Assessment of a poisson animal model for embryo yield in a simulated multiple ovulation-embryo transfer scheme

Abstract

Estimation and prediction techniques for Poisson and linear animal models were compared in a simulation study where observations were modelled as embryo yields having a Poissson residual distribution. In a one-way model (fixed mean plus random animal effect) with genetic variance (σµ2) equal to 0.056 or 0.125 on a log linear scale, Poisson marginal maximum likelihood (MML) gave estimates of σµ2 with smaller empirical bias and mean squared error (MSE) than restricted maximum likelihood (REML) analyses of raw and log-transformed data. Likewise, estimates of residual variance (the average Poisson parameter) were poorer when the estimation was by REML. These results were anticipated as there is no appropriate variance decomposition independent of location parameters in the linear model. Predictions of random effects obtained from the mode of the joint posterior distribution of fixed and random effects under the Poisson mixed-model tended to have smaller empirical bias and MSE than best linear unbiased prediction (BLUP). Although the latter method does not take into account nonlinearity and does not make use of the assumption that the residual distribution was Poisson, predictions were essentially unbiased. After log transformation of the records, however, BLUP led to unsatisfactory predictions. When embryo yields of zero were ignored in the analysis, Poisson animal models accounting for truncation outperformed REML and BLUP. A mixed-model simulation involving one fixed factor (15 levels) and 2 random factors for 4 sets of variance components was also carried out; in this study, REML was not included in view of highly heterogeneous nature of variances generated on the observed scale. Poisson MML estimates of variance components were seemingly unbiased, suggesting that statistical information in the sample about the variances was adequate. Best linear unbiased estimation (BLUE) of fixed effects had greater empirical bias and MSE than the Poisson estimates from the joint posterior distribution, with differences between the 2 analyses increasing with the genetic variance and with the true values of the fixed effects. Although differences in prediction of random effects between BLUP and Poisson joint modes were small, they were often significant and in favor of those obtained with the Poisson mixed model. In conclusion, if the residual distribution is Poisson, and if the relationship between the Poisson parameter and the fixed and random effects is log linear, REML and BLUE may lead to poor inferences, whereas the BLUP of breeding values is remarkably robust to the departure from linearity in terms of average bias and MSE.