I have 20 items rated on 25 dimensions. Each item was rated on each dimension ~30 times. Each of ~40 participants rated 15 of the 20 items on all of the dimensions.
I had originally thought to do PCA on the item means (i.e. averaging across all ratings for that item), but realized that I will have fewer observations than dimensions, which I understand is not idea for PCA.
My question is, can I do PCA at the trial level (i.e. using each individual rating [e.g. participant #1 rating item #1 on dimension #1])? It seems that I should somehow account for the fact that the data are non-independent (i.e. nested within subjects and items). I've seen PCA with random effects mentioned on here, but haven't come across a definitive way to do this.
Is it okay to do PCA at the trial level? Are there additional steps I need to take?