I am using PCA to create an index for my research. In my original dataset, I have 4 main items, (Suppose A,B,C,and D) and one of the items have 4 subitems (for instance, B has 4 subitems, let's say, 1b,2b,3b, and 4b. So, I have 7 items in my original dataset.
Then, I use PCA, and I retained 3 principal components based on Eigenvalues. My first component explained 38 percent of the variation, the second one explained 19 percent of the variation, and the third one explained 16 percent of the variation. My first component is correlated with 6 items in the original dataset (the one that is not correlated is 2b, and the second component is correlated with 5 items (4 subitems of B, and C) in the dataset. Correlation between the second component and 4 subitems of B is higher than that of component 1 and the subitems of B.
So I am wondering if it is possible to use the predicted scores of the second component as my index.