Dealing with multicollinearity across dependent variables In an experiment, participants rated each of several musical stimuli on 5 dimensions (ratings A to E). For each of the ~3,000 trials, the independent variables were (* = critical manipulation):

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**ensemble/group size (1 or 2)

*learning condition (1, 2, or 3)

*repetition (1 or 2)

*musical training (continuous score)

I'd like to find which rating (or combination of ratings) can best predict 'ensemble size'. The screenshot below shows the data structure, for clarity:

I analysed this data in two ways:
(1) I performed one LME for each of the 5 ratings, taking rater and stimulus ID as RFX and the remaining IVs as FFX:
    rating ~ ensembleSize + condition + rep + training + 
               (1|id_rater) + (1|stimulus)

(2) I switched the question round and, using fitglm in Matlab, created a logistic binomial model of the probability of each stimulus having been an ensembleSize=1 or 2, as a function of the 5 ratings, separately for the 3 learning conditions. So here the ratings are the IVs, and ensembleSize is the DV.
My questions:

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*Which of the two approaches is in fact more appropriate? IV=ensembleSize, DVs=ratings, as with the LME approach? Or the logistic model where IV and DV are reversed?


*THe LME I did ignores the fact that there's high multicollinearity among the 5 ratings (A to E). I know "multicollinearity" is normally defined among IVs, but in this case my DVs are the ratings, and it seems wrong to do an LME for each if there is in fact (let's say) only one latent variable behind them all.
Perhaps a suitable correction is to compute VIFs (Variance Inflation Factors)? Or perhaps a Variance-Covariance Matrix? Or is it best to define a single multilevel model, in which the different ratings are nested within raters, themselves nested within 'stimulus' and 'learning condition'?
So far I used Matlab for this data set, but I could also continue this in R or Python, if it makes the implementation easier. Thank you for any inputs!

Multicollinearity is not a problem.
In the world of mixed effects modeling, it's thought of as within, vs between, cluster variation, and is assessed using the intra-class correlation (ICC).
However, higher ICC means that you have less power than if the ICC was lower. This is why, if all else is equal, you would rather have fewer ratings from more participants, than more ratings from fewer participants. More participants = more power, even if the total number of ratings is equal.
