Page 356 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

joint and full conditional distributions progeny performance 109
(continued) sire and grandsire 119–120
multiple chain/short chain matrix algebra
approach 264 addition and subtraction 302
parameters 262 column vector 299
definition 299
diagonal matrix 300
Legendre polynomials direct product 302–303
evaluation 325–326 eigenvalues and eigenvectors 305
linear equations inverse matrix 303–304
description 271 multiplication 302
direct inversion 271 rank of matrix 304
iteration, mixed model equations see singular matrix 305
iteration, mixed model square matrix 300
equations symmetric matrix 301
PCG see preconditioned conjugate transpose, matrix 301
gradient (PCG) triangular matrix 300–301
longitudinal data MBLUP see multivariate best linear unbiased
beef cattle 130 prediction (MBLUP)
CFs see covariance functions (CFs) MCMC see Markov chain Monte Carlo
covariance function and RRM (MCMC) methods
equivalence 155 MGS model see maternal grandsire (MGS)
fixed regression model 131–136 model
repeated measurements 130 mixed model equations (MME)
RRM see random regression model animal and dominance genetic
(RRM) effects 206–208
test day records 130 total genetic merit 208
MME see mixed model equations (MME)
multi-trait across-country evaluations
MACE see multi-trait across-country (MACE)
evaluations (MACE) analysis, DYD 86–87
Markov chain Monte Carlo (MCMC) computing
methods 260 EDC 88–89
maternal grandsire (MGS) model sire breeding values 89–91
description 30 dependencies 88
inbreeding coefficients 31 and DRP 87, 89
pedigree 32 maternal grandsire model 87–88
pertains to males 30–31 MME 87
recoding sires 32 partitioning, bull evaluations 91–94
−1
−1
T and D matrix, pedigree 32–33 multivariate analysis
without inbreeding 32 effects 95
maternal trait models factor analysis
animal covariances 102
birth weight, beef calves 110–111 FA model 105
BLUE 110 loadings 102
design matrices 111–114 multi-trait linear mixed
genetic and permanent model 102–103
environmental effects 110 WWG and PWG 103–104
RAM 115–119 limitations 95
components 109 parameter estimation and genetic
measurements 109 evaluation 95
phenotypic expression 109 principal component analysis

340 Index