Validation of models for analysis of ranks in horse breeding evaluation

The underlying model responsible for ranks performed well with unstructured competitions by drawing liabilities in the Gibbs sampler according to the following rule: the liability of each horse must be drawn in the interval formed by the liabilities of horses ranked before and after the particular horse. The estimated repeatability was the simulated one (0.25) and regression between estimated competing ability of horses and true ability was close to 1. Underestimations of repeatability (0.07 to 0.22) were obtained with other traditional criteria (normal score or raw ranks), but in the case of a structured competition, repeatability was underestimated (0.18 to 0.22). Our results show that the effect of an event, or category of event, is irrelevant in such a situation because ranks are independent of such an effect. The proposed mixture model pools horses according to their participation in different categories of competition during the period observed. This last model gave better results (repeatability 0.25), in particular, it provided an improved estimation of average values of competing ability of the horses in the different categories of events.The underlying model was validated. A correct drawing of liabilities for the Gibbs sampler was provided. For a structured competition, the mixture model with a group effect assigned to horses gave the best results.Ranks in competitions have been used in genetic evaluation of sport and race horses for a long time. Langlois [1] used transformed ranks to predict breeding values for jumping horses. Ranks were used through earnings; these are, roughly, a transcription of ranks into a continuous scale. Later, Tavernier [2,3], inspired by the model proposed by Henery [4] for races, used a model including underlying liabilities (" underlying model" hereinafter). This model explains the ranks as the observable outcome of a hierarchy of underlying normal performances of horses in competition. These underlying performances serve to es