BAYESIAN AND LIKELIHOOD INFERENCE USING MTGSAM:MULTIPLE TRAIT GIBBS SAMPLER FOR ANIMAL MODELS

Authors: Van Tassell, Curtis - Curt; Van Vleck, Lloyd

Submitted to: Western Regional Coordinating Committee for National Cattle Evaluation
Publication Type: Proceedings
Publication Acceptance Date: 2/2/1996
Publication Date: N/A
Citation: N/A

Interpretive Summary: A set of general Fortran computer programs were developed to implement a new statistical tool, Gibbs sampling. The programs are available to the public. The theoretical background for the method is described. There are several advantages to using Gibbs sampling. First, a distribution of para- meter is estimated rather than a single point estimate which is obtained with traditional maximum likelihood methods. Second, larger data sets may be used for analysis because of the nature of the numerical algorithm. Finally, more complex models (including more traits) may be used than with traditional methods. The programs were evaluated using simulated data. The average parameter estimates agreed well with those obtained using a standard maximum likelihood method. Both methods were empirically unbiased. .36.

Technical Abstract: A set of flexible 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 sample for two traits. Simulation parameters and averages of posterior mean estimates of variance components using MTGSAM with informative and flat prior distributions for variance components and multiple trait derivative free restricted maximum likelihood (MTDFREML) indicate that all three methods were empirically unbiased. The correlations of estimates from MTGSAM using flat priors and MTDFREML all exceeded .99. For MTGSAM, informative prior distributions for variance components were inverted Wishart variables with 10 df and means equal to the simulation parameters. A total of 15,000 Gibbs sampling rounds were completed for each sample, with 2000 rounds discarded for burn-in. For MTDFREML, starting values for the variance components were the simulation parameters.