Variance Component Estimation in General Mixed Model of Analysis of Variance

A brief review is given of prediction of breeding values when the genetic and phenotypic variances of the trait are known. In many situations, however, these variances are not known and must be estimated from the data. A review is given of the traditionally used analysis of variance (ANOVA) type methods of variance component estimation and of the more recently developed methods of maximum likelihood (ML), restricted maximum likelihood (REML), minimum norm quadratic unbiased estimation (MINQUE) and some variations on MINQUE. Criteria for choosing among methods are discussed and the consequences of applying estimates obtained by these methods in place of known variances to the prediction of breeding values are considered. The methods are illustrated for estimation of paternal half-sib heritability and prediction of breeding values of sires using a small numerical example. Lastly, the consequences of selection on prediction of breeding values and estimation of components of variance for populations under selection are discussed.

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Breeding Value and Variance Component Estimation From Data Containing Inbred Individuals: Application to Gynogenetic Families in Common Carp (Cyprinus carpio L.)

Genetics ◽

10.1093/genetics/145.4.1243 ◽

1997 ◽

Vol 145 (4) ◽

pp. 1243-1249 ◽

Cited By ~ 1

Author(s):

Piter Bijma ◽

Johan A M Van Arendonk ◽

Henk Bovenhuis

Keyword(s):

Variance Component ◽

Mixed Model ◽

Estimation Procedure ◽

Breeding Value ◽

Relationship Matrix ◽

Variance Component Estimation ◽

Numerator Relationship Matrix ◽

Component Estimation ◽

Small Advantage ◽

General Method

Under gynogenetic reproduction, offspring receive genes only from their dams and completely homozygous offspring are produced within one generation. When gynogenetic reproduction is applied to fully inbred individuals, homozygous clone lines are produced. A mixed model method was developed for breeding value and variance component estimation in gynogenetic families, which requires the inverse of the numerator relationship matrix. A general method for creating the inverse for a population with unusual relationships between animals is presented, which reduces to simple rules as is illustrated for gynogenetic populations. The presence of clones in gynogenetic populations causes singularity of the numerator relationship matrix. However, clones can be regarded as repeated observations of the same genotype, which can be accommodated by modifying the incidence matrix, and by considering only unique genotypes in the estimation procedure. Optimum gynogenetic sib family sizes for estimating heritabilities and estimates of their accuracy were derived and compared to those for conventional full-sib designs. This was done by means of a deterministic derivation and by stochastic simulation using Gibbs sampling. Optimum family sizes were smallest for gynogenetic families. Only for low heritabilities, there was a small advantage in accuracy under the gynogenetic design.

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Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model

Journal of the Royal Statistical Society Series B (Statistical Methodology) ◽

10.1046/j.1369-7412.2003.05211.x ◽

2004 ◽

Vol 66 (1) ◽

pp. 131-143 ◽

Cited By ~ 25

Author(s):

John Haslett ◽

Dominic Dillane

Keyword(s):

Variance Component ◽

Mixed Model ◽

Linear Mixed Model ◽

Variance Component Estimation ◽

Component Estimation ◽

Deletion Diagnostics

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GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

Journal of Navigation ◽

10.1017/s0373463321000564 ◽

2021 ◽

pp. 1-16

Author(s):

Hong Hu ◽

Xuefeng Xie ◽

Jingxiang Gao ◽

Shuanggen Jin ◽

Peng Jiang

Keyword(s):

Stochastic Model ◽

Least Squares ◽

Stochastic Models ◽

Variance Component ◽

Satellite System ◽

Variance Component Estimation ◽

Short Baseline ◽

Component Estimation ◽

Zero Baseline ◽

Global Navigation Satellite

Abstract Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

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