I do use G*power for mixed models, but haven't done so when there is more than one within-subjects factor. Can it do an a priori power analysis when I have one between subjects factor (either 2 or 4 levels - we haven't quite decided yet) and two within subjects factors (both with 3 levels). I'd be very grateful for any suggestions, pointers, hints etc.
Do I understand it correctly: your within-subject effects are two dependent variables (in which case you are talking about MANOVA rather than ANOVA)? I am pretty sure that G*Power can deal with MANOVA.
I would guess you could specify the linear regression model option in the Statistical Test window and get an analysis that way, by specifying the number of predictors (g - 1 for each factor). But G*power will only give you a power analysis for a single parameter. If you have multiple hypotheses within that model, you may need to obtain multiple power analyses.
Another direction I have seen others write about is to use simulation for a sample size estimate in a complex model, with multiple parameters of interest. This reference is pretty heavily weighted toward SEM, and MPlus as the software in particular:
https://www.statmodel.com/download/FinalSEMsingle.pdf
But it may be general enough to get an idea.
Gelman & Hill (2007) Chapter 20 is a more general approach.
Gelman A. & Hill, J. (2007). Data Analysis using Regression and Multilevel/Hierarchical Models. Cambridge.
I am not sure if this too late or not, but it may be useful for the future: simr is an R-package specifically tailored to handle power analysis of lmer and glemr objects
Use longpower package in R
or use this online way
http://samplesizeshop.org
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