In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies the relationship between an independent variable and a dependent variable, through the inclusion of a third hypothetical variable known as a mediator variable (also referred to as an intermediate variable or intervening variable). In this framework, the relationship is not conceived as a direct causal link between the independent and the dependent variable, but rather as one in which the independent variable influences the mediator variable, which in turn affects the dependent variable. In this way, the mediator variable helps to clarify the nature of the causal relationship between them. Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable. In particular, mediation analysis can contribute to better understanding the relationship between an independent variable and a dependent variable when these variables do not have an obvious direct connection.
Baron and Kenny's (1986) steps for mediation analysis In 1986, two social psychologists at the University of Connecticut, Reuben M. Baron and David A. Kenny, laid out several requirements that must be met to form a true mediation relationship. They are outlined below using a real-world example. See the diagram above for a visual representation of the overall mediating relationship to be explained. The original steps are as follows.
Step 1 Relationship Duration
Regress the dependent variable on the independent variable to confirm that the independent variable is a statistically significant predictor of the dependent variable. Independent variable → {\displaystyle \to } dependent variable
Y = β 10 + β 11 X + ε 1 {\displaystyle Y=\beta _{10}+\beta _{11}X+\varepsilon _{1}}
β11 is significant
Step 2 Regress the mediator on the independent variable to confirm that the independent variable is a significant predictor of the mediator. If the mediator is not associated with the independent variable, then it couldn’t possibly mediate anything. Independent variable → {\displaystyle \to } mediator
M e = β 20 + β 21 X + ε 2 {\displaystyle Me=\beta _{20}+\beta _{21}X+\varepsilon _{2}}
β21 is significant
Step 3 Regress the dependent variable on both the mediator and independent variable to confirm that a) the mediator is a significant predictor of the dependent variable, and b) the strength of the coefficient of the previously significant independent variable in Step #1 is now greatly reduced, if not rendered nonsignificant. Independent variable + mediator → {\displaystyle \to } dependent variable
Y = β 30 + β 31 X + β 32 M e + ε 3 {\displaystyle Y=\beta _{30}+\beta _{31}X+\beta _{32}Me+\varepsilon _{3}}
β32 is significant β31 should be smaller in absolute value than the original effect for the independent variable (β11 above)
Example The following example, drawn from Howell (2009), explains each step of Baron and Kenny's requirements to understand further how a mediation effect is characterized. Step 1 and step 2 use simple regression analysis, whereas step 3 uses multiple regression analysis.
How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable). How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator). Your feelings of competence and self-esteem (i.e., mediator) predict how confident you feel about parenting your own children (i.e., dependent variable), while controlling for how you were parented (i.e., independent variable). Such findings would lead to the conclusion implying that your feelings of competence and self-esteem mediate the relationship between how you were parented and how confident you feel about parenting your own children. If step 1 does not yield a significant result, one may still have grounds to move to step 2. Sometimes there is actually a significant relationship between independent and dependent variables but because of small sample sizes, or other extraneous factors, there could not be enough power to predict the effect that actually exists.
Direct versus indirect effects
In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ". The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held constant and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit.
In linear systems, the total effect is equal to the sum of the direct and indirect (C' + AB in the model above). In nonlinear models, the total effect is not generally equal to the sum of the direct and indirect effects, but to a modified combination of the two.
Full mediation versus partial mediation A mediator variable can either account for all or some of the observed relationship between two variables.
Full mediation
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