Genetic analysis of fertility in dairy cattle using negative binomial mixed models

Two negative binomial mixed models with different dispersion specifications were compared for analysis of dairy reproduction count data. The first model was developed previously and had heterogeneous overdispersion in an associated logarithmic scale, assigning greater uncertainty to observations with smaller conditional expectations. The second model postulated homogeneous overdispersion across all data. A simulation study was used to compare marginal modal estimates of additive genetic variance, based on these two negative binomial models, with analogous estimates computed by an overdispersed Poisson mixed model. Estimators from the second negative binomial and overdispersed Poisson models had better frequentist properties than did those from the first negative binomial model. Nevertheless, application to a data set of number of artificial inseminations until conception in Holstein heifers suggested a slightly better fit of the first negative binomial model. A marginal likelihood ratio test indicated that the additive genetic variance was significant. Cross-validation analyses suggested that the two negative binomial mixed models had slightly better predictive ability than a linear mixed model.