An 'average information' restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices

Genetics Selection Evolution

Volumn 29, Issue 2, 1997, Pages 97-116

  Meyer, K ^a  

^a UNIVERSITY OF NEW ENGLAND   (Australia)

Author keywords

average information; covariance components; covariance function; equal design matrices; reduced rank; REML

Indexed keywords

ALGORITHM; ANIMAL MODEL; ARTICLE; AVERAGE; COVARIANCE; DERIVATIZATION; LINEAR SYSTEM; NONHUMAN; QUANTITATIVE TRAIT;

EID: 0030960213     PISSN: 0999193X     EISSN: None     Source Type: Journal    
DOI: 10.1051/gse:19970201     Document Type: Article

References (27)

1. Abramowirz M, Stegun IA (1965) Handbook of Mathematical Functions. Dover. New York
2. Flury B, Constantine G (1985) Algorithm AS 211: The F-G diagonalization algorithm. Appl Stat. 177-180
3. George A, Liu J W-H (1981) Computer Solution of Large Positive Definite Systems. Prentice-Hall Inc. Englewood Cliffs, New Jersey
4. Gilmour AR, Thompson R, Cullis BR (1995) Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics 51, 1440-1450
5. Graser HU, Smith SP, Tier B (1987) A derivative-free approach for estimating variance components in animal models by restricted maximum likelihood. J Anim Sci 64, 1362-1370
6. Graybill, FA (1969) Introduction to Matrices with Applications in Statistics. Wadsworth Publishing Company. Inc, Belmont, California
7. Harville, DA (1977) Maximum likelihood approaches to variance component estimation and related problems. J Amer Stat Ass 72, 320-338
8. Jensen J, Mao IL (1988) Transformation algorithms in analysis of single trait and of multitrait models with equal design matrices and one random factor per trait: a review. J Anim Sci 66, 2750-2761
9. Jensen J, Mantysaari E, Madsen P, Thompson R (1995) Restricted Maximum Likelihood estimation of (co)variance components in multivariate linear models using average of observed and expected information. In: 2nd European Workshop on Advanced Biometrical Methods in Animal Breeding, Salzburg, 12-20 June, 1995, Mimeo, 17 p
10. Johnson DL, Thompson R (1994) Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. Proc 5th World Congr Genet Appl Livest Prod, University of Guelph, Guelph, vol 18, 410-413
11. Johnson DL, Thompson R (1995) Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. J Dairy Sci 78, 449-456
12. Kirkpatrick M, Heckman N (1989) A quantitative genetic model for growth, shape and other infinite-dimensional characters. J Math Biol 27, 429-450
13. Kirkpatrick M, Lofsvold D, Bulmer M (1990) Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124, 979-993
14. Kirkpatrick M, Hill WG, Thompson R (1994) Estimating the covariance structure of traits during growth and aging, illustrated with lactations in dairy cattle. Genet Res 64, 57-69
15. Lin CY, Smith S.P. (1990) Transformation of multi-trait to unitrait mixed model analysis of data with multiple random effects. J Dairy Sci 73, 2494-2502
16. Lindstrom MJ, Bates DM (1988) Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. J Amer Stat Ass 83, 1014-1022
17. Madsen P, Jensen J, Thompson R (1994) Estimation of (co) variance components by REML in multivariate mixed linear models using average of observed and expected information. Proc 5th World Congr Genet Appl Livest Prod, University of Guelph, Guelph, Vol 22, 19-22
18. Marquardt DW (1963) An algorithm for least squares estimation of nonlinear parameters. SIAM J 11, 431-441
19. Meyer K (1985) Maximum likelihood estimation of variance components for a multivariate mixed model with equal design matrices. Biometrics 41, 153-166
20. Meyer K (1989) Restricted maximum likelihood to estimate variance components for animal models with several random effects using a derivative-free algorithm. Genet Select Evol 21, 317-340
21. Meyer K (1991) Estimating variances and covariances for multivariate animal models by restricted maximum likelihood. Genet Selct Evol 23, 67-83
22. Meyer K, Smith SP (1996) Restricted maximum likelihood estimation for animal models using derivatives of the likelihood. Genet Select Evol 28, 23-49
23. Meyer K. Hill WG (1997) Estimation of genetic and phenotypic covariance functions for longitudinal or 'repeated' records by restricted maximum likelihood. Livest Prod Sci (in press)
24. Misztal I (1994) Comparison of computing properties of derivative and derivative-free algorithms in variance component estimation by REML. J Anim Breed Genet 111, 346-355
25. Searle SR (1982) Matrix Algebra Useful for Statistics. John Wiley & Sons, New York
26. Smith SP (1995) Differentiation of the Cholesky algorithm. J Comp Graph Stat 4, 134-147
27. Takahashi K, Fagan J, Chin MS (1973) Formation of sparse bus impedance matrix and its application to short circuit study. Proc 8th Inst PICA Conf Minneapolis, Mineapolis, 63-69; cited by Smith (1995)