Additive relationship matrix — A.mat • sommer

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

Usage

A.mat(X,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.
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 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 $c = \sum_k{d_k}/k$, 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)