I have a list of 25 air pollutants many of which are strongly correlated. I was hoping to reduce down to a short list of eigenvectors which would each be composed of a small number of the pollutants.
I mostly followed this tutorial video so far.
When I tried varimax rotation on all of the PCs (as seems to be done at the end of this video) I get each of the 25 PCa having a score of 1 or -1 for only one variable, with every variable accounted for, i.e. all PCs and variables accounted for by unique pairings. It seems sort of intuitive that this would have happened now that I think about it but I don't understand why it didn't happen in the tutorial video.
Have I done something wrong or if not then why did the example in the video not also do the same? Could it be something to do with my data having many more dimensions?
Depending on the selection criteria (Kaiser criterion; levelling-off of scree plot) the top 7 or top 13 are the important ones. Putting just these 7 or 13 components in gives more the sort of output I had expected.
Does anyone have any suggestions which of these options (7 or 13 components) I should choose or is it a fairly arbitrary decision based on how much I want to compress the data?