Kernel covariance of a replicated-line predictor

Formula: K_* = Var(Z u) = sigma2_u * Z K Z'

Usage

Kernblup(Z, K, sigma2_u = 1)

Arguments

Z

Incidence matrix mapping records to lines.

K

Kernel (relationship) matrix between lines.

sigma2_u

Variance component of the line effects.

Value

List with K_star, n, J.

References

Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, doi:10.1007/978-3-030-89010-0. Chapter 8, Eq. (8.9) p. 282: with replicated individuals the model is Y = 1 mu + Z u + e; BGLR cannot take that predictor directly, so the covariance of the predictor, Z K Z', is precomputed and used as the kernel.

Examples

Kernblup(Z = c(1, 2, 3, 4, 5, 6, 7, 8), K = 5L)
#> $K_star
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,]    5   10   15   20   25   30   35   40
#> [2,]   10   20   30   40   50   60   70   80
#> [3,]   15   30   45   60   75   90  105  120
#> [4,]   20   40   60   80  100  120  140  160
#> [5,]   25   50   75  100  125  150  175  200
#> [6,]   30   60   90  120  150  180  210  240
#> [7,]   35   70  105  140  175  210  245  280
#> [8,]   40   80  120  160  200  240  280  320
#> 
#> $n
#> [1] 8
#> 
#> $J
#> [1] 1
#> 
#> $method
#> [1] "Replicated-line kernel covariance, MVSML Eq. (8.9)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"