Validation of models for analysis of ranks in horse breeding evaluation

Ranks have been used as phenotypes in the genetic evaluation of horses for a long time through the use of earnings, normal score or raw ranks. A model, ("underlying model" of an unobservable underlying variable responsible for ranks) exists. Recently, a full Bayesian analysis using this model was developed. In addition, in reality, competitions are structured into categories according to the technical level of difficulty linked to the technical ability of horses (horses considered to be the "best" meet their peers). The aim of this article was to validate the underlying model through simulations and to propose a more appropriate model with a mixture distribution of horses in the case of a structured competition. The simulations involved 1000 horses with 10 to 50 performances per horse and 4 to 20 horses per event with unstructured and structured competitions.

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.