Estimating covariance functions for longitudinal data using a random regression model

Genetics Selection Evolution

Volumn 30, Issue 3, 1998, Pages 221-240

  Meyer, Karin ^a,b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF NEW ENGLAND   (Australia)

Author keywords

Covariance functions; Genetic parameters; Longitudinal data; Random regression model; Restricted maximum likelihood

Indexed keywords

EID: 0001426561     PISSN: 0999193X     EISSN: None     Source Type: Journal    
DOI: 10.1051/gse:19980302     Document Type: Article

References (36)

1. Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, Dover, New York, 1965.
2. Anderson S., Pedersen B., Growth and food intake curves for group-housed gilts and castrated male pigs, Anim. Sci 63 (1996) 457-464.
3. Frayley C., Burns P.J., Large-scale estimation of variance and covariance components, SIAM J. Sci. Comp. 16 (1995) 192-209.
4. Graybill F.A., An Introduction to Linear Statistical Models, Volume I, McGraw-Hill, Inc., New York, 1961.
5. Graybill F.A., Matrices with Applications in Statistics, 2nd ed., Wadsworth Inc., 1983.
6. Groeneveld E., A reparameterisation to improve numerical optimisation in multivariate REML (co)variance component estimation. Genet. Sel. Evol. 26 (1994) 537-545
7. Härdle W., Applied Nonparametric Regression, Cambridge University Press, 1990.
8. Harville D.A., Maximum likelihood approaches to variance component estimation and related problems, J. Am. Stat. Assoc. 72 (1977) 320-338.
9. Henderson C.R. Jr., Analysis of covariance in the mixed model: Higher-level, non-homogeneous and random regressions, Biometrics 38 (1982) 623-640.
10. Jamrozik J., Schaeffer L.R., Estimates of genetic parameters for a test day model with random regressions for production of first lactation Holsteins, 3. Dairy Sci. 80, 1997) 762-770.
11. Jamrozik J., Schaeffer L.R., Dekkers J.C.M., Genetic evaluation of dairy cattle using test day yields and random regression model, J. Dairy Sci. 80 (1997) 1217-1226.
12. Jennrich R.I., Schluchter M.D., Unbalanced repeated-measures models with structured covariance matrices, Biometrics 42 (1986) 805-820.
13. Johnson D.L., Thompson R., Restricted Maximum Likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information, J. Dairy Sci. 78 (1995) 449-456.
14. Kettunen A., Mäntysaari E., Stranden I., Pösö J., Genetic parameters for test day milk yields of Finnish Ayrshires with random regression model, J. Dairy Sci. 80 Suppl. 1, 197 (1997) (abstr.).
15. Kirkpatrick M., Lofsvold D., Bulmer M., Analysis of the inheritance, selection and evolution of growth trajectories, Genetics 124 (1990) 979-993.
16. Kirkpatrick M., Hill W.G., Thompson R., Estimating the covariance structure of traits during growth and aging, illustrated with lactations in dairy cattle, Genet. Res. 64 (1994) 57-69.
17. Lindsey J.K., Models for Repeated Measurements, Oxford Statistical Science Series, Clarendon Press, Oxford, 1993.
18. Lindstrom M.J., Bates D.M., Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data, J. Am. Stat. Assoc. 83 (1988) 1014-1022.
19. Longford N.T., Random Coefficient Models, Oxford Statistical Science Series, Clarendon Press, Oxford, 1993.
20. Madsen P., Jensen J., Thompson R., 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. Vol. 22 (1994) 19-22.
21. Meyer K., Estimating variances and covariances for multivariate animal models by Restricted Maximum Likelihood, Genet. Sel. Evol. 23 (1991) 67-83.
22. Meyer K., An "average information" Restricted Maximum Likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices, Genet. Sel. Evol. 29 (1997) 97-116.
23. Meyer K., 'DXMRR' - A program to estimate covariance functions for longitudinal data by Restricted Maximum Likelihood, Proc. 6th World Congr. Genet. Appl. Livest. Prod. Vol. 27 (1998) 465-466.
24. Meyer K., Hill W.G., Estimation of genetic and phenotypic covariance functions for longitudinal or 'repeated' records by restricted maximum likelihood, Livest. Prod. 47 (1997) 185-200.
25. Meyer K., Smith S.P., Restricted Maximum Likelihood estimation for animal models using derivatives of the likelihood, Genet. Sel. Evol. 28 (1996) 23-49.
26. Pinheiro J.C., Bates D.M., Unconstrained parameterizations for variance-covariance matrices, Stat. Comp. 6 (1996) 289-296.
27. Robert-Granié C., Ducrocq V., Foulley J.L., Heterogeneity of variance for type traits in the Montbeliarde cattle breed, Genet. Sel. Evol. 29 (1997) 545-570.
28. Schaeffer L.R., Dekkers J.C.M., Random regressions in animal models for test-day production in dairy cattle, Proc. 5th World Congr. Genet. Appl. Livest. Prod. Vol. 18 (1994) 443-446.
29. Self S.G., Liang K.Y., Asymptotic properties of the maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, J. Am. Stat. Assoc. 82 (1987) 605-610.
30. Shah A., Laird N., Schoenfeld D., A random-effects model for multiple characteristics with possibly missing data, J. Am. Stat. Assoc. 92 (1997) 775-779.
31. Stram D.A., Lee J.W., Variance component testing in the longitudinal model, Biometrics 50, (1994) 1171-1177.
32. Thompson R., The estimation of maternal genetic variance, Biometrics 32 (1976) 903-917.
33. Varona L., Moreno G., Garcia-Cortes L.A., Altarriba J., Multiple trait genetic analysis of underlying biological variables of production functions, Livest. Prod. Sci. 47 (1997) 201-210.
34. Vonesh E.F., Chinchilli V.M., Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker Inc, New York, 1997.
35. Wishart J., Growth-rate determinations in nutrition studies with the bacon pig and their analysis, Biometrics 30 (1938) 16-28.
36. Wolfinger R.D., Heterogeneous variance-covariance structures for repeated measures data, J. Agric. Biol. Environ. Stat. 1 (1996) 205-230.