- Volume 44 Issue 2
DOI QR Code
Bayesian Analysis for Categorical Data with Missing Traits Under a Multivariate Threshold Animal Model
다형질 Threshold 개체모형에서 Missing 기록을 포함한 이산형 자료에 대한 Bayesian 분석
- Lee, Deuk-Hwan (Dept. of Animal Life and Resources, Hankyong National University)
- 이득환 (한경대학교 동물생명자원학과)
- Published : 2002.04.30
Genetic variance and covariance components of the linear traits and the ordered categorical traits, that are usually observed as dichotomous or polychotomous outcomes, were simultaneously estimated in a multivariate threshold animal model with concepts of arbitrary underlying liability scales with Bayesian inference via Gibbs sampling algorithms. A multivariate threshold animal model in this study can be allowed in any combination of missing traits with assuming correlation among the traits considered. Gibbs sampling algorithms as a hierarchical Bayesian inference were used to get reliable point estimates to which marginal posterior means of parameters were assumed. Main point of this study is that the underlying values for the observations on the categorical traits sampled at previous round of iteration and the observations on the continuous traits can be considered to sample the underlying values for categorical data and continuous data with missing at current cycle (see appendix). This study also showed that the underlying variables for missing categorical data should be generated with taking into account for the correlated traits to satisfy the fully conditional posterior distributions of parameters although some of papers (Wang et al., 1997; VanTassell et al., 1998) presented that only the residual effects of missing traits were generated in same situation. In present study, Gibbs samplers for making the fully Bayesian inferences for unknown parameters of interests are played rolls with methodologies to enable the any combinations of the linear and categorical traits with missing observations. Moreover, two kinds of constraints to guarantee identifiability for the arbitrary underlying variables are shown with keeping the fully conditional posterior distributions of those parameters. Numerical example for a threshold animal model included the maternal and permanent environmental effects on a multiple ordered categorical trait as calving ease, a binary trait as non-return rate, and the other normally distributed trait, birth weight, is provided with simulation study.
Threshold animal model;Missing trait;Bayesian nference;Liability;Identifiability
- Blasco, A. 2001. The Bayesian controversy in animal breeding. J. Anim. Sci. 79:2023-2046.
- Box, G. E. P. and Tiao, G. C. 1992. Bayesian inference in statistical analysis. New York. Wiley.
- Berger, P. J., Lin, E. C., Van Arendonk, J. and Janss, L. 1995. Properties of genetic parameter estimates from selection experiments by Gibbs sampling. J. Dairy Sci. 78 (Suppl 1):246.
- Datta, G. S. and Maiti, T. 1998. Multivariate Bayesian small area estimation: An application to survey and satellite data. The Indian J. of Statistics. 60:344-362.
- Djemali, M., Berger, P. J. and Freeman, A. E. 1987. Ordered categorical sire evaluation for dystocia in Holsteins. J. Dairy Sci. 70:2374-2384. https://doi.org/10.3168/jds.S0022-0302(87)80298-9
- Foulley, J. L., Gianola, D. and Hoeschele, I. 1987. Empirical Bayes estimation of parameters for n polygenic binary traits. Genet. Sel. Evol. 15:407-424.
- Foulley J. L., Gianola, D. and Thompson, R. 1983. Prediction of genetic merit from data on binary and quantitative variates with an application to calving difficulty, birth weight and pelvic opening. Genet. Sel. Evol. 15:407-424.
- Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. 1995. Bayesian data analysis. Chapman & Hall.
- Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intel. 6:721-741.
- Gianola, D. 1982. Theory and analysis of threshold characters. J. Anim. Sci. 54:1079-1096.
- Gianola, D. and Fouley, J. L. 1983. Sire evaluation for ordered categorical data with a threshold model. Genet. Sel. Evol. 15:201-244. https://doi.org/10.1186/1297-9686-15-2-201
- Hobert, J. and Casella, G. 1996. Effect of improper prior on Gibbs sampling in hierarchical linear mixed model. J. Am. Stat. Assoc. 91:1461- 1473.
- Hoeschele, I. B. and Tier, B. 1995. Estimation of variance components of threshold characters by marginal posterior mode and means via Gibbs sampling. Genet. Sel. Evol. 27:519-540.
- Jensen, J., Wang, C. S., Sorensen, D. and Gianola, D. 1994. Bayesian inference on variance and covariance components for traits influenced by maternal and direct genetic effects using the Gibbs sampler. Acta Agric Scand, Sect A, Anim. Sci. 44:193-201.
- Korsgaard, I. G., Andersen, A. H. and Sorensen, D. 1999. A usefull reparameterisation to obtain samples from conditional inverse Wishart distributions. Genet. Sel. Evol. 31:177-181.
- Lee, D. H., Rekaya, R. and Misztal, I. 2002. Analysis of Binary Data: Effect of Different Parameterizations on the Bias of Genetic Parameters. Asian J. Anim. Sci. (Submitted).
- Lee, D. H., Misztal, I., Bertrand, J. K. and Rekaya, R. 2001. Bayesian analysis of multiple- linear and categorical traits with varying number of categories. J. Anim. Sci. 79(suppl. 1):342.
- Li, S. C. and Lee, D. H. 2002. Bayesian analysis of threshold animal models with Gibbs sampling. Korean J. Stat. Sci. (accepted).
- Raftery, A. E. and Lewis, S. M. 1992. How many iterations in the Gibbs sampler? In: Bayesian Statistics IV, Oxford University Press, UK, 763-773.
- Rekaya, R. 2001. Bayesian inference in mixed linear model using Dirichlet process prior. J. Anim. Sci. 79(suppl. 1):110.
- Sorensen, D. A., Andersen, S., Gianola, D. and Korsgaard, I. 1995. Bayesian inference in threshold models using Gibbs sampling. Genet. Sel. Evol. 27:229-249.
- Sorensen, D. 1996. Gibbs sampling in quantitative genetics. Internal reports no. 82. from the Danish Institute of Animal Science.
- Sorensen, D., Wang, C. S., Jensen, J. and Gianola, D. 1994. Bayesian analysis of genetic trend due to selection to beef cattle breeding. Genet. Sel. Evol. 25:3-30.
- VanTassell, C. P., VanVleck, L. D. and Gregory, K. E. 1998. Bayesian analysis of twinning and ovulation rates using a multiple-trait threshold model and Gibbs sampling. J. Anim. Aci. 76: 2048-2061.
- Wang, C. S., Rutledge, J. J. and Gianola, D. 1994. Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs. Genet. Sel. Evol. 26:91-115.
- Wang, C. S., Quaas, R. L. and Pollak, E. J. 1997. Bayesian analysis of calving ease scores and birth weights. Genet. Sel. Evol. 20:117-143.
- Wright, S. 1934. An analysis of variability in number of digits in an inbred strain of guinea pigs. Genetics 19:506-536.