In fbzwsqualitasag/qzwslrm: Validation of Predicted Breeding Values Using the LR-Method

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
s_bib_path <- "bibliography.bib"
met <- rmdhelp::MendeleyExportToolR6$new()
met$set_local_bib_file(ps_local_bib_file = s_bib_path)

library(qzwslrm)

Disclaimer

The comparison between PBLUP and GBLUP evaluation is described in this document. In the paper r met$add("Legarra2018") available at https://link.springer.com/article/10.1186/s12711-018-0426-6, this special comparison is explained on page 10.

Background

The addition of marker data to a pedigree based evaluation which corresponds to moving from a PBLUP to a (SS)GBLUP evaluation can also be viewed as having more data. Thus a way to check the increase in accuracy caused by the addition of marker data in a genetic evaluation is to view the data with marker information as the "whole" dataset and the data without marker as the "partial" dataset.

Using subscript $G$ to refer to EBV based on data with marker information and $A$ to EBV based on data without markers, this yields

$$\rho_{A,G} = \frac{\left( \hat{\mathbf{u}}_A - \overline{\hat{\mathbf{u}}}_A \right)^T \left( \hat{\mathbf{u}}_G - \overline{\hat{\mathbf{u}}}_G\right)} {\sqrt{\left( \hat{\mathbf{u}}_A - \overline{\hat{\mathbf{u}}}_A \right)^T \left( \hat{\mathbf{u}}_A - \overline{\hat{\mathbf{u}}}_A\right) \left( \hat{\mathbf{u}}_G - \overline{\hat{\mathbf{u}}}_G \right)^T \left( \hat{\mathbf{u}}_G - \overline{\hat{\mathbf{u}}}_G\right)}}

= \frac{acc_A}{acc_G} $$

This assumes $Cov(\hat{\mathbf{u}}_G, \hat{\mathbf{u}}_A) = Var(\hat{\mathbf{u}}_A)$ which has formally been proven only for a single marker that was fitted as a correlated trait (r met$add("Legarra2015a")). The procedure above uses the same phenotypes for evaluations with either $G$ or $A$. An alternative approach might be to compare the increase in accuracy from partial to whole in both in both approaches. In this case the following procedure is proposed

1. Compute EBV with all data ("whole") with the method that is deemed to be optimal which is assumed to be GBLUP
2. Choose a cutoff date and create a partial dataset by setting all phenotypes after the cutoff to missing
3. Compute GEBV based on partial data using GBLUP

if (knitr::is_html_output()) cat("## References\n")

fbzwsqualitasag/qzwslrm documentation built on Sept. 13, 2022, 3:28 p.m.