Mediation Analysis

Mediation analysis is used in social sciences, biology, epidemiology, and other fields in order to evaluate the mechanism through which an independent variable (X) affects a dependent variable (Y). The variable transmitting the influence of the independent variable onto the dependent variable is called the mediator (M), and the indirect effect through the mediator is called the mediated effect. In prevention research, mediation analysis is used to improve future interventions by discovering the mediator(s) through which the intervention (X) affects the outcome of interest (Y); for example, an [Page 1046]intervention designed to reduce smoking (X) affects self-efficacy (M), which in turn affects the number of cigarettes smoked (Y). The mediated effect in this example represents the indirect effect of the intervention on the number of cigarettes smoked through participants’ self-efficacy. In fields such as social psychology, mediation analysis is used to uncover the intermediate variable that transmits the effect of an independent variable onto a dependent variable; for example, exposure to a certain message (X) affects attitudes (M), which then affect behavior (Y). The mediated effect is the indirect effect of the message on the behavior through the attitude.

It is also possible to have a model with two parallel mediators or several sequential mediators. The effect of age (X) on typing proficiency (Y) is mediated through skill (M1) and manual dexterity (M2) in a parallel two mediator model. In this case, there could be several effects of interest: the mediated effect through skill alone, the mediated effect through manual dexterity alone, and the total mediated effect through skill and manual dexterity. Some theories posit a sequence of mediators between an independent variable and a dependent variable, and in order to evaluate these effects, one would fit a sequential mediator model. For example, being assigned to receive a treatment versus placebo (X) affects sleep quality (M1), which then affects alertness (M2), which affects the number of automobile accidents (Y). In this model, the mediated effect has three paths, from X to M1, from M1 to M2, and from M2 to Y. There are several ways of computing point and interval estimates of the mediated effect. The following sections describe the simplest mediation model, mention several more complex mediation models, and discuss recent methodological advances in the field of mediation analysis.

Single Mediator Model

The single mediator model is the simplest example of mediation analysis. In this model, the independent variable (X) affects the mediator (M), which in turn affects the outcome (Y; see Figure 1).

Figure 1 Single mediator model

The single mediator model is described using three equations:

$$\begin{array}{c}Y=\tau X+{\epsilon }_1,\end{array}$$

$$\begin{array}{c}M=\alpha X+{\epsilon }_2,\text{and}\\ Y={\tau }^{\prime }X+\beta M+{\epsilon }_3,\end{array}$$

where X is the independent variable, M is the mediator, Y is the dependent variable, τ is the coefficient for predicting Y from X, α is the coefficient for predicting M from X, and τ′ and β are the coefficients for predicting Y from X and M, respectively. The residual terms ε1, ε2, and ε3 are assumed to follow normal distributions with means of zero and variances of ${\sigma }_1^2$, ${\sigma }_2^2$, and ${\sigma }_3^2$, respectively. The last two equations are sufficient for estimating the mediated effect, αβ.

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