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**1 - 2**of**2**### Moderated Mediation Analysis Using Bayesian Methods

, 2015

"... Conventionally, moderated mediation analysis is conducted through adding relevant interaction terms into a mediation model of interest. In this study, we illustrate how to conduct moderated mediation analysis by directly modeling the relation between the indirect effect components including a and b ..."

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Conventionally, moderated mediation analysis is conducted through adding relevant interaction terms into a mediation model of interest. In this study, we illustrate how to conduct moderated mediation analysis by directly modeling the relation between the indirect effect components including a and b and the moderators, to permit easier specification and interpretation of moderated mediation. With this idea, we introduce a general moderated mediation model that can be used to model many different moderated mediation scenarios including the scenarios described in Preacher, Rucker, and Hayes (2007). Then we discuss how to estimate and test the conditional indirect effects and to test whether a mediation effect is moderated using Bayesian approaches. How to implement the estimation in both BUGS and Mplus is also discussed. Performance of Bayesian methods is evaluated and compared to that of frequentist methods including maximum likelihood (ML) with 1st-order and 2nd-order delta method standard errors and mL with bootstrap (percentile or bias-corrected confidence intervals) via a simulation study. The results show that Bayesian methods with diffuse (vague) priors implemented in both BUGS and Mplus yielded unbiased estimates, higher power than the ML methods with delta method standard errors, and the ML method with bootstrap percentile confidence intervals, and comparable power to the ML method with bootstrap bias-corrected confidence intervals. We also illustrate the application of these methods with the real data example used in Keywords: Bayesian methods, moderated mediation, model specification As described in Baron and Kenny (1986), mediation and moderation are two statistically distinct concepts. Baron and Kenny defined a mediator as a variable that can account for the relation between an input variable and an outcome variable, whereas they defined a moderator as a variable that affects the direction or strength of the relation between an input variable and an outcome variable (also see where i represents intercept and e represents error. The indirect effect of X on Y via M, the mediation effect, can be quantified as the product of the two regression coefficients a and b in Equation 1. To obtain an interval estimate of the indirect effect ab or test whether there is a statistically significant indirect effect (using the null hypothesis H 0 :ab = 0), multiple inferential methods have been proposed, used, and compared. For example, MacKinnon, Lockwood, Hoffman, West, and Sheets (2002) compared multiple single-sample methods for testing the product ab. They found that the traditional Sobel test

### Moderated Mediation Analysis

, 2014

"... Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suit ..."

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Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at