Hello Nina.  Jos Twisk's nice (introductory) book on multilevel models includes a chapter on sample size estimation.  HTH.

UPDATE:  I just noticed that PASS uses simulation to perform sample size estimation for "mixed effects models".  See the second link below.

http://www.cambridge.org/ca/academic/subjects/medicine/epidemiology-public-health-and-medical-statistics/applied-multilevel-analysis-practical-guide-medical-researchers?format=PB&isbn=9780521614986

https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/PASS/Mixed_Models-Simulation.pdf

https://www.ncss.com/software/pass/pass-documentation/#Simulation

I vote for the suggestion to use simulation. R does this nicely, but many other programs will too.

Thank you very much, everyone!

Jake Westfall has a calculator for mixed effect (and a couple of good papers together with Judd). Go on this site: http://jakewestfall.org/ (Web apps).

You also find simulations on a paper I submitted as a project. Personally, I've come to conclusion that I won't do much research anymore with less than 1,600 observations per cell (40 participants 40 stimuli, or 20 participants 80 stimuli, or 80 participants 20 stimuli). Such a design allows you to find anything that is interesting, even though it may be slightly overpower for large effects).

Marc Brysbaert Do you have publish this paper yet? I would like to apply your rule of 1600 observations per cell. I am also wondering hoy the type of factor (within versus between) may influence this number. For instance in my case I have an interaction between a within (2 types of stimuli) and a between (2 groups of subject). Thanks in advance Boris

I found this one: Article Power Analysis and Effect Size in Mixed Effects Models: A Tutorial

Yes, that's the reference. It works for a pairwise comparison. Unfortunately, you will need more observations (participants) for the interaction you are after, as you can read here:

https://psyarxiv.com/2v4yx/

Will be published shortly in the Journal of Cognition

Thank you very much, Boris

Marc Brysbaert. With some colleagues we are running a study examining the evolution of performance (correct vs. incorrect response) across task duration using logistic mixed-effect models. We have 2 conditions. One with low difficulty (Less inhibiting trials) and the second with high (more inhibiting trials). Our main test will be to assess the moderating effect of the condition on the evolution of the performance across the task: i.e., a trials number (continuous) x conditions (easy vs. difficult)  on the performance (0 vs 1). We are struggling to estimate the correct sample size as the main test is no comparing the absolute performance difference between group but the evolution, that is we want to have the accurate level of power to test for this evolution of time, and we are not sure to know the minimum number of observation by group and time needed,

Another point: we will not have the same number of observations between group (150 observations in the low difficulty group vers 450 in the other; this is because our dependent variable is directly related to the manipulation). We are wondering how manage such unbalanced data observation (1/3 differences).

If you have some time, your help will be very much appreciated. Boris

Probably the best is to run a simulation of what you intend to do (and hope to find). You can adapt one of the programs I used for the latest power analysis paper.

Thank you very much. I will do it.

Simulation is definitely the way to go in my view. More generally, though, I find that power analysis often has to rely on so many unverified a priori assumptions that it probably won't be of much more use than general experience-based rules of thumb (cf. Marc’s response).

Are there any papers in support of this view, i.e.，general expeirence-based rules of thumb？