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Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects.

Kizilkaya K, Garrick DJ, Fernando RL, Mestav B, Yildiz MA - Genet. Sel. Evol. (2010)

Bottom Line: For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach.Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings.Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Animal Science, Iowa State University, Ames, 50011, USA. kadirk@iastate.edu

ABSTRACT

Background: The distribution of residual effects in linear mixed models in animal breeding applications is typically assumed normal, which makes inferences vulnerable to outlier observations. In order to mute the impact of outliers, one option is to fit models with residuals having a heavy-tailed distribution. Here, a Student's-t model was considered for the distribution of the residuals with the degrees of freedom treated as unknown. Bayesian inference was used to investigate a bivariate Student's-t (BSt) model using Markov chain Monte Carlo methods in a simulation study and analysing field data for gestation length and birth weight permitted to study the practical implications of fitting heavy-tailed distributions for residuals in linear mixed models.

Methods: In the simulation study, bivariate residuals were generated using Student's-t distribution with 4 or 12 degrees of freedom, or a normal distribution. Sire models with bivariate Student's-t or normal residuals were fitted to each simulated dataset using a hierarchical Bayesian approach. For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach. Residuals were defined to follow bivariate normal or Student's-t distributions with unknown degrees of freedom.

Results: Posterior mean estimates of degrees of freedom parameters seemed to be accurate and unbiased in the simulation study. Estimates of sire and herd variances were similar, if not identical, across fitted models. In the field data, there was strong support based on predictive log-likelihood values for the Student's-t error model. Most of the posterior density for degrees of freedom was below 4. Posterior means of direct and maternal heritabilities for birth weight were smaller in the Student's-t model than those in the normal model. Re-rankings of sires were observed between heavy-tailed and normal models.

Conclusions: Reliable estimates of degrees of freedom were obtained in all simulated heavy-tailed and normal datasets. The predictive log-likelihood was able to distinguish the correct model among the models fitted to heavy-tailed datasets. There was no disadvantage of fitting a heavy-tailed model when the true model was normal. Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings. Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.

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Posterior densities of direct (D) and maternal (M) heritabilities of gestation length (GL) and birth weight (BW) obtained from bivariate Student's-t (BSt) or normal (BN) models. h2D and h2M represent direct and maternal heritabilities.
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Figure 2: Posterior densities of direct (D) and maternal (M) heritabilities of gestation length (GL) and birth weight (BW) obtained from bivariate Student's-t (BSt) or normal (BN) models. h2D and h2M represent direct and maternal heritabilities.

Mentions: Posterior densities of direct and maternal heritabilities, and genetic correlations from BSt and BN models for GL and BW are shown in Figures 2 and 3. Posterior means of direct (0.47) and maternal (0.29) heritabilities from BSt and BN models were similar for GL. However, posterior means of direct (0.28) and maternal (0.23) heritabilities from BN models were higher than those (0.23 and 0.18) from the heavy-tailed model for BW (Figure 2). In contrast to our findings, Cardoso et al. [7] and Chang et al. [8] have found no real difference in posterior means for heritabilities whether using Student's-t, Slash or normal models. Posterior means of direct heritabilities from BSt and BN models for GL and BW traits were lower; however, those of maternal heritabilities were higher than the values reported by Ibi et al. [26] and Crews [27]. Posterior means (-0.87, -0.86) of genetic correlations between D and M effects of GL, and those (-0.73, -0.71) of BW from BSt and BN models in Figure 3 were significantly negative and very similar with overlapping posterior densities. They were higher than those reported in literature [26,27], and the negative posterior mean of the genetic correlation implies an antagonistic relationship between D and M effects. The posterior densities of genetic correlations between D effects on one trait and M effects on another included zero, indicating non-significant correlations.


Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects.

Kizilkaya K, Garrick DJ, Fernando RL, Mestav B, Yildiz MA - Genet. Sel. Evol. (2010)

Posterior densities of direct (D) and maternal (M) heritabilities of gestation length (GL) and birth weight (BW) obtained from bivariate Student's-t (BSt) or normal (BN) models. h2D and h2M represent direct and maternal heritabilities.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2909158&req=5

Figure 2: Posterior densities of direct (D) and maternal (M) heritabilities of gestation length (GL) and birth weight (BW) obtained from bivariate Student's-t (BSt) or normal (BN) models. h2D and h2M represent direct and maternal heritabilities.
Mentions: Posterior densities of direct and maternal heritabilities, and genetic correlations from BSt and BN models for GL and BW are shown in Figures 2 and 3. Posterior means of direct (0.47) and maternal (0.29) heritabilities from BSt and BN models were similar for GL. However, posterior means of direct (0.28) and maternal (0.23) heritabilities from BN models were higher than those (0.23 and 0.18) from the heavy-tailed model for BW (Figure 2). In contrast to our findings, Cardoso et al. [7] and Chang et al. [8] have found no real difference in posterior means for heritabilities whether using Student's-t, Slash or normal models. Posterior means of direct heritabilities from BSt and BN models for GL and BW traits were lower; however, those of maternal heritabilities were higher than the values reported by Ibi et al. [26] and Crews [27]. Posterior means (-0.87, -0.86) of genetic correlations between D and M effects of GL, and those (-0.73, -0.71) of BW from BSt and BN models in Figure 3 were significantly negative and very similar with overlapping posterior densities. They were higher than those reported in literature [26,27], and the negative posterior mean of the genetic correlation implies an antagonistic relationship between D and M effects. The posterior densities of genetic correlations between D effects on one trait and M effects on another included zero, indicating non-significant correlations.

Bottom Line: For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach.Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings.Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Animal Science, Iowa State University, Ames, 50011, USA. kadirk@iastate.edu

ABSTRACT

Background: The distribution of residual effects in linear mixed models in animal breeding applications is typically assumed normal, which makes inferences vulnerable to outlier observations. In order to mute the impact of outliers, one option is to fit models with residuals having a heavy-tailed distribution. Here, a Student's-t model was considered for the distribution of the residuals with the degrees of freedom treated as unknown. Bayesian inference was used to investigate a bivariate Student's-t (BSt) model using Markov chain Monte Carlo methods in a simulation study and analysing field data for gestation length and birth weight permitted to study the practical implications of fitting heavy-tailed distributions for residuals in linear mixed models.

Methods: In the simulation study, bivariate residuals were generated using Student's-t distribution with 4 or 12 degrees of freedom, or a normal distribution. Sire models with bivariate Student's-t or normal residuals were fitted to each simulated dataset using a hierarchical Bayesian approach. For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach. Residuals were defined to follow bivariate normal or Student's-t distributions with unknown degrees of freedom.

Results: Posterior mean estimates of degrees of freedom parameters seemed to be accurate and unbiased in the simulation study. Estimates of sire and herd variances were similar, if not identical, across fitted models. In the field data, there was strong support based on predictive log-likelihood values for the Student's-t error model. Most of the posterior density for degrees of freedom was below 4. Posterior means of direct and maternal heritabilities for birth weight were smaller in the Student's-t model than those in the normal model. Re-rankings of sires were observed between heavy-tailed and normal models.

Conclusions: Reliable estimates of degrees of freedom were obtained in all simulated heavy-tailed and normal datasets. The predictive log-likelihood was able to distinguish the correct model among the models fitted to heavy-tailed datasets. There was no disadvantage of fitting a heavy-tailed model when the true model was normal. Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings. Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.

Show MeSH