Bayesian Mediation Analysis

Milica Miočević, PhD
Utrecht University

Abstract: Mediation analysis is used to study intermediate variables (M) that transmit the effect an independent variable (X) has on a dependent variable (Y). For example, a researcher might be interested in whether an intervention designed to reduce unhealthy lifestyle behaviors (X) affects fruit and vegetable consumption (M), which in turn affects general health (Y). In this study, the quantity of interest is the indirect effect of the intervention on general health through fruit and vegetable consumption. Two prominent approaches to data analysis are the classical (also called “frequentist”) and the Bayesian approach. In recent years researchers in social sciences have turned to Bayesian methods when they encounter convergence issues (Chen, Choi, Weiss, & Stapleton, 2014), issues due to small samples (Lee & Song, 2004), and when they wish to report the probability that a parameter lies within a certain interval (Rindskopf, 2012).In the frequentist framework, evidence for the presence of mediation is obtained by testing the statistical significance of the product of coefficients comprising the indirect effect. The distribution of the mediated effect is often asymmetric (Craig, 1936; Lomnicki, 1967; Springer & Thompson, 1966), and the best classical methods for evaluating the significance of the mediated effect either take the asymmetric distribution of the product into account or make no distributional assumptions at all (Cheung 2007, 2009; MacKinnon, Fritz, Williams, & Lockwood 2007; MacKinnon, Lockwood, & Williams, 2004; MacKinnon, Lockwood, Hoffmann, West, & Sheets, 2002; MacKinnon, et al., 1995; Shrout & Bolger, 2002; Tofighi & MacKinnon, 2011; Valente, Gonzalez, Miočević, & MacKinnon, 2016; Yuan & MacKinnon, 2009).Bayesian methods offer an easy way to take into account the asymmetric distribution of the mediated effect, and to compute functions of the mediated effect, e.g. effect size measures and causal estimates of indirect and direct effects. Furthermore, Bayesian methods provide an intuitive framework for the inclusion of relevant prior information into the statistical analysis. In this talk I will discuss the pros and cons of Bayesian methods for mediation analysis, and I will illustrate some advantages and challenges of Bayesian mediation analysis using an example data set from a study of alcohol consumption of college students in the United States. I will conclude with recommendations that can be made for applied researchers based on the methodological literature on Bayesian mediation analysis thus far, and with some future directions for this line of research.