Generalized linear mixed models in dairy cattle breeding.

Fitness and fertility traits of dairy cattle are of increasing importance and are often measured on a discrete scale. The development and application of generalized linear mixed models to the genetic analysis of these traits are reviewed. Because current genetic evaluation systems are predominantly based on animal models, the inferential challenges of highly parameterized generalized linear mixed models are discussed. Development and adoption of new methods for drawing appropriate inferences on dispersion parameters are essential. Recent hierarchical extensions have been proposed for generalized linear mixed models, allowing for complex dispersion patterns that accommodate heteroscedasticity and outlier robustness. Steady advances in available computing power have facilitated multiple-trait analyses involving continuous and discrete measures. Full Bayesian inference via the development of Markov Chain Monte Carlo methods will continue to allow even greater generality and dimensions in the genetic model.