A Structural Equation Modeling Approach for the Analysis of Mediated Moderation and Moderated Mediation

Moderation and mediation analyses are widespread in psychological research. Moderation occurs when the direction and/or strength of the relation between an independent variable and a dependent variable depends on the level of a moderating variable. Mediation, on the other hand, occurs when the effect of an independent variable on a dependent variable is transmitted through a mediating variable (Baron & Kenny, 1986). Psychologists often move beyond these two processes and ask more complex questions such as how a moderating effect takes place or when a mediating process varies in different contexts. The former question has been referred as mediated moderation while the latter one has been referred as moderated mediation. Despite the fact that there are many discussions about the analysis of mediated moderation and moderated mediation in the literature, the confusion over the interpretation of these two processes persists. In addition, the SEM method, which is known to be more flexible than traditional regression method for the analysis of mediated moderation and moderated mediation is rarely discussed in the literature. In response to these issues, the main objective of the present study was to examine the methods for the analysis of mediated moderation and moderated mediation in the SEM framework. The first part of this study resolved the confusion over the current interpretation of the mediated moderation and moderated mediation by demonstrating these two processes using five typical conceptual models of mediated moderation and moderated mediation. In the second part, a new unified method was proposed to provide some general rules for translating the conceptual models of mediated moderation and moderated mediation into the SEM working models. The empirical performance of SEM analysis against regression analysis was assessed by a simulation study. Results showed the two methods performed similarly across different model conditions. In the last part, the unconstrained indicant product approach (Marsh, et al., 2004) for latent moderation analysis was introduced and combined with the unified approach for the analysis of latent variable mediated moderation and moderated mediation models. Simulation findings suggested that this method performed satisfactorily for testing mediated moderating and moderated mediating effects in most simulation conditions. However, chi-square statistics for the evaluation of model fit should be used with cautious as simulation results indicated that they were not accurate in most cases.