I have the results of a rating study in which ~30 participants rated a subset
of 20 items on 25 different dimensions. 

I would like to perform PCA on these ratings to reduce the 25 different
dimensions. However, instead of doing this on the mean ratings for each
item, I would like to perform the PCA at the level of individual ratings. I
am assuming that in order to do this I have to specify the fact that ratings
are nested within participants and within items (i.e., crossed random
effects for subjects and items). Is this possible?



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