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I would like to calculate a compound scores of several normal distributed continues standardized (z-score) variables.

Some of these measures are correlated, some are not. Hence, I would like to take into account to correlation among them.

If I understand correctly, the Mahalanobis distance (MD) gives me the compound distance from the mutual multivariate center. However, this is an absolute distance that has only positive values.

I was wondering if it would be possible to get a Mahalanobis distance with both positive and negative values, where negative values represent the distance from the mean that represents worse than average scores, and positive scores represent better than average scores.

Example: 3 test of cognitive functioning - memory - concentration - processing speed

If a certain subject scores on average (relatively) bad on these tests, I would like to see a negative MD. If a certain subject scores on average (relatively) good on these tests, I would like to see a positive MD.

Is this possible? If not, is there a measure that does this?

Best,

Vincent

Vincent
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    Distance cannot be negative by definition. Euclidean or Mahalanobis d, in particularly, are computed out of their squared versions, as the root, so they cannot be negative. – ttnphns May 10 '14 at 05:04
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    There is a close relationship between PCA and MD. Since signs are usually used in the context of a one dimensional measurement, maybe it could make sense to look at the scores of the first principal component. – Michael M May 10 '14 at 10:51

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