Hello Mangalani,

You seek an index score, but for what purpose? How best to combine scores depends on the intended use of the linear composite.

In general, the individual component score that yields the largest variance for a sample is the one that will have the most impact in separating cases. That's one possible use.

If the goal is to determine an index that best corresponds with some external variable, then multiple regression could be useful for identifying weights.

That doesn't cover all of the possibilities, of course. Perhaps you could elaborate on your aims for the proposed index.

Do recall that component scores among your chosen three-component solution will be uncorrelated with one another unless you rotated the resultant solution with an oblique rotation (such as promax or oblimin).

Good luck with your work.

Good explanation from Prof. David Morse. Adding the principal components is not a good option. PC1 will definitely have the greatest influence in separating your data.

Mangalani Peter Makananisa, although you have given some good advice up above, it's possible that you haven't provided enough information for others to be really helpful.

I hope that the following helps:

The general recommendation seems to be that factor analysis is better than principal components analysis. Also, how did you determine that there were three factors in your data? For some time, parallel analysis has been recommended for determining the number of factors in a data set, but few researchers seem to know about it, let alone use it despite it being quite easy. Then, if you discover that your factors are not highly related (following rotation - preferably oblique), it would be best not to just combine the scores on the different factors because doing so could be like adding apples and oranges.

Finally, I recommend taking the average of the items on a factor because doing so gives you an indication about where the scores lie relative to the response options that participants were offered.