I performed a PCA on the results of 4 different tests. Each test can only have whole integers as a score, and is measured on a scale of 0-5.
From what I've read, you are not supposed to conduct a PCA on categorical data, which is similar in structure to my data. However, I've also read that this assumption or rule is often broken/relaxed, as interpretation might be valuable nonetheless.
Out of curiosity I decided to simply see what would happen, and I find that my PCA generates exactly four components. Moreover, each of my test score variables load perfectly on one of these 4 components.
Loadings: PC1 PC2 PC3 PC4 Test1 1 Test2 1 Test3 1 Test4 1
Q1: I was wondering what is happening here. Could someone (in simple terms) explain what this means and how this could be the case?
Q2: I have a list of 8 more tests which are all measured on a continuous scale. I have also performed a PCA on this data. However, I was hoping to also add these 4 tests to that PCA. I wish to do this as the results of the 4 tests mentioned above are better understood than the results of the remaining 8 tests. Would it be acceptable to include all 12 tests (8 continuous + 4 from above)?