So I’ve had some other issues to iron about, but I’m now back at this.
I think I was looking at this the wrong way.
Some more detail about the data:
I have 400 participants, for each I have 4 psychological measures (questionnaire scores) and 1 behavioural measure and some more covariates of no interest (age, gender). The 4 psychological measures are correlated.
I have fitted in brms (a very simple nonhierarchical model):
brm(formulat=behaviour ~ psych1 +psych2+psych3+ psych 4 + age+gender,
data=myData,family='gaussian')
I find say that for psych 1 the 95% interval does not include zero. And my aim is to find out what my sample size should be for a replication sample to replicate this effect with 95% power.
Now this thread (https://github.com/paulbuerkner/brms/issues/191) @tomwallis seems relevant, but I can’t quite work out what to do…
I’m wondering whether the steps should be:
1A) Fit a multivariate normal distribution to generate new participants (like here: https://baezortega.github.io/2018/05/28/robustcorrelation/) [this would allow to generate combinations of psych1, psych 2, psych3, psych4 behaviour,age and gender that respect the correlations in the real data.
1B) Fit a multivariate normal distribution to generate new participants only for the psychological measures and covariates (age and gender) and then generate the behavioural measure from the regression above, using BRMs predict? I’m not sure whether this would be any better or worse? Just seems that in 1A I did not actually use the brms output…
1C) Is there a way to not have to fit a multivariate model to generate new data, but instead only use the brms model?

Analyse the new participants with the same model as above and check the credible interval for psych 1.

Repeat steps 1 and 2 for different sample sizes (say between 400 and 1000 participants) say 500 times each to see what percentage of credible intervals do not contain zero. Pick the sample size for which this is the case at least 95% of the time (to get 95% power)