A sample of 100 subjects responded to two personality tests. These tests have slightly different wordings but are generally the same, i.e. they both measure the same 4 attitudes. Therefore, I have 2 matrices like this, with 4 scores per subject:
>test1
subj A1 A2 A3 A4
1 -2.14 1.21 0.93 -1.72
2 0.25 1.17 0.67 0.67
>test2
subj A1 A2 A3 A4
1 -1.99 1.11 1.00 -1.52
2 0.24 1.20 0.71 0.65
I'd like to evaluate the similarity of profiles in the two tests, i.e. the similarity of two sets of 4 scores for each individual. I feel like the mahalanobis distance is the measure I need and I checked some packages (HDMD, StatMatch) but couldn't find the right function.
One approach to this is to create a difference score matrix and then calculate the Mahalanobis distances on the difference scores.
testDiff <- test1 - test2
testDiffMahalanobis <- mahalanobis(testDiff,
center = colMeans(testDiff),
cov = cov(testDiff))