[cbrnr]

Unfortunately, I didn’t have the time to finish the work on this particular data set, so there is no publication (yet). There are still several open questions I have myself, and once I have time to revisit my analysis I would appreciate advice from @henrik. For example, I was thinking about what if I want to see in which channels I get differences in activation – then I can’t use channels as a random effect. I was thinking that I’d probably need to perform some kind of permutation cluster test, but I wasn’t able to wrap my head around this so far.

@SeeArrr could you share your research question and your planned analysis? I’d be interested in how it is similar to what I was trying to achieve.

[cbrnr]

Thank you for your detailed response, this is really helpful!

If you measured the same 64 channels for each subject this means these two variables are crossed and not nested. Nested means that some specific levels of one factors (e.g., EEG channel) only appears within specific levels of another factors (e.g., ID). So for example, a nesting would exist if for each participant you would have an idiosyncratic set of EEG channels. Which of course seems quite unlikely.

You are right, thanks for clarifying the difference between nested and crossed variables.

However, one thing to consider is that ist is also a within-channel factor. So maybe
m <- mixed(erds ~ difficulty * ist + (difficulty | id) + (difficulty * ist| chan), erds, method="S") might be more appropriate (i.e., reflect the maximum random-effects structure justified by the design).

Is this really appropriate? IST is a person-specific measure like IQ, measured by a pencil and paper test before the EEG session. Therefore, channels do not contribute to random variation of IST (which is really constant within each person).

Anyway, even if I try to run the extended model as you suggested, I get convergence errors. I guess this means that even if this model was justified by the design, I would have to reduce it to get a stable model (which would be the model I proposed initially).

Regarding the centering issue, I can now see how centering can affect regression coefficients of main effects. I have two additional questions:

First, centering on the sample mean implies that this process depends on the sample. This could not be ideal if someone tries to replicate the experiment with a different sample – which mean does the other person need to subtract, my sample mean or the mean of the new sample? Alternatively, I could also center on some theoretical value (30 in my case, because the IST ranges from 0 to 60), but then I’d still get the warning by afex that the variable is not centered on 0. Or maybe this is not a problem at all? What is your recommendation on centering?

Second, I wonder why I don’t get a significant interaction given that the results of the difficulty main effect change so drastically whether I center IST or not. I was expecting either a significant interaction given the differences in centering, or no dramatic changes in regression coefficients given a non-significant interaction.

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