Generalizing the use of the canonical transformation for the solution of multivariate mixed model equations

Genetics Selection Evolution

Volumn 29, Issue 3, 1997, Pages 205-224

  Ducrocq, V ^a   Chapuis, H ^a,b  

^a CEMAGREF   (France)

^b BETINA Sélection   (France)

Author keywords

Animal model; Computing algorithm; Genetic evaluation; Mixed model; Multiple trait

Indexed keywords

ALGORITHM; ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; QUANTITATIVE GENETICS; QUANTITATIVE TRAIT; THEORY;

ANIMALIA;

EID: 0030818681     PISSN: 0999193X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Arnason T (1986) Practical aspects in the estimation of breeding values for multi-trait selection. World Rev Anim Prod. 22, 75-84
2. Carabaño MJ, Najari S, Jurado, JJ (1992) Solving iteratively the Mixed Model equations. Genetic and numerical criteria. In: 43rd Annual Meeting of the EAAP. Madrid, Spain. 14-17 September 1992, vol I (Abstr)
3. Dempster AP, Laird NM, Rubin DR (1977) Maximum likelihood estimation for incomplete data via the EM algorithm (with discussion). J Royal Stat Soc B 39, 1-38
4. Ducrocq V (1992) Solving animal model equations through an approximate incomplete Cholesky decomposition. Gen Sel Evol 24, 193-209
5. Ducrocq V (1994a) Approches algorithmiques du modèle animal. In: Séminaire Modèle animal, Département de génétique animale, Inra, La Colle-sur-Loup, France, 26-29 septembre, (JL Foulley, M Molénat, eds), Inra, France, 13-24
6. Ducrocq V (1994b) Multiple trait prediction: Principles and problems. In: 5th World Congr Genet Appl Livest Prod, Guelph, 7-12 August 1994, University of Guelph, Guelph. vol XVIII, 5WCGALP Organizing Commitee, 455-462
7. Ducrocq V, Besbes B (1993) Solution of multiple trait animal models with missing data on some traits. J Anim Breed Genet 110, 81-92
8. Foulley JL, Calomiti S, Gianola D (1982) Ecriture des équations du blup multicaractères. Ann Génét Sél Anim 14, 309-326
9. Gengler N, Misztal I (1996) Approximation of reliability for multiple-trait animal models with missing data by canonical transformation. J Dairy Sci 79, 317-328
10. Groeneveld E, Kovac M (1990) A generalized computing procedure for setting up and solving mixed linear models. J Dairy Sci 73, 513-531
11. Groeneveld E, Kovac M (1992) Performance characteristics of different solving strategies in multivariate mixed models. Livest Prod Sci 30, 319-331
12. Groeneveld E, Kovac M, Wang T (1990) PEST, a general purpose BLUP package for multivariate prediction and estimation. In: 4th World Congr Genet Appl Livest Prod, Edinburgh, UK, 23-27 July 1990 (WG Hill, R Thompson, JA Woolliams, eds), vol XIII, 488-491
13. Hackbusch W (1994) Iterative Solution of Large Sparse Systems of Equations. Springer-Verlag, New-York
14. Henderson CR, Quaas RL (1976) Multiple trait evaluation using relatives' records. J Anim Sci 43, 1188-1197.
15. Jensen J, Mao I (1988) Transformation algorithms in analysis of single trait and of multiple trait models with equal design matrices and one random effect. J Anim Sci 66, 2750-2761
16. Lin CY, Smith SP (1990) Transformation of multitrait to unitrait mixed model analysis of data with multiple random effects. J Dairy Sci 73, 2494-2502
17. Meyer K (1985) Maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices. Biometrics 41, 153-165
18. Misztal I, Gianola D (1987) Extrapolation and convergence criteria with Jacobi and Gauss-Seidel iteration in animal models. J Dairy Sci 70, 2577-2584
19. Misztal I, Weigel K, Lawlor T (1995) Approximation of estimates of (co)variance components with multiple-trait restricted maximum likelihood by multiple diagonalization for more than one random effect. J Dairy Sci 78, 1862-1872
20. Pollak EJ, Quaas RL (1982) Alternative strategy for building multiple trait mixed model equations. J Dairy Sci 65, 102 (suppl 1)
21. Quaas RL (1988) Additive genetic model with groups and relationships. J Dairy Sci 71, 1338-1345
22. Quaas RL (1984) Linear prediction in BLUP school handbook. In: Use of Mixed Models for Prediction and for Estimation of (Co)variance Components, 5-7 February 1984, Animal Genetics and Breeding Unit, Univ of New England, New South Wales
23. Quaas RL, Pollak EJ (1981) Mixed model methodology for farm and ranch beef cattle testing programs. J Anim Sci 51, 1277-1287
24. Reents R, Swalve H (1991) Convergence in multi-trait animal models. In: 42nd Annual Meeting of the EAAP, Berlin, 8-12 February, vol I, 160 (Abstr)
25. Schaeffer LR (1984) Sire and cow evaluation under multiple trait models. J Dairy Sci 67, 1567-1580
26. Schaeffer LR, Kennedy B W (1986) Computing solutions to mixed model equations. In: 3rd World Congr Genet Appl Livest Prod, Lincoln, Nebraska, USA, 16-22 July 1986, vol XII, 382-393
27. Thompson R, Meyer K (1986) A review of theoretical aspects in the estimation of breeding values for multi-trait selection. Livest Prod Sci 15, 299-313
28. van der Werf J, van Arendonk J, de Vries A (1992) Improving selection of pigs using correlated characters. In: 43rd Annual Meeting of the EAAP, Madrid, 14-17 September 1992. vol I, 14 (Abstr)