendations
Appendix A: Demonstration of SEM-Based Methods for Evaluating Mediation
  Joint significance of the two effects involved in the mediation.
  Sobel test and its variants.
  Bias-corrected bootstrap.
  Bayesian estimation using the MCMC technique.
  The effect ratio.
Appendix B: Demonstration of Two-Mediator, Two-Sample SEM and Contrasts Using Bayesian Custom-Estimands in Amos

Correspondence to
Erik Woody, Department of Psychology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Mediation; mediational analysis; bootstrap; Bayesian estimation; effect ratio; structural equation modeling; moderated mediation; mediated moderation; experimental design

Received 5 Aug 2010; Revised 26 Oct 2010; Accepted 26 Oct 2010; In Press 5 May 2011

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