Mixed effects linear models with t-distributions for quantitative genetic analysis: A Bayesian approach

Genetics Selection Evolution

Volumn 31, Issue 1, 1999, Pages 25-42

  Strandén, Ismo ^a,b   Gianola, Daniel ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b ANIMAL PRODUCTION RESEARCH   (Finland)

Author keywords

Bayesian inference; Gibbs sampling; Mixed effects models; Robust estimation; Student's t distribution

Indexed keywords

ARTICLE; BAYES THEOREM; BREEDING; CATTLE; DATA ANALYSIS; EMBRYO TRANSFER; GENETIC ANALYSIS; OVULATION; SAMPLING; SIMULATION; STATISTICAL MODEL;

EID: 0033012612     PISSN: 0999193X     EISSN: None     Source Type: Journal    
DOI: 10.1051/gse:19990102     Document Type: Article

References (42)

1. Albert J.H., Chib S., Bayesian analysis of binary and polychotomous response data, J. Am. Stat. Assoc. 88 (1993) 669-679.
2. Besag J., Green P., Higdon D., Mengersen K., Bayesian computation and stochastic systems, Stat. Sci. 10 (1995) 3-66.
3. Box G.E.P., Tiao G.C., Bayesian Inference in Statistical Analysis, Wiley, New York, 1973.
4. Bulmer M.G., The Mathematical Theory of Quantitative Genetics, Clarendon Press, Oxford, 1980.
5. Casella G., George E.I., Explaining the Gibbs sampler, Am. Stat. 46 (1992) 167-174.
6. Falconer D.S., McKay T.F.C., An Introduction to Quantitative Genetics, 4th ed., Longman, New York, 1996.
7. Geweke J., Bayesian treatment of the independent Student-t linear model, J. Appl. Econometrics 8 (1993) S19-S40.
8. Gianola D., Fernando R.L., Bayesian methods in animal breeding theory, J. Anim. Sci. 63 (1986) 217-244.
9. Gianola D., Foulley J.L., Variance estimation from integrated likelihoods, Genet. Sel. Evol. 22 (1990) 403-417.
10. Gianola D., Foulley J.L., Fernando R.L., Prediction of breeding values when variances are not known, Genet. Sel. Evol. 18 (1986) 485-498.
11. Gianola D., Foulley J.L., Fernando R.L., Henderson C.R., Weigel K.A., Estimation of heterogeneous variances using empirical Bayes methods: theoretical considerations, J. Dairy Sci. 75 (1992) 2805-2823.
12. Goffinet B., Selection on selected records, Genet. Sel. Evol. 15 (1993) 91-97.
13. Harville D.A., Bayesian inference for variance components using only error contrasts, Biometrika 61 (1974) 383-385.
14. Harville D.A., Maximum likelihood approaches to variance component estimation and to related problems, J. Am. Stat. Assoc. 72 (1977) 320-340.
15. Harville D.A., BLUP (Best Linear Unbiased Prediction) and beyond, in: Gianola D., Hammond K. (Eds.), Advances in Statistical Methods for Genetic Improvement of Livestock, Springer-Verlag, Berlin, 1990, pp. 239-276.
16. Hazel L.N., The genetic basis for constructing selection indexes, Genetics 28 (1943) 476-490.
17. Henderson C.R., Specific and general combining ability, in: Gowan J.W. (Ed.), Heterosis, Iowa State College Press, Ames, IA, 1950, pp. 352-370.
18. Henderson C.R., Estimation of variance components and covariance components, Biometrics 9 (1953) 226-252.
19. Henderson C.R., Sire evaluation and genetic trends, in: Proceedings of the Animal Breeding and Genetics Symposium in honor of Dr J.L. Lush, Blacksburg, VA, August 1973, American Society of Animal Science, Champaign, IL, 1973, pp. 10-41.
20. Henderson C.R., Best linear unbiased estimation and prediction under a selection model, Biometrics 31 (1975) 423-447.
21. Henderson C.R., Applications of Linear Models in Animal Breeding, University of Guelph Press, Guelph, 1984.
22. Hobert J.P., Casella G., The effect of improper priors on Gibbs sampling in hierarchical linear models, J. Am. Stat. Assoc. 91 (1996) 1461-1473.
23. Kuhn M.T., Freeman A.E., Biases in predicted transmitting abilities of sires when daughters receive preferential treatment, J. Dairy Sci. 78 (1995) 2067-2072.
24. Kuhn M.T., Boettcher P.J., Freeman A.E., Potential biases in predicted transmitting abilities of females from preferential treatment, J. Dairy Sci. 77 (1994) 2428-2437.
25. Laird N.M., Ware J.H., Random effects models for longitudinal data, Biometrics 38 (1982) 963-974.
26. Lange K.L., Little R.J.A, Taylor J.M.G., Robust statistical modeling using the t distribution, J. Am. Stat. Assoc. 84 (1989) 881-896.
27. Lynch M., Walsh B., Genetics and Analysis of Quantitative Traits, Sinauer Associates, Sunderland, MA, 1997.
28. Meuwissen T.H.E., Goddard M., Selection of farm animals for non-linear traits and profits, Anim. Sci. 65 (1997) 1-8.
29. Patterson H.D., Thompson R., Recovery of interblock information when block sizes are unequal, Biometrika 58 (1971) 545-554.
30. Pinheiro J.C., Liu C., Wu Y., Robust estimation in linear mixed effects models using the multivariate-t distribution, Bell Labs Technical Report, 1997, 04/97.
31. San Cristobal M., Foulley J.L., Manfredi E., Inference about multiplicative heteroscedastic components of variance in a mixed linear Gaussian model with an application to beef cattle breeding, Genet. Sel. Evol. 25 (1993) 3-30.
32. Searle S.R., Casella G., McCulloch C., Variance Components, John Wiley, New York, 1992.
33. Smith H.F., A discriminant function for plant section, Ann. Eugenics 7 (1936) 240-250.
34. Sorensen D.A., Wang C.S., Jensen J., Gianola D., Bayesian analysis of genetic change due to selection using Gibbs sampling, Genet. Sel. Evol. 26 (1994) 333-360.
35. Strandén I., Robust mixed effects linear models with t-distributions and application to dairy cattle breeding, Ph.D. thesis, University of Wisconsin, Madison, WI, 1996.
36. Strandén I., Gianola D., Attenuating effects of preferential treatment with Student-t mixed linear models: a simulation study, Genet. Sel. Evol. 30 (1998) 565-583.
37. Sutradhar B.C., Ali M.M., Estimation of the parameters of a regression model with a multivariate t error variable, Comm. Stat. Theory Meth. 15 (1986) 429-450.
38. Verdinelli I., Wasserman L., Bayesian analysis of outlier problems using the Gibbs sampler, Stat. Comput. 1 (1991) 105-117.
39. Wang C.S., Rutledge J.J., Gianola D., Marginal inferences about variance components in a mixed linear model using Gibbs sampling, Genet. Sel. Evol. 25 (1993) 41-62.
40. Wang C.S., Rutledge J.J., Gianola D., Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs, Genet. Sel. Evol. 26 (1994) 91-135.
41. West M., Outlier models and prior distributions in Bayesian linear regression, J. R. Stat. Soc. B Met. 46 (1984) 431-439.
42. Zellner A., Bayesian and nou-Bayesian analysis of the regression model with multivariate Student-t error terms, J. Am. Stat. Assoc. 71 (1976) 400-405.