Multiple-trait Gibbs sampler for animal models: flexible programs for Bayesian and likelihood-based (co)variance component inference.

A set of FORTRAN programs to implement a multiple-trait Gibbs sampling algorithm for (co)variance component inference in animal models (MTGSAM) was developed. The MTGSAM programs are available to the public. The programs support models with correlated genetic effects and arbitrary numbers of covariates, fixed effects, and independent random effects for each trait. Any combination of missing traits is allowed. The programs were used to estimate variance components for 50 replicates of simulated data. Each replicate consisted of 50 animals of each sex in each of four generations, for 400 animals in each replicate for two traits. For MTGSAM, informative prior distributions for variance components were inverted Wishart random variables with 10 df and means equal to the simulation parameters. A total of 15,000 Gibbs sampling rounds were completed for each replicate, with 2,000 rounds discarded for burn-in. For multiple-trait derivative free restricted maximum likelihood (MTDFREML), starting values for the variance components were the simulation parameters. Averages of posterior mean of variance components estimated using MTGSAM with informative and flat prior distributions for variance components and REML estimates obtained using MTDFREML indicated that all three methods were empirically unbiased. Correlations between estimates from MTGSAM using flat priors and MTDFREML all exceeded.99.

[1]  K. Meyer,et al.  DFREML—A Set of Programs to Estimate Variance Components Under an Individual Animal Model , 1988 .

[2]  Daniel Sorensen,et al.  Estimation of Genetic Variances from Unselected and Selected Populations , 1984 .

[3]  D. Gianola,et al.  Marginal inferences about variance components in a mixed linear model using Gibbs sampling , 1993, Genetics Selection Evolution.

[4]  I. D. Boer,et al.  Estimation of additive genetic variance when base populations are selected. , 1990 .

[5]  P. Odell,et al.  A Numerical Procedure to Generate a Sample Covariance Matrix , 1966 .

[6]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  J. V. D. van der Werf,et al.  Estimation of additive genetic variance when base populations are selected. , 1990, Journal of animal science.

[8]  K. Meyer Present status of knowledge about statistical procedures and algorithms to estimate variance and covariance components. , 1990 .

[9]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[10]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[11]  C. R. Henderson Comparison of Alternative Sire Evaluation Methods , 1975 .

[12]  C. R. Henderson Applications of linear models in animal breeding , 1984 .

[13]  D. Gianola,et al.  Variance estimation from integrated likelihoods (VEIL) , 1990, Genetics Selection Evolution.

[14]  D Gianola,et al.  Bayesian analysis of genetic change due to selection using Gibbs sampling , 1994, Genetics Selection Evolution.

[15]  D. Gianola,et al.  Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs , 1994, Genetics Selection Evolution.

[16]  L. Schaeffer Sire and Cow Evaluation Under Multiple Trait Models , 1984 .

[17]  D. Gianola,et al.  A framework for prediction of breeding value. , 1990 .

[18]  E. J. Pollak,et al.  Effects of Selection on Estimates of Variance Components Using Gibbs Sampling and Restricted Maximum Likelihood , 1995 .

[19]  Daniel Gianola,et al.  Bayesian Methods in Animal Breeding Theory , 1986 .

[20]  D Gianola,et al.  Bayesian inference in threshold models using Gibbs sampling , 1995, Genetics Selection Evolution.

[21]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[22]  D. Gianola,et al.  Bayesian Inference on Variance and Covariance Components for Traits Influenced by Maternal and Direct Genetic Effects, Using the Gibbs Sampler , 1994 .