Inverse kinship matrix to decorrelate relatedness

Question

[famstats]

Hi,

reading this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4143681/pdf/1753-6561-8-S1-S28.pdf

Says the following: a transformation matrix was calculated as the inverse of the decomposition of the kinship matrix. Then, this transformation matrix was used to decorreate the family data by multiplying it with both the phenotype and genotypes matrices.

I did that on a non-normal phenotype, but I don't quite believe the results, because my dataset has some clear outliers and after the decorrelation, I lost some.

Is there someone who can validate this approach? searching I didn't find other papers that use the same methodology.

[Jean-Karim Heriche]

According to the paper you linked to, this method is not published yet. However, I believe that decomposition of the kinship matrix refers to eigendecomposition of the matrix. If so and only some principal components are retained, the original matrix is only approximated. This is usually done to remove some noise but it could lead to the loss of outliers that you observe.

Answer 1

[famstats]

Thanks for the answer.

More or less I understand what he does, but for example here: https://stats.stackexchange.com/questions/342137/inverse-covariance-matrix-as-linear-transform I think they say he does it wrong.

But despite that, now, after having tried some whitening methods, I don't understand why all this just for removing a covariance matrix which you can estimate it's effect with a linear mixed model. If you extract the conditional residuals of that model, you can have your phenotype decorrelated with almost the same distribution as before and use it for whatever you want keeping things simple. I don't see how a whitening method can be better to decorrelate pedigree relatedness.

If anyone thinks I'm mistaken please go ahead, I just honestly don't see a reason.

[Jean-Karim Heriche]

Please use the 'add reply' button to reply to a comment. Don't create an answer that doesn't actually answer the question.

It's hard to say what's correct or not given that we don't have access to the details of the method.

[famstats]

yes sorry, I miss clicked.

At the end what they are doing is really similar to a thing called "whitening" (there are various methods, I'm referring it as a generalization) and in my opinion this is not necessary in the case of decorrelating a kinship matrix.

But I understand your answer, I just wanted to say sorry but ended up talking and talking. Thanks for answering.