In the analysis of qualification data from the FIRST Robotics Competition, the ratio of the number of observations to the number of parameters has been found to be quite small for the commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such a three-on-three game. With the finding of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models, we develop an effective method to estimate the number of clusters, clusters of robots, and robot strengths. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. Different from existing hierarchical classification systems, each step of ours is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the designed non-hierarchical classification system is to examine the possibility of reassigning robots to other cluster sets of robots. To reduce the overestimation of clusters by the mean squared prediction error criteria, the corresponding BIC are established as alternatives for model selection. By assembling these essential elements into a coherent whole, a systematic procedure is presented to perform the estimation. In addition, we propose two indices to measure the nested relation between cluster sets of two models and monotonic association between robot strengths of two models.
翻译:在对第一批机器人竞赛的资格数据进行分析时,发现观测数量与参数数量的比例对于常用的赢利率比值评级模型(WMPR)来说相当小。这通常导致在三对三的游戏中作出不精确的估算和不准确的预测。随着在估计机器人强力中发现一组特征,提议了一个具有潜在机器人群集的更灵活模型,以缓解WMPR模型的过分分解。由于其结构可被视为WMPR模型参数空间的尺寸缩小,因此机器人强力组的识别自然转化为模型选择问题模型。我们没有将大量相互竞争的模型进行比较,而是在这种三对三对三的游戏中得出不准确的估算和不准确的预测。新的方法包括两个部分:(一) 将等级和非等级的机器人分类组合组合组合结合起来,以确定候选模型的模式;和(二) 选择最佳模型,选择最佳模型。与现有的等级分类制度不同,我们每一步骤都是基于从先前的更精确的预测指数模型估算机器人强度模型,而不是将一个更精确的机器人强势的模型,将机器人强势的机组群集的精度和机体的机体结构的精度的精度的精度比再分析。