Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions

1996 ◽  
Vol 44 (12) ◽  
pp. 3069-3078 ◽  
Author(s):  
P. Stoica ◽  
M. Viberg
Keyword(s):  
Maximum Likelihood ◽  
Rank Estimation ◽  
Reduced Rank ◽  
Linear Regressions

Genetic principal components for live ultrasound scan traits of Angus cattle

2005 ◽  
Vol 81 (3) ◽  
pp. 337-345 ◽  
Author(s):  
K. Meyer
Keyword(s):  
Genetic Variation ◽  
Maximum Likelihood ◽  
Principal Components ◽  
Muscle Area ◽  
Genetic Covariance ◽  
Eye Muscle ◽  
Rank Estimation ◽  
Reduced Rank ◽  
Angus Cattle ◽  
Rank Estimates

AbstractMultivariate restricted maximum likelihood analyses were carried out for a large data set comprising records for eye-muscle area, fat depth at the 12/13th rib and the rump P8 site, and percentage intramuscular fat, recorded via live ultrasound scanning of Australian Angus cattle. Records on heifers or steers were treated as separate traits from those on bulls. Reduced rank estimates of the genetic covariance matrix were obtained by restricted maximum likelihood, estimating the leading three, four, five, six, seven and all eight principal components and these were contrasted with estimates from pooled bivariate analyses.Results from analyses fitting five or six genetic principal components agreed closely with estimates from bivariate and eight-variate analyses and literature results. Heritabilities and variances for ‘fatness’ traits measured on heifers or steers were higher than those recorded for bulls, and genetic correlations were less than unity for the same trait measured in different sexes. Eye-muscle area showed little association with the other traits.Reduced rank estimation decreased computational requirements of multivariate analyses dramatically, in essence corresponding to those of an m-variate analysis for m principal components considered. Five or six principal components appeared to be necessary to model genetic covariances adequately. The first three of these components then explained about 97% of the genetic variation among the eight traits.A simulation study showed that errors in reduced rank estimates of the genetic covariance matrix were small, once three or more principal components from analyses fitting five or more components were used in constructing the estimates. Similarly, accuracy of genetic evaluation for the eight traits using the first four components was only slightly less than that using all principal components.Results suggest that reduced rank estimation and prediction is applicable for the eight scan traits considered. The leading three to four principal components sufficed to describe the bulk of genetic variation between animals. However, five or more principal components needed to be considered in estimating covariance matrices and the ‘loadings’ of the original traits to the principal components.

Reduced-rank estimation of genetic parameters for egg production traits and cluster analyses with predicted breeding values

2018 ◽  
Vol 68 (2) ◽  
pp. 81-86
Author(s):  
Luara Afonso de Freitas ◽  
Rodrigo Pelicioni Savegnago ◽  
Natalia Vinhal Grupioni ◽  
Salvador Boccaletti Ramos ◽  
Nedenia Bonvino Stafuzza ◽  
...  
Keyword(s):  
Egg Production ◽  
Genetic Parameters ◽  
Production Traits ◽  
Breeding Values ◽  
Cluster Analyses ◽  
Rank Estimation ◽  
Reduced Rank ◽  
Estimation Of Genetic Parameters

scholarly journals Rank estimation in reduced-rank regression

2003 ◽  
Vol 87 (1) ◽  
pp. 159-176 ◽  
Author(s):  
Efstathia Bura ◽  
R.Dennis Cook
Keyword(s):  
Reduced Rank Regression ◽  
Rank Regression ◽  
Rank Estimation ◽  
Reduced Rank
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