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I am aware that there are some useful threads already on free software for calculating sample sizes (see here). However I couldn't find anything specific to cross-classified MLM and repeated measures.

I do psychophysiological research, that is, I look at over-time changes in physiological variables to infer psychological processes. The most common design in my experiments is something like this (I use lme4):

PhysioVar ~ Condition * Time + (1|Participant) + (1|Stimuli)

Reviewers in journals always ask for an a priori power analysis to justify sample size in this type of experiments. I always end up getting away without doing it arguing that it's complicated, that the normal tools typically employed by researchers (e.g. Gpower) are actually not well suited for this complex of a model, where the time variable can have more than 100 levels (e.g. a video that is more than 100 seconds).

It should be noted that physio variables don't typically show huge effect sizes because the main purpose of the peripheral nervous system (e.g., those processes that determine heart rate, skin conductance...) is not to tell us what we are thinking but to keep homeostasis and keep the body alive. Having 100 seconds of a physio measure shouldn't be considered as equally powerful as having 100 different stimuli or participants.

Resources I already know:

  1. I'm familiar with Westfall and Judd's online power analysis for MLM. It's great because it doesn't require programming skills but it's quite limited because 1. it doesn't include repeated measures 2. it seems to work only if the variable of interest is also included as random slope, and we don't always include that, that's quite the conservative analysis.
  2. I'm also familiar with Blair et al.'s DeclareDesign online tool but again it does not account for repeated measures.

Does anyone know what's the best way to go about this?

Luminosa
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    The simr R package is excellent for this. If you're able to fit a model on similar data (either simulated or from a prior similar project), you manually fix the parameter of interest (e.g., the condition:time coefficient) at the specified value you wish to be powered for and simr calculates power/required sample size by simulation. Provides tools to extend number of within-person observations or total sample size to whatever level you wish. https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12504 – Lachlan Sep 27 '22 at 13:12
  • So I've been trying it out since you recommended it and I don't know what the issue is, but I keep getting weird errors for the powerCurve() function (which I think is the best tool to calculate sample sizes), when using a preexisting dataset. Do you have any suggestions for tutorials on simr? – Luminosa Sep 28 '22 at 13:47
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    The author of the package has a few tutorials. Also have a look on Github - I remember there was an error I couldn't figure out and it had been explained in one of the closed issues there. It's a bit touchy at first but great to use once you get the hang of it. – Lachlan Sep 29 '22 at 11:41

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