Hello Veronica,

You have several questions you're trying to address with this model. A separate analysis may need to be run for each one, then you would go with the analysis which called for the largest requisite N, if you're doing this as a priori planning for your study.

1. For moderation, the typical question is, is an interaction between the IV and the moderator significantly different from zero? Consider the simplest model: One IV, one moderator, and the DV. In this scenario, a base regression model would have two predictors: (a) the IV; and (b) the moderator. The "full" regression model would have three (or more) predictors: (a) the IV; (b) the moderator; and (c) the interaction term/s (if the IV and/or the moderator are categorical with more than two levels, then you would need multiple interaction terms to capture all the information). The statistical question could be posed as, is the difference in model R-squared between the base model and full model different from zero? In g*power, that would be addressed by using F test family, Linear multiple regression: Fixed model, R-squared increase option.

2. For mediation, the typical question is, what is the relative size of the indirect effect relative to the direct effect of an IV, or is the indirect effect different from zero? The simplest model: One IV, one mediator, and the DV. The indirect effect being non-zero requires that the IV -> mediator path is nonzero (e.g., as if you ran a regression of mediator scores on the IV) AND the mediator -> DV path as non-zero in a regression of DV on mediator and IV. You'll need to decide which approach works for your situation: (a) testing indirect effect = 0; or (b) testing relative size of indirect effect to direct effect (e.g., IV -> DV).

3. Finally, you could test a base model, in which DV is regressed on IV, moderator, and the three mediators, all as direct effects only, vs. a full model in which the interaction and indirect effects are included. Some level of change in R-squared for the DV could serve as the target effect of interest. However, doing this doesn't guarantee that the moderation and mediator 1 and mediator 2 and mediator 3 are all influential. It could be that just one element or some subset of elements has an impact.

In each case, the challenge is identifying a defensible target effect size (ES) which you'd like your study to be capable of detecting, should it actually exist in the population of interest.

Good luck with your work.

Veronica Sobczak I don't know about "simple" (because the moderated mediation model itself is not so simple), but the most comprehensive and efficient way to determine sample size requirements for such an analysis may be via a Monte Carlo simulation of the entire path model. This would not only allow you to determine the sample size requirement / power for all relevant effects (direct, indirect, moderated/interaction), but also to examine the degree of parameter and standard error bias as well as the behavior of model fit statistics such as the chi-square test of model fit under different sample size conditions. Simulations of path models are fairly straightforward to set up in Mplus and other programs for structural equation modeling. For a good tutorial, see, for example

Article How to Use a Monte Carlo Study to Decide on Sample Size and ...

I offer a free mini-workshop on sample size planning /power analysis via simulation in Mplus that you can find here:

https://www.goquantfish.com/courses/sample-size-planning-in-mplus