Abstract:

Mediation and moderation models are frequently used in the research of psychology and many other social science disciplines. Mediation indicates that the effect of an independent variable on a dependent variable is transmitted through a third variable, namely a mediator. For example, students’ gratitude promoted their academic achievement medially by increasing everyday academic resilience. Moderation occurs when the effect of an independent variable on a dependent variable varies according to the level of a third variable, which interacts with the independent variable. For instance, adolescents’ perceptions of their teachers’ authoritative teaching moderated the effect of antisocial disruption on peer acceptance. It is not uncommon for hypotheses about moderation and mediation relationships to occur in the same context where more than three variables are involved. When a mediation effect is moderated by a moderator, the effect is termed moderated mediation and the model is moderated mediation model. For example, everyday academic resilience acts as a mediator between gratitude and academic achievement, and this mediation process is moderated by stressful life events. There are several methods for testing moderated mediation models. The moderated mediation models being used for proposed testing methods are different. We are wondering whether different testing methods are competitors, or some of them are only backups. We discussed the different testing methods based on the most general type of model. The traditional testing method is the moderated causal steps approach, in which the regression coefficients are tested in sequence. Modern methods include the testing of the products of coefficients by using Bootstrap method or MCMC method, and testing of the difference between the maximum and minimum of the mediation effects. On the basis of the previous studies it can be summarized that the power of test with the moderated causal steps approach is the lowest among the three testing methods, whereas the testing of the difference between the maximum and minimum of the mediation effects has the highest power of test. After comparing significant results of the three testing methods by reviewing the simplification, implication, information, and explanation, we concluded that the moderated causal steps approach should be recommended first; testing of the products of coefficients by using Bootstrap method or MCMC method should be treated as a backup; testing of the difference between the maximum and minimum of the mediation effects should be the final choice. We proposed a hierarchical procedure for testing moderated mediation models as follows: Step 1. Adopt the moderated causal steps approach to test the model. If the significant result is obtained from the test, the mediating effect is moderated. Otherwise, go to Step 2. Step 2. Test the products of coefficients by using Bootstrap method or MCMC method. If any product is significantly different from zero, the mediating effect is moderated. Otherwise, go to Step 3. Step 3. Test the difference between the maximum and minimum of the mediation effects. If the difference is significant, the mediating effect is moderated. Otherwise, the mediating effect is not moderated. As an illustration, the procedure was applied to an empirical study in which everyday academic resilience played the role of a mediator between gratitude and academic achievement, and this mediation process moderated by stressful life events. The relationship and difference between moderated mediation models and mediated moderation models were also discussed.

Key words: mediation, moderation, moderated mediation, mediated moderation