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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?

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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.

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  • $\begingroup$ Thank you for your thoughts on this. Very helpful and hadn't considered that perspective. $\endgroup$
    – ReadBeard
    Jun 29, 2022 at 15:26

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