I would like to compute a measure of overlap between two sets of ratings made by the same individual. To illustrate, let’s assume the following:

A sample of individuals (

*N*= 20) are asked to rate their own personality on nine different dimensions (e.g., emotional stability, extraversion, self-confidence). Then they are asked to do the exact same ratings of a person they have just met. Hence, for each individual we have one set of nine ratings pertaining to themselves (self1, self2, self3, etc.) and one set of nine ratings pertaining to the other person (other1, other2, other3, etc.). The other person is the same for all individuals in the sample.

Now, for each individual I would like to compute a measure of similarity (or dissimilarity) representing the degree of overlap between the self and the other person (in terms of the rated variables). My first idea was to simply compute the Euclidian distance:

View attachment 4880

In my understanding, however, Euclidian distance is misleading when two or more of the variables are correlated, which in fact they are here (e.g., extraversion and self-confidence). If that is the case, the recommendation seems to be to compute Mahalanobis distance instead, which essentially “decorrelates” the variables before computing the distance:

My problem is which covariance matrix (

*S*-1) to use in the computation of Mahalanobis distance. Because the two sets of ratings (self and other) are two different distributions, I end up with two covariance matrices. Can I somehow compute a pooled covariance matrix and enter that in the formula? Or is Mahalanobis distance simply not applicable when the two sets of ratings come from different distributions?

If this is doable, then any suggestions how to implement this in statistical software (SPSS, R, MatLab) are most welcome.

Best,

Kalle

Ps. This is my first post, so I apologize for any rookie mistakes.