perfectwhiten {PCFAM}

The covariance preserving whitening function.

Description

This algorithm generates a new scaled 'genotype' dataset which keeps the same covariance structure as the original data, except that family members have been made orthogonal to each other, and singletons are unchanged.

Usage

perfectwhiten(Xun, Xfam, delta = 3e-04, threshold = 0.35, eta = NULL, addfuzz = F)

Arguments

Xun

A matrix of (possibly scaled) genotypes, (number of SNPs)*(number of singletons)

Xfam

A matrix of (possibly scaled) genotypes, (number of SNPs)*(number of individuals belonging to families)

delta

A slight offset used to ensure that the target covariance matrix is of full rank

threshold

The correlation threshold used to determine pairs of relatives. The choice should be less than the degree desired. For example, 0.35 captures first degree relatives (expected correlation 0.5), 0.15 captures first and second degree relatives (expected correlation for second degree relatives is 0.25).

eta

This argument is the replacement value used for matrix substitution. The default is NULL, resulting in substitution by the median.

addfuzz

The default is FALSE. Deprecated.

Value

Xplusscaled

The row-scaled full genotype data, including both singletons and family members

Y

The (scaled) genotype matrix after whitening, and should have a covariance matrix very close to Mtarget. Column means are zero

Ynotcolcentered

The same as Y, but with column means matching those of Xplusscaled

M

The covariance matrix of the full data

Mtilde

The covariance matrix after matrix substitution of all family pairs identified with correlations exceedingeta

whichbig

The set of indexes of M that have correlation exceeding threshold

covY

The covariance matrix of Y, useful to compare to M or to Mtarget

Author(s)

Yi-Hui ZHou, Fred A. Wright

References

Computation of ancestry scores with mixed families and unrelated individuals. arXiv:1606.08416.

Examples

X <- matrix(rbinom(1000*20,2,0.4),1000,20)
X[,1]=X[,2]*0.9
X=rowscale(X)
Xresid=residualize(X)
library(PCFAM)
corXresid=cor(Xresid)
myfam=findfamilies(corXresid,0.1)
K=3
perfect.result=perfectwhiten(X[,which(myfam==0)],X[,which(myfam==1)])