In charlotte-ngs/asmss2022: Applied Statistical Methods in Animal Science - Spring Semester 2022

knitr::opts_chunk$set(echo = FALSE)

Independence Assumption

So far

• random residuals: $var(e) = I * \sigma_e^2$ and
• random sire effects: $var(s) = I * \sigma_s^2$

In real livestock datasets, this is not realistic, because sires are related

Example Dataset

tbl_sire_model <- tibble::tibble(Animal = c(4:8),
                                 Sire   = c(1,3,1,4,3),
                                 Sex    = c("M","F","F","M","M"),
                                 WWG    = c(4.5, 2.9, 3.9, 3.5, 5.0))
knitr::kable(tbl_sire_model,
             booktabs = TRUE,
             longtable = TRUE)

Relationship

• For son $i$ and sire $k$ of $i$

\begin{equation} cov(s_i, s_k) = 1/2 * \sigma_s^2 \notag \end{equation}

Sire Relationship Matrix

library(pedigreemm)
ped_sire <- pedigree(sire = c(rep(NA,2), 1), 
                     dam = rep(NA,3), 
                     label = as.character(c(1,3,4)))
mat_A <- getA(ped = ped_sire)

cat(paste0(rmdhelp::bmatrix(pmat = as.matrix(mat_A), ps_name = "A", ps_env = "$$"), collapse = "\n"), "\n")

Sire Model

• pedigreemm

lmem_sire <- pedigreemm(
  formula = WWG ~ Sex + (1 | Sire), 
  data = tbl_sire_model,
  pedigree = list(Sire = ped_sire)
)
summary(lmem_sire)

Mixed model equations

• pedigreemm: Cannot specify assumed variance components

\begin{equation} \left[ \begin{array}{cc} X^TX & X^TZ \ Z^TX & Z^TZ + \lambda A_s^{-1} \end{array} \right] \left[ \begin{array}{c} \hat{b} \ \hat{s} \end{array} \right] = \left[ \begin{array}{c} X^Ty \ Z^Ty \end{array} \right] \notag \end{equation}

charlotte-ngs/asmss2022 documentation built on June 7, 2022, 1:33 p.m.