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.