Multi-trait genomic linear mixed model

Formula: stacking the n_T traits of each line, Y = (1 (x) I_nT) mu + Z b + eps with b ~ N(0, G (x) Sigma_T) and eps ~ N(0, I_J (x) R_nT) (eq. 5.5). Sigma_T is the genetic covariance between traits. When Sigma_T and R are diagonal the fit is equivalent to fitting a univariate GBLUP per trait.

Usage

Msm026(Y, Z, G, Sigma_T, R_T)

Arguments

Y

Lines-by-traits response matrix (J x n_T).

Z

Random-effects incidence matrix over lines.

G

Genomic relationship matrix.

Sigma_T

Genetic covariance between traits.

R_T

Residual covariance between traits.

Value

List with estimate, mu, b, b_by_line, method.

References

Montesinos Lopez, Montesinos Lopez & Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, eq. (5.5) p.153. DOI 10.1007/978-3-030-89010-0.

Examples

set.seed(12)
J <- 6; nT <- 2
G <- crossprod(matrix(rnorm(J * J), J)) / J
Y <- matrix(rnorm(J * nT, 5), J, nT)
f <- Msm026(Y, Z = diag(J), G = G, Sigma_T = diag(nT), R_T = diag(nT))
f$mu
#> [1] 4.721263 4.647514