A collection of functions for calculating kinship matrices using different algorithms. The following algorithms are included: astle (Astle and Balding, 2009), Identity By State (IBS) and VanRaden (VanRaden, 2008) for marker matrices. For method identity an identity kinship matrix is returned.
Usage
kinship(
X,
method = c("astle", "IBS", "vanRaden", "identity"),
MAF = NULL,
denominator = NULL
)Arguments
- X
An n x m marker matrix with genotypes in the rows (n) and markers in the columns (m).
- method
The method used for computing the kinship matrix.
- MAF
The minor allele frequency (MAF) threshold used in kinship computation. A numerical value between 0 and 1. SNPs with MAF below this value are not taken into account when computing the kinship. If NULL all markers are used regardless of their allele frequency.
- denominator
A numerical value. See details.
Marker matrices
In all algorithms the input matrix X is first cleaned, i.e. markers
with a variance of 0 are excluded from the calculation of the kinship matrix.
Then some form of scaling is done which differs per algorithm. This gives a
scaled matrix Z. The matrix \(ZZ^t / denominator\) is returned.
By default the denominator is equal to the number of columns in Z for
astle and IBS and \(2 * p * (1-p)\) where
\(p = colSums(X) / (2 * nrow(X))\) for vanRaden. This denominator
can be overwritten by the user, e.g. when computing kinship matrices by
splitting X in smaller matrices and then adding the results together
in the end.
References
Astle, William, and David J. Balding. 2009. “Population Structure and Cryptic Relatedness in Genetic Association Studies.” Statistical Science 24 (4): 451–71. doi:10.1214/09-sts307 .
VanRaden P.M. (2008) Efficient methods to compute genomic predictions. Journal of Dairy Science 91 (11): 4414–23. doi:10.3168/jds.2007-0980 .
Examples
## Create example matrix.
M <- matrix(c(1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1), nrow = 4)
## Compute kinship matrices using different methods.
kinship(M, method = "astle")
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3111111 0.1333333 -0.1333333 -0.3111111
#> [2,] 0.1333333 0.6666667 -0.3111111 -0.4888889
#> [3,] -0.1333333 -0.3111111 0.3111111 0.1333333
#> [4,] -0.3111111 -0.4888889 0.1333333 0.6666667
kinship(M, method = "IBS")
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0000000 0.6666667 0.6666667 0.3333333
#> [2,] 0.6666667 1.0000000 0.3333333 0.0000000
#> [3,] 0.6666667 0.3333333 1.0000000 0.6666667
#> [4,] 0.3333333 0.0000000 0.6666667 1.0000000
kinship(M, method = "vanRaden")
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2857143 0.0952381 -0.0952381 -0.2857143
#> [2,] 0.0952381 0.6666667 -0.2857143 -0.4761905
#> [3,] -0.0952381 -0.2857143 0.2857143 0.0952381
#> [4,] -0.2857143 -0.4761905 0.0952381 0.6666667
## Only use markers with a Minor Allele Frequency of 0.3 or more.
kinship(M, method = "astle", MAF = 0.3)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.6666667 0.6666667 -0.6666667 -0.6666667
#> [2,] 0.6666667 0.6666667 -0.6666667 -0.6666667
#> [3,] -0.6666667 -0.6666667 0.6666667 0.6666667
#> [4,] -0.6666667 -0.6666667 0.6666667 0.6666667
## Compute kinship matrix using astle and balding method with denominator 2.
kinship(M, method = "astle", denominator = 2)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.4666667 0.2000000 -0.2000000 -0.4666667
#> [2,] 0.2000000 1.0000000 -0.4666667 -0.7333333
#> [3,] -0.2000000 -0.4666667 0.4666667 0.2000000
#> [4,] -0.4666667 -0.7333333 0.2000000 1.0000000