Calculating power for 4-way mixed factorial design

[hyunjeehale]

I am trying to find a way to calculate the power and sample size necessary for a 2x2x2x4 mixed factorial design as well as calculate the power necessary for a moderator analysis.

I have one between factor with two levels and three within factors (2 levels, 2 levels, 4 levels respectively).

http://meeting.spsp.org/2016/sites/default/files/Lane%2C%20Hennes%2C%20West%20SPSP%20Power%20Worksho...

The above resource has been the best one I have found, but I am feeling a big lost. The PASS program doesn't appear to have the ability to handle more than two within factors for a repeated measures mixed model and Gpower doesn't have a mixed model component that allows a user to indicate more than one within factor.

Is there a resource or guidance anyone can provide on the best way to calculate the necessary sample size?  Most of the resources I've in programs such as R are limited to the number of within factors you can have in the simulation.

[sld]

For a model of this complexity, basically your options are simulation or a clever use of PARMS / HOLD that Walt Stroup has written about:

PROC GLIMMIX as a Teaching and Planning Tool for Experiment Design

Ch 16 in

Generalized Linear Mixed Models: Modern Concepts, Methods and Applications

Even with this tool, you may still be a bit lost because of the challenge of specifying one (or many) alternative hypotheses in a four-way factorial treatment design. I would be, anyway.

Good luck!