I am interested in understanding if it is possible to use PCA twice, first on several subsets of data, and then again on the main components of those data subsets. I'm not entirely sure if this will give me the answer I am looking for.
For example: I have water chemistry concentrations (Ca,Mg,Na,Si) from different streams located within different land types (agricultural, urban, woods, alpine). These different streams all flow to one main river. I'd like to find out how much one land type contributes to a river, given its chemistry data. This somewhat lies along a method called End Member Mixing Analysis.
I am wondering if it is possible to find the principal components within each data subset (each land type) using the chemistry data (Ca,Mg,Na,Si). Then use the resulting principal component that explains the most variance, as a variable to represent that land type. Ultimately, trying to find out how much one land type contributes to the chemistry of the downstream river.
Does this make sense? Is this the right method for the question, which land type is most responsible for the variation in river chemistry?