Organizational researchers frequently propose and test hypotheses that involve relationships between variables. Beyond simple bivariate associations, more complex models may involve third variables that provide greater explanatory power. Two common types of explanatory mechanisms are mediator and moderator variables. Importantly, mediator and moderator variables have fundamentally different effects in causal models and must be kept conceptually and statistically distinct. A mediator variable is part of a longer causal chain. In the simplest case, an antecedent variable causes the mediator variable, which, in turn, causes an outcome variable. Alternatively, a moderator variable does not imply a particular causal sequence. A variable is said to act as a moderator to the extent that the relationship between two other variables changes depending on the level of the moderator. Because of the different nature of these variables, mediator and moderator variables are discussed separately, as well as the statistical tests typically associated with evaluating their presence.

In this discussion, x represents the predictor variable, y represents the criterion variable, and m represents either the mediator or moderator.

## Mediator Variables

Graphically, mediation may be represented by the simple model x — m — y. In this model, m mediates the relationship between x and y. As this model illustrates, a mediator variable transmits variance between two other variables. Thus, a mediator serves as an explanatory mechanism in the model. That is, the mediator provides an explanation of how and, to some extent, why two variables are related. For example, consider a model in which a researcher believes that student learning is negatively related to class size (i.e., students in smaller classes learn more than students in larger classes). To explain this effect, the researcher includes a mediator variable (e.g., the amount of student-teacher interaction) in the model. That is, in smaller classes, teachers are expected to spend more time with each student, and that, in turn, is related to student learning. The amount of student-teacher inter-action provides a mechanism through which the bivariate relationship between class size and learning can be explained.

The extent to which a variable serves as a mediator can be easily tested using a three-step process of ordinary least squares regression. In the first analysis, y is regressed on x. This step is necessary insofar as there must be a relationship for m to mediate. If x and y are unrelated, m cannot mediate a relationship that does not exist. In a second analysis, m is regressed on x. If x and m are unrelated, m cannot serve as a mediating mechanism. Finally, y is regressed on both x and m together, and the regression coefficient associated with x is compared with the regression weight computed in the first step. The extent to which m mediates the x-y relationship is defined in terms of the difference between these coefficients. If the regression weight associated with x is reduced to zero, m is said to fully mediate the relationship between x and y. In short, the effect of x on y is fully explained when m is included in the model. Evidence for partial mediation is provided to the extent that the regression weight associated with x drops but is not reduced to zero. In this case, m explains some of the variance in the x-y relationship, but there is still a direct effect of x on y. The Sobel test is often used to test for the presence of this indirect (i.e., mediated) effect.

Recently, scholars have debated the extent to which these steps are required to argue for mediation; some have argued that the relationship between xand yneed not be significant in order for m to serve as a mediator variable. In this alternative process of testing for mediation, the first step is unnecessary when the x-y relationship is relatively small in magnitude or when suppression is a possibility.

## Moderator Variables

A variable is said to moderate a relationship to the extent that the relationship between x and y changes depending on the level of m. In short, moderation is fundamentally an interactive effect. Again, ordinary least squares regression may be used to test for moderation. Two steps are required to test for moderation. First, the main effects of x and m are entered in the first step of an analysis in which y is the criterion variable. In the second step, the product of x and m is entered and the change in Rs quared from the first to the second model is evaluated for statistical significance. If this value is significant, evidence is provided for moderation.

When the interaction term is significant, the nature of moderation (i.e., ordinal versus disordinal interaction) can easily be illustrated in a two-dimensional graphical representation. For example, imagine a test of general reading ability (x) and college performance measured by teacher ratings (y). Assume that a researcher who is interested in evaluating whether the relationship between these variables is the same across gender (m) subgroups applies the statistical technique described in the previous paragraph and observes the following regression equation:

Y = .58 (x) + 31.03(m) + (-.24)(x)(m) + (-9.92)

This equation can be used to plot the regression lines for these two groups using values from both x and m.

Though conceptually distinct, mediation and moderation analyses share several common issues. For example, both analyses can be strongly influenced by multicollinearity. In the case of mediation, a strong correlation between x and m can influence the precision of estimates of regression coefficients in the final equation. In tests of moderation, given that the interaction term is directly computed as the product of x and m, this term can be strongly related to either or both of the individual predictors. To address this issue, x and m are often centered by subtracting each observed score from the corresponding mean prior to forming the interaction term.

Finally, mediation and moderation can be present within the same causal model. Mediated moderation is said to exist when the interactive effect of two variables on an outcome of interest passes through an intervening variable. Alternatively, moderated mediation is said to exist when a mediation model is stronger for one group than another.

### References:

- Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.
- Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.
- Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7, 422-445.