Poisson mixed models for the analysis of counts with an application to dairy cattle breeding

Several fitness traits in dairy cattle breeding are observed as counts and, therefore, may be appropriately studied with statistical models based on the Poisson distribution. In this thesis, attention was focussed on models for analysis of embryo yields after superovulation, and of number of artificial inseminations until conception.; An algorithm for computation of marginal maximum likelihood estimates of variance components in Poisson mixed models was developed. Laplacian integration of fixed and random effects was employed to marginalize the joint posterior density of all parameters. Computations are analogous to those in "derivative free" procedures employed in animal breeding. This method also permits hypothesis testing of variance components.; Embryo yields in the context of nucleus breeding schemes were simulated to assess mean squared error in parameter estimation. Poisson mixed models were better than linear models for estimation of fixed effects and variance components, but had a negligible superiority for prediction of random effects. Their advantages tended to increase with increasing true values of the fixed effects and of the variance components. The Bayes hierarchy in the Poisson mixed model was extended to allow for "extra-Poisson" variation due to uncertainty in the model structure; this leads to a negative binomial mixed model. With simulated overdispersed data, the negative binomial model was better than the Poisson model for estimation of variance components and prediction of random effects, but not for estimation of fixed location parameters.; The negative binomial and a linear mixed model were used to analyze number of artificial inseminations until conception in Holstein heifers. Service sire was an insignificant source of variation, whereas technician, herd and additive genetic components of variance were significant. Differences in predictive ability between the two models were trivial in spite of a larger heritability estimate (5.2% versus 1.3%) obtained with the negative binomial model.; A bivariate normal-Poisson mixed model, allowing for censoring, was developed. This model may be useful for investigating genetic and environmental relationships between production and fertility. Further extensions of models for analysis of counted variates in dairy cattle breeding were suggested.