INRA, UMR 1313, 78352 Jouy-en-Josas, France.
Genet Sel Evol. 2010 Jan 28;42(1):3. doi: 10.1186/1297-9686-42-3.
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.
长期以来，排名一直被用作马匹遗传评估的表型，通过使用收益、标准分或原始排名。存在一种模型（负责排名的不可观测潜在变量的“基础模型”）。最近，开发了一种使用该模型的全贝叶斯分析。此外，在现实中，比赛根据与马匹技术能力相关的技术难度类别进行结构化（被认为是“最佳”的马匹与它们的同类竞争）。本文的目的是通过模拟验证基础模型，并在结构化比赛的情况下，提出一种更合适的混合马分布模型。模拟涉及 1000 匹马，每匹马有 10 到 50 次表现，每个比赛有 4 到 20 匹马，有无结构化和结构化比赛。
无结构化比赛中，排名的基础模型表现良好，通过根据以下规则在 Gibbs 采样器中抽取负债：每匹马的负债必须在该特定马前后排名的马的负债之间的区间内抽取。估计的可重复性为模拟值（0.25），并且马的估计竞争能力与真实能力之间的回归接近 1。使用其他传统标准（标准分或原始排名）时，可重复性会被低估（0.07 到 0.22），但在结构化比赛的情况下，可重复性会被低估（0.18 到 0.22）。我们的结果表明，在这种情况下，事件或事件类别的影响是无关紧要的，因为排名独立于这种影响。所提出的混合模型根据马在观察期间参加不同比赛类别的情况对其进行分组。最后一个模型给出了更好的结果（可重复性 0.25），特别是它提供了对不同类别的比赛中马的竞争能力的平均值的更好估计。
验证了基础模型。为 Gibbs 采样器提供了正确的负债抽取。对于结构化比赛，分配给马的群组效应混合模型给出了最佳结果。
