A Mixed Effects Model for Overdispersed Count Data in Animal Breeding

Abstract

Count data models are developed for breeding applications to account for more variability than in a Poisson mixed effects model. A gamma distribution is assigned to Poisson parameters, thereby leading to a negative binomial model. The natural log of the expected value of the Poisson parameter is expressed as a linear function of fixed and random polygenic effects. The negative binomial and Poisson mixed models were compared in two simulations. In the first, marginal maximum likelihood (MML) estimates of genetic variances obtained under a Poisson sire model (PSM) and under a Poisson animal model (PAM), accounting for half-sib relationships, were different, contrary to what occurs in a Gaussian mixed linear model. MML estimates of genetic variance under a negative binomial sire model were less biased than estimates under a PSM, and had a slightly smaller mean squared error (MSE). The second simulation compared animal models in which the variance of the residuals was larger than the genetic variance. Empirical relative bias and MSE of MML estimates of genetic variance were larger under a PAM that ignored the residuals than under a negative binomial model. Differences in performance widened as genetic variance increased. An application to the analysis of number of artificial inseminations until conception in dairy heifers is presented to illustrate potential differences in genetic variance estimates under the two models.