I needed to run a PCA on a dataset with a multilevel structure. My question is similar to the one asked here: Principal components analysis on nested data
In my case, however, the two levels are crossed rather than nested. Is there an R package for this? Would it be better to just report by-item and by-subject results?
A bit of context on the study: the data results from experiments where proofreaders (subjects) checked a number of written sentences (items). All proofreaders saw all sentences. I want to investigate correlations across multiple measures of proofreading behaviour (proofreading time, number of editing operations, etc.)
I'd be happy to just go with by-item and by-subject analyses, but results are quite different and I'm not sure about how to interpret this. Biplots show that the proofreading behaviour variables are much more correlated with each other in the by-item analysis. Would this be due to high between-subject variability, making the by-item analysis more reliable?