0
$\begingroup$

i want to create an index. it has 3 subindices A,B,C. each subindex further consists of 3 different variables A1,A2,A3,B1,B2,B3 and so on. in total there are 9 variables. i want to assign weights using PCA. my question is do i assign weights to the variables A1,A2,A3 then aggregate to find an overall score for subindex A, repeat the process for subindex B and C and then assign weights to subindex A,B and C, or do i calculate it for all the variables combined together?

$\endgroup$
1
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    May 14 at 11:58

1 Answer 1

1
$\begingroup$

I think that you could defend either position. In my opinion, it should depend on whether you need to capture as much of the variance of the full set as possible (extract weights from one PCA) or whether you want to maximize coherence of each of the extracted components (you could justify doing individual PCAs).

If you use the PCA scores from the full data set, for each component you will likely have strongly positive scores that will clearly inform each that latent variable, but remember that all variables get scores on each dimension. Some will have scores near zero and will be, effectively, influencing that latent dimension very little. However, you might also get strongly negative scores for some variables on one dimension (that are likely strongly positive on a different dimension). PCA is trying to use the scores/loadings/weights to explain as much variance as possible. Look at the positive and negative loadings ask whether you can make sense of each dimension. If there are very strong negative loadings that make it difficult to explain what that dimension means, you might consider separating them.

If you separate the variables by group and run individual PCAs, you will likely get only positive scores, and each latent variable can only be influenced by that subset. You will get more coherent latent dimensions, but know that you are explaining less (perhaps much less) of the total variance that existed in the full data set.

You might also consider identifying the variable groups with PCA, then using CFA with the subgroups to test for coherence and get your final indices.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.