2
$\begingroup$

In my understanding, "the absolute correlation" is not such a common expression. Can anyone kindly explain the significance of the built-in symbol AbsoluteCorrelation, especially compared with Pearson's and Spearman's correlation coefficients?

$\endgroup$
1
1
$\begingroup$

I'd say it's not only "not such a common expression" but at best a very misleading expression. What one obtains is not a correlation measure in the sense that the values are only between 0 and 1.

From the online help for multivariate probability distributions one obtains

Definition of AbsoluteCorrelation

As an example:

d = MultinormalDistribution[{3, 2, 1}, {{2, -2/3, -1/3}, {-2/3, 3, -1/3}, {-1/3, -1/3, 7}}];
AbsoluteCorrelation[d] // MatrixForm

Example of AbsoluteCorrelation matrix

So one is not getting correlations. I would steer clear of it for any statistical applications at least until the documentation gets better (or even never).

Addition:

Because of the definition used (as described in the online help), there is no apparent use of "absolute value" (at least when real numbers and statistical distributions are concerned). Consider the following example:

d = MultinormalDistribution[{0, 0, 0}, {{1, -2/3, -1/3}, {-2/3, 1, -1/3}, {-1/3, -1/3, 1}}];
AbsoluteCorrelation[d] // MatrixForm

AbsoluteCorrelation matrix

All but the diagonal elements are negative.

$\endgroup$
1
  • $\begingroup$ Thank you. I'm a bit surprised that the (curated) built-in symbol lacks a sufficient description. I've used the AbsoluteCorrelation function for my analysis and got an interesting result. I hope somebody will provide a document for that. $\endgroup$ – Satoshi Oota Mar 22 '20 at 4:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.