Submitted to: Journal of Animal Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/1/1996
Publication Date: N/A
Interpretive Summary: Theoretically, nonlinear statistical methods are more appropriate than linear methods for analysis of traits that fall into discrete classes such as fertility and number of lambs born. However, nonlinear methods are computationally more difficult than linear methods. Therefore, it is important to determine how advantageous nonlinear models are relative to linear models under the same set of circumstances. The purpose of this paper was to compare goodness of fit and predictive ability of linear, threshold, Poisson and Negative Binomial sire and animal models for reproductive traits in sheep. In terms of goodness of fit, nonlinear mixed models did not show any advantage over linear mixed models in the analysis of reproductive data in this study. Linear and threshold mixed models yielded similar results, and both outperformed Poisson and Negative Binomial mixed models. With respect to predictive ability, differences between linear and nonlinear mixed models were almost negligible. However due to problems in estimating variances with Poisson and Negative Binomial mixed models, no definitive conclusions can be drawn from these analyses. Animal and sire models did not differ in goodness of fit or predictive ability. Models for analyzing reproductive traits such as those analyzed in this study should take into account permanent environmental effects.
Technical Abstract: The performance of linear and nonlinear sire and animal models in the analyses of reproductive traits (fertility, litter size and ovulation rate) in two sheep populations was compared using the criteria of goodness of fit and predictive ability. Linear sire (LSM) and animal (LAM) models were used with all traits. Nonlinear models were the threshold, Poisson and Negative Binomial. Threshold sire (TSM) and animal (TAM) models were also used with all traits. Litter size and ovulation rate were also analyzed with Poisson and Negative Binomial sire (PSM and NBSM, respectively) and animal (PAM and NBAM, respectively) models. Variance components were those reported in a companion paper. For PAM a new set of variance components derived from the heritability found with the linear animal model was used (PAM-L). Mean square error (MSE) and correlations between fitted and observed values were the criteria for goodness of fit. Predictive ability was assessed by partitioning the data sets for the different traits into two subsets with the restriction that all levels of fixed effects were represented in each subset. Parameters from one subset were employed to predict observations in the other, and then MSE and correlations between observed and predicted values were used as criteria for model comparison. Within estimation procedure, breed and trait, goodness of fit of sire and animal models was rather similar. Linear and threshold models resulted in similar fit and both outperformed Poisson and Negative Binomial models. In terms of predictive ability, linear and threshold models performed only slightly better than Poisson and Negative Binomial models. Goodness of fit and predictive ability generally were better when models included permanent environment effects.