Classical and Bayesian Prediction as Applied to an Unbalanced Mixed Linear Model

Unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications, in small-area estimation, and in the analysis of comparative experiments. The problem considered is that of the point or interval prediction of the value of a linear combination of the fixed and random effects or the value of a future data point. A common approach is "empirical BLUP (best unbiased prediction)," in which an estimate of the variance ratio is regarded as the true value. Empirical BLUP is satisfactory-or can be made satisfactory by introducing appropriate modifications-unless the estimate of the variance ratio is imprecise and is close to zero, in which case more sensible point and interval predictions can be obtained by adopting a Bayesian approach. Two animal breeding examples are used to illustrate the similarities and differences between the Bayesian and empirical BLUP approaches.