[R] Permutation test and R2 problem

[Meyners, Michael, LAUSANNE, AppliedMathematics]

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Alex Roy
> Sent: Freitag, 14. August 2009 12:05
> To: r-help at r-project.org
> Subject: [R] Permutation test and R2 problem
> 
> Hi,
> 
> 
> I have optimized the shrinkage parameter (GCV)for ridge  and  
> got my r2 value is 70% . to check the sensitivity of the 
> result, I did permutation test. I permuted the response 
> vector and run for 1000 times and draw a distribution. But 
> now, I get r2 values highest 98% and some of them more than 
> 70 %. Is it expected from such type of test?

Depends on what exactly you are doing and on your data, but surely this
is not "unexpected" (even less given the information we have).
 
> *I was under impression that, r2 with real data set will 
> always maximum! And permutation will not be effected i.e. 
> permuted r2 will always less than real one! *

Why would that be? And even more, why would you do a permutation test
then if you knew in advance that all permuted values are below your
observed one? You optimize the shrinkage parameter for your data, not
your data for your shrinkage parameter. In the latter case you would
have been right. Given any fixed shrinkage parameter, you can always
find "some data" (e.g. the predicted values) that fit better than the
original. I guess that in most non-artificial cases with a reasonable
amount of data, there are at least some permutations that give a higher
r2.

Not sure what kind of sensitivity you want to check, but probably you'd
have to optimize the shrinkage parameter as well. And of course to make
sure that your permutations correspond to the original constraints. But
this opens a wide field, refer to any textbook on this matter for
further detail (e.g. Edgington & Onghena, Randomization tests).

HTH, Michael