Multiple-breed genetic inference using heavy-tailed structural models for heterogeneous residual variances.

Multiple-breed genetic models recently have been demonstrated to account for the heterogenous genetic variances that exist between different beef cattle breed groups. We extend these models to allow for residual heteroskedasticity (heterogeneous residual variances), specified as a function of fixed effects (e.g., sex, breed proportion, breed group heterozygosity) and random effects such as contemporary groups (CG). We additionally specify the residual distributions to be either Gaussian or based on heavier-tailed alternatives such as the Student's t or Slash densities. For each of these three residual densities using either homoskedastic (homogeneous variance) or heteroskedastic error specifications, we analyzed 22,717 postweaning gain records from a Nelore-Hereford population based on a Markov chain Monte Carlo animal model implementation. The heteroskedastic Student's t error model (with estimated df = 7.33 +/- 0.48) was clearly the best-fitting model based on a pseudo-Bayes factor criterion. Breed group heterozygosity and, to a lesser extent, calf sex seemed to be marginally important sources of residual heteroskedasticity. Specifically, the residual variance in F1 animals was estimated to be 0.70 +/- 0.16 times that for purebreds, whereas the male residual variance was estimated to be 1.13 +/- 0.09 times that for females. The CG effects were important random sources of residual heteroskedasticity (i.e., the coefficient of variation of CG-specific residual variances was estimated to be 0.72 +/- 0.06). Purebred Nelores were estimated to have a larger genetic variance (124.84 +/- 21.75 kg2) compared with Herefords (40.89 +/- 6.70 kg2) under the heteroskedastic Student's t error model; however, the converse was observed from results based on a homoskedastic Student's t error model (46.24 +/- 10.90 kg2 and 60.11 +/- 8.54 kg2, respectively). These results indicate that allowing for robustness to outliers and accounting for heteroskedasticity of residual variances has potentially important implications for variance component and genetic parameter estimates from data on multiple-breed populations.