# Good measure of non-linear correlation

#### noetsi

##### Fortran must die
Many of the measures of correlation, notably pearson but I think Spearman rho as well, do not measure non-linear relationships well. Are there any that do measure it well?

I would guess that it would depend on the form the non-linear relationship took

#### Miner

##### TS Contributor
Spearman's rho will work on nonlinear relationships provided they are monotonic increasing/decreasing. Wikipedia has some good examples. For a non-monotonic, nonlinear relationship, I found reference to Hoeffding’s D, but know nothing about it.

I found in another paper that there is an R package for it: "The R function for Hoeffding’s D test is hoeffd (package Hmisc). The package Hmisc can be downloaded from the R Web page (http://www.r-project.org)."

SAS also has this.

#### noetsi

##### Fortran must die
Usually I look on line. In this case I was not even sure where to look for this. In part because I don't know what the class of correlation estimators such as pearson, spearman, polychoric correlation are called.

I was sure spearman's rho would not work for non-linear relationships. Obviously that is not, completely, correct.

thanks.

#### hlsmith

##### Not a robit
Nonlinear correlation, well that sounds like a transformation away from a linear correlation.

#### Dragan

##### Super Moderator
Yes, there is. It's referred to as the L-correlation; which is based on L-comoments. L-comomentns are the expected values of linear combinations of the order statistics of the data....a difficult subject to delve into.

#### rogojel

##### TS Contributor
Spearman's rho will work on nonlinear relationships provided they are monotonic increasing/decreasing. Wikipedia has some good examples. For a non-monotonic, nonlinear relationship, I found reference to Hoeffding’s D, but know nothing about it.

I found in another paper that there is an R package for it: "The R function for Hoeffding’s D test is hoeffd (package Hmisc). The package Hmisc can be downloaded from the R Web page (http://www.r-project.org)."

SAS also has this.
Great article Miner, many thanks!
BTW the distance correlation and the maximal information content seem to be performing much better then Hoeffdings D. I will certainly try them.

regards