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Inverse of the single-step relationship matrix H

Source: R/pedigree.R
h_inverse.Rd

H^-1 = A^-1 + [0 0; 0 G*^-1 - A22^-1] (Aguilar et al. 2010; Christensen and Lund 2010), built by the same code the Gaussian fitters use: G of VanRaden (2008) with the allele frequencies of the genotyped, brought to the scale of A22 by the affine adjustment and blended with it (G* = (1 - w) G_adj + w A22), and inverted exactly, by the APY (apy_core =, "auto" included) or by the Vecchia recursion (vecchia_k =). This is the door for the fitters written in R, model_threshold() and model_survival(), which call it when given genotypes =; the result also enters anywhere k_inverse = is taken.

Usage

h_inverse(
  pedigree,
  genotypes,
  blend = 0.05,
  apy_core = NULL,
  vecchia_k = NULL,
  metafounders = NULL,
  gamma = NULL
)

Arguments

pedigree

data.frame animal, sire, dam (or a sire_mgs() pedigree)

genotypes

list with ids and m (0/1/2, NA imputed by the marker mean), checked as in model(): a repeated id, rownames that contradict ids or an animal below a 0.90 call rate are refused, and a parent-offspring conflict with the pedigree is a warning (see parentage_check())

blend

weight of A22 in G*, the usual 0.05

apy_core

ids of the APY core, "auto", or the result of apy_core_select()

vecchia_k

neighbours per animal in the Vecchia inverse of G*

metafounders, gamma

metafounder labels and their Gamma, as in model(): then H(Gamma) = A(Gamma)^-1 + [0 0; 0 G*^-1 - A22^-1], with G the one of allele frequencies 0.5 scaled by m/2 (G05), A22 taken from A(Gamma), and G* = (1 - w) G05 + w A22 WITHOUT the affine adjustment, which is the base correction Gamma already makes (Legarra et al., 2015; Garcia-Baccino et al., 2017). Every unknown parent must then be a metafounder

Value

triplets of the lower triangle, list(i, j, x, n, id) as a_inverse() returns, plus h_prior and h_prior_row (the diagonal of G* of each genotyped animal, named by animal, and its row in id, which accuracy() uses as the prior), n_imputed, n_monomorphic and apy (the core used, when there is one)

References

Aguilar, I., Misztal, I., Johnson, D.L., Legarra, A., Tsuruta, S. & Lawlor, T.J. (2010). Journal of Dairy Science 93:743-752.

Christensen, O.F. & Lund, M.S. (2010). Genetics Selection Evolution 42:2.

Garcia-Baccino, C.A., Legarra, A., Christensen, O.F., Misztal, I., Pocrnic, I., Vitezica, Z.G. & Cantet, R.J.C. (2017). Metafounders are related to Fst fixation indices and reduce bias in single-step genomic evaluations. Genetics Selection Evolution 49:34.

Legarra, A., Christensen, O.F., Vitezica, Z.G., Aguilar, I. & Misztal, I. (2015). Ancestral relationships using metafounders: finite ancestral populations and across population relationships. Genetics 200:455-468.