So I have twelve variables that theoretically belong to the same dimension and I want do reduce them to one single item. A hierarchical factor analysis gives really low loadings at the second level. However, if I do PCA at both levels I get good results, but does it make sense to do a hierarchical PCA? What are the implications of it? I have read that PCA is only done when you have no underlying theory and just want to see what patterns emerge. However, in my case I do have a strong case why those variables belong together.
I have read in a paper from Welzel and Inglehart 2016, that if one follows compository logic (rather than dimensional logic), it is ok to combine variables that do not load well with each other, if a strong theoretical case can be made. So in that sense, should I just use the factor analysis with lower loadings?
Here is the paper:
https://www.researchgate.net/profile/Christian_Welzel2/publication/293636204_Misconceptions_of_Measurement_Equivalence_Time_for_a_Paradigm_Shift/links/57c5351608aecd4514159a62.pdf