sommer: A.mat – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

A.mat

Additive relationship matrix

Description

Calculates the realized additive relationship matrix. Currently is the C++ implementation of Endelman and Jannink (2012) and van Raden (2008).

Usage

A.mat(X,endelman=TRUE,min.MAF=0,return.imputed=FALSE)

Arguments

`X`	Matrix (n \times m) of unphased genotypes for n lines and m biallelic markers, coded as {-1,0,1}. Fractional (imputed) and missing values (NA) are allowed.
`endelman`	Set endelman=TRUE to use the method from Endelman and Jannink (2012) (without the shrinkage, for that method look at the rrBLUP package). If FALSE, regular vanRaden is used.
`min.MAF`	Minimum minor allele frequency. The A matrix is not sensitive to rare alleles, so by default only monomorphic markers are removed.
`return.imputed`	When TRUE, the imputed marker matrix is returned.

Details

For endelman method: At high marker density, the relationship matrix is estimated as A=W W'/c, where W_{ik} = X_{ik} + 1 - 2 p_k and p_k is the frequency of the 1 allele at marker k. By using a normalization constant of c = 2 ∑_k {p_k (1-p_k)}, the mean of the diagonal elements is 1 + f (Endelman and Jannink 2012).

For vanraden method: the marker matrix is centered by subtracting column means M= X - ms where ms is the coumn means. Then A=M M'/c, where c = ∑_k{d_k}/k, the mean value of the diagonal values of the M M' portion.

Value

If return.imputed = FALSE, the n \times n additive relationship matrix is returned.

If return.imputed = TRUE, the function returns a list containing

$A: the A matrix
$X: the imputed marker matrix

References

Endelman, J.B., and J.-L. Jannink. 2012. Shrinkage estimation of the realized relationship matrix. G3:Genes, Genomes, Genetics. 2:1405-1413. doi: 10.1534/g3.112.004259

Covarrubias-Pazaran G (2016) Genome assisted prediction of quantitative traits using the R package sommer. PLoS ONE 11(6): doi:10.1371/journal.pone.0156744

Examples

####=========================================####
#### random population of 200 lines with 1000 markers
####=========================================####
X <- matrix(rep(0,200*1000),200,1000)
for (i in 1:200) {
  X[i,] <- ifelse(runif(1000)<0.5,-1,1)
}

A <- A.mat(X)

####=========================================####
#### take a look at the Genomic relationship matrix 
#### (just a small part)
####=========================================####
# colfunc <- colorRampPalette(c("steelblue4","springgreen","yellow"))
# hv <- heatmap(A[1:15,1:15], col = colfunc(100),Colv = "Rowv")
# str(hv)

sommer

Solving Mixed Model Equations in R

v4.1.3

GPL (>= 2)

Authors

Giovanny Covarrubias-Pazaran

Initial release

2021-04-01