The analysis of mediated moderation using VS

The analysis of moderation and mediation effects has long been an important methodological question in psychological research. Generally speaking, moderation occurs when the relationship between the independent variable (X) and the dependent variable (Y) varies as a function of a third variable (moderator). Mediation, on the other hand, occurs when the effect of X on Y is transmitted through an intervening variable (mediator). In reality, however, the relationship among the variables is often more complicated and a simple moderation and mediation model might fail to describe the underlying psychological process adequately. Consequently, psychologists have started to consider a more general theoretical framework that combines both moderation and mediation into a single model, which is commonly regarded as moderated mediation (moME) or mediated moderation (meMO). In the literature, moME has been well studied and there are specific computer programs for handling it, such as PROCESS (Hayes, 2013). By contrast, meMO has received much less attention due to both statistical and conceptual reasons. Statistically, it is difficult to differentiate moME from meMO because these two processes basically share the same underlying mathematical model. Second, it is difficult to interpret the process meaningfully because meMO concerns the mechanism of a product term, which usually does not carry any substantive meaning. The purpose of the present study, therefore, is to propose an alternative formulation for meMO. This new meMO is intuitively meaningful and it is statistically unique so that one will not get it confused with the traditional moME. Computationally, a new structural equation modeling based statistical tool, VS, is introduced for analyzing this model. Real examples are given to demonstrate how VS can be used to examine meMO, moME, and other models that involve conditional process in general.