SEM Approach to the Mediation Analysis of the Two-Condition Within-Subject Design

The effects of the two-condition within-subject (TCWS) conditional mediation model are developed using the SEM approach. The structural equation model for the within-subject mediator and the within-subject outcome with the specification of a between-subject moderator is developed to derive the indirect effects. Formulas are derived for the indirect effects of two conditions in the TCWS conditional mediation model. These effects are calculated on the rotated outcomes, which are the difference and sum of the outcomes, through two mediators. The derivation is done under both natural and rotated condition approaches. The rotated outcome is expressed as a linear function of the two natural mediators in the natural condition approach, whereas in the rotated condition approach, it is expressed as a function of the two rotated mediators. The total indirect effect on each rotated outcome in both natural and rotated condition approaches consists of two individual indirect effects: one through the within-condition mediator and the other through the crossed-condition mediator. Comparison of two individual indirect effects can reveal the nature of causal relations between conditions and outcomes. The TCWS conditional mediation model is generalized by considering multiple within-subject mediators and multiple between-subject moderators as well as the multiple conditions case. The bootstrapping confidence intervals are used to estimate and test the conditional indirect effects. The total and individual conditional indirect effects are probed by overlaying their bootstrap confidence intervals for given moderator values, and this multi-plot helps the understanding of magnitudes and mechanisms of the moderator on the indirect effects.