Hello Joane,

In what way(s) will you use your desired index score? If, for example, the goal was to construct an index that best related to some third variable, then PCA (using scores on the two latent variables, A & B) will not accomplish this. Regression (or, in the case of multiple external variables, canonical correlation) could.

Since there is but one correlation (for your sample) between the two scores, I'm not clear how incorporating this to derive the index would result in different scores for individual cases.

If you desired an index that equally weighted the two contributing scores, then you should first standardize each score to a common scale (for example, z-scores), then sum or average them. Otherwise, if you combine two scores by summing or averaging, the one having the larger variance will have the most emphasis in the composite (proportional to the relative sizes of the standard deviations).

Good luck with your work!

It is not possible to do factor analysis of any kind on a single correlation, and doing a regression of one on the other will just give you back the original correlation (i.e., the standardized regression coefficient will be equal to the correlation).

It appears that you want to find some way to assign weights to the two variables (other than giving them equal weights by simply adding them). Unfortunately, I do not know of any way to do that with only two variables.

David L Morgan and David Morse . Thank you for your answers. So in my case, Variables A and B are two dimensions with 5 items each, therefore, if I want to create a composite new variable C it is fine to go with a PCA? This new variable C, will be my dependent variable and my main question was to test how the relationship between A and B, as well as variance in C, might be affected by culture and cognitive styles (as an example).

Basically, I did a moderation analysis and mediation analysis to try to explain the relationship between A and B, but I do think that maybe, the combination of A and B as a single index might be another way to test why in a certain situation A and B are negatively correlated and why in another context they are positively correlated. My guess is that in one situation, A and B have the same weight and should not me analyze separately.

I hope that my explanation makes more sense now.

First, I do not recommend PCA for most social science data. Instead, I would do a Principal Factors Analysis with an oblique (correlated factors) rotation. But note that if your original assumptions are correct, this will yield two scales, which once again have a single correlation, with no way to convert that to a single index.

A different alternative would be to use Structural Equation Modeling, which would treat your two scales as a pair of independent variables in a regression. If the scales are dependent variables, then you can treat them as a single correlated dependent variable.

David L Morgan Thank you so much for your reply. I will look further on the second alternative, I was also thinking that I was going in the wrong direction. As you mentioned, what I want to do, is to use my variables as a pair of independent variables and use them as a single correlated dependent variable. Do you have any articles or recommendations on SEM? thank you in advance.

SEM is a broad topic, with several introductory texts. If possible, I would suggest choosing a text that matches your field. Otherwise, I like Bollen's Structural Equations with Latent Variables.

David L Morgan Thank you.

As I said, there are many textbooks on SEM.

If you are using AMOS, Byrne's book is a good choice.

Partha Sarathi Mishra and David L Morgan thank you for the recommendations. I am using AMOS so I will focus on books related to it.