Relations between variables are often more complex than simple bivariate relations between a predictor and a criterion. Rather these relations may be modified by, or informed by, the addition of a third variable in the research design. Examples of third variables include suppressors, confounders, covariates, mediators, and moderators (). Many of these third variable effects have been investigated in the research literature, and more recent research has examined the influences of more than one third variable effect in an analysis. The importance of investigating mediation and moderation effects together has been recognized for some time in prevention science, but statistical methods to conduct these analyses are only now being developed. Investigations of this kind are especially valuable in prevention research where data may present several mediation and moderation relations.

Previous research has described the differences between mediation and moderation and has provided methods to analyze them separately (e.g., ; ; ; ). More recent research has presented models to simultaneously estimate mediation and moderation to investigate how the effects work together (e.g., ; ; ; ). A review of the substantive literature illustrates that few applied research examples have used these models, however. Although analyzing mediation and moderation separately for the same data may be useful, as described later in this paper, simultaneous examination of the effects is often relevant and allows for the investigation of more varied, complex research hypotheses.