My question is very similar to this one, which was not solved unfortunately.
I am working on a project for which I want to rank countries by means of their HIV/AIDS burden. So I collected a lot of data for all countries in the world. For simplicity let's assume that I have following variables for each country:
- DEA: Deaths due to HIV
- LIV: People living with HIV
- PRV: HIV prevalence rate
- DALY: number of healthy years lost due to HIV
- DALY ratio: proportion of healthy years lost due to HIV in total number of healthy years lost due to disease in general.
So all these variables somehow measure the same thing: the HIV burden. Now I want to combine all these variables into one 'score', such that I can rank countries by means of their HIV burden.
The first thing that came into my mind was to to perform a principal component analysis and retain one PC. However, if we look at the loadings of this first PC we see the following:
- DEA: 0.366
- LIV: -0.392
- PRV: -0.442
- DALY: 0.466
- DALY ratio: 0.481
Because of the high pairwise correlations between the variables I would have expected each of the loadings to have the same sign. Now countries with a high HIV burden (so scoring high on each of the variables) now get a lower score for the first PC on one side (due to the negative loadings of 'LIV' and 'PRV') and a higher score for the first PC on the other side (due to the positive effects of 'DEA', 'DALY' and 'DALY ratio').
Is it correct that looking at the scores for the first PC is not a proper way to give a score for HIV burden to each of the countries because of the contrary loadings as explained above?
Can you suggest another (better way) to combine all the information into one single score?