Fit GBLUP by REML

Fits the genomic best linear unbiased prediction model y = X b + g + e, with g ~ N(0, G s2u) and e ~ N(0, I s2e), estimating the variance components by restricted maximum likelihood (REML). The solver uses the spectral / eigendecomposition approach of Endelman (2011) (the same method as rrBLUP::mixed.solve): the REML log-likelihood is profiled to a one-dimensional optimisation over the variance ratio lambda = s2e / s2u.

Usage

gblup(y, geno = NULL, K = NULL, X = NULL)

Arguments

y

Numeric phenotype vector (length n), no missing values.

geno

Optional marker matrix (n x m, coded 0/1/2). Used to build K and to derive marker effects for out-of-sample prediction.

K

Optional n x n genomic relationship matrix. If NULL, built from geno. If you pass K directly (no geno), out-of-sample prediction is not available.

X

Optional fixed-effects design matrix (n x p). Defaults to an intercept.

Value

An object of class gblup: a list with Vu, Ve, h2, beta (fixed effects), gebv (length-n GEBVs), lambda, K, and — when geno was given — marker_effects, marker_means (2p) and intercept.

Details

When geno is supplied, the equivalent ridge-regression marker effects are also returned, so the fit can predict breeding values for new genotypes via predict.gblup().

References

Endelman, J. B. (2011) "Ridge regression and other kernels for genomic selection with R package rrBLUP." The Plant Genome 4, 250-255. doi:10.3835/plantgenome2011.08.0024

Examples

sim <- simulate_population(n = 120, m = 500, seed = 1)
fit <- gblup(sim$pheno, sim$geno)
fit$h2
#> [1] 0.6814213
cor(fit$gebv, sim$bv)
#> [1] 0.773269