Sample size calculation for moderated moderation (three way interaction: continuous x continuous x continuous) If I am planning to analyses some data using a moderated moderation (Hayes - model 3). What is the most appropriate technique to calculate required sample size?
Currently, I have written a simulation in R, but I wonder if there is an alternative approach? The main difficulty with the simulation is that accurate specification of all parameter estimates is difficult as we don't have a good idea of the magnitude of the parameters. I suppose that this is part of the assumptions of that sample size approach.
If the three way interaction is the effect of interest, is sample size based on Cohen’s f^2 appropriate?


The main difficulty with the simulation is that accurate specification of all parameter estimates is difficult as we don't have a good idea of the magnitude of the parameters.

I see that as a strength of simulation.
In a situation like this you don't want to have your study design depend on a single estimate. Simulation allows you to evaluate a range of assumptions about predictor-variable distributions and regression coefficients, including both individual coefficients and interaction terms.
You can do a lot of simulations, based on different sets of assumptions, in a short period of time. Discuss the simulation results and the underlying assumptions with your colleagues. Then find a sample size and experimental design that gives adequate power to cover a wide range of potential parameter values that are consistent with your current understanding of the subject matter and with the magnitude of the effect that you want to detect.
