Tracy-Widom statistics

[denis laloe]

In the revision r953 concerning the struc.pca (septembre 03, 2009), it
is written :

> From struct.pca remove support for Tracy-Widom statistics -- they're really
pointless.

I'm currently working in the genetic structuration of bovine cattle
with genome-wide data, and a colleague of mine asks me to use these
Tracy-Widom statistics.
I've worked with PCA since many years now, and I'm not convinced of
the interest of the TW statistics, at least in this topic.
So, I'd like to know what leads you to this conclusion.

[Kevin Jacobs <jacobs@bioinformed.com>]

Hi Denis,

In my experience, TW statistics don't lead to making useful decisions for the types of problems I face.  Specifically, I'm looking for the best set of linear adjusters to account for population stratification in tests of association between a phenotype and genotypes observed in a genome-wide scan.  My typical procedure to select the top 10-20 eigenvectors and fit a null association model with all covariates, but no genetic effects.  Any eigenvector  that is significant under that model is a potential confounder and should be included to control for potential stratification effects.  

I used to select the number of eigenvectors to test based on TW p-values, but I've observed eigenvectors that are significant confounders with non-significant TW statistics.  This is why I decided not to bother computing them.

Hope this helps,

~Kevin