rrBLUP (version 3.8)

A.mat: Additive relationship matrix

Description

Calculates the realized additive relationship matrix.

Usage

A.mat(G,min.MAF=NULL,max.missing=NULL,impute=TRUE,tol=0.02,n.core=1,return.G=FALSE)

Arguments

G

Matrix ($n \times m$) of unphased genotypes for $n$ lines and $m$ biallelic markers, coded as {-1,0,1} = {aa,Aa,AA}. Fractional (imputed) and missing values (NA) are allowed.

min.MAF

Minimum minor allele frequency; default removes monomorphic markers.

max.missing

Maximum proportion of missing data; default removes completely missing markers.

impute

If TRUE, missing genotypic data are imputed (see below). If FALSE, A is calculated from pairwise complete observations, which does not guarantee positive semidefiniteness (this can cause problems with mixed.solve

tol

Specifies convergence criterion for imputing missing data with an EM algorithm (see details). If tol < 0, missing data are imputed with the population mean for each marker.

n.core

For Mac, Linux, and UNIX users, setting n.core > 1 will enable parallel execution on a machine with multiple cores. R package multicore must be installed for this to work. Do not run multicore from within the R GUI; you must use the command line.

return.G

If TRUE (and impute = TRUE), the imputed marker matrix is returned. When the EM algorithm is used, the imputed alleles can lie outside the interval [-1,1]. Polymorphic markers that do not meet the min.MAF and max.missing criteria are not imputed.

Value

• If return.G = FALSE, the $n \times n$ additive relationship matrix is returned. If return.G = TRUE, a list containing [object Object],[object Object]

Details

The A matrix is calculated as $W W'/c$, where $W_{ik} = G_{ik} + 1 - 2 p_k$ and $p_k$ is the frequency of the 1 allele at marker k. The normalization constant is $c = 2 \sum_k {p_k (1-p_k)}$. When marker data are missing, by default an EM algorithm is used to impute genotypes and converge on the maximum likelihood solution for A. The EM algorithm stops at iteration t when the RMS error = $n^{-1} \|A_{t} - A_{t-1}\|_2$ < tol. If the user passes a negative value for tol, or if the number of markers is less than the number of lines, missing alleles are imputed with the population mean for each marker.

Examples

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

#Additive relationship matrix
A <- A.mat(G)