The Plackett-Luce model (PL) for ranked data assumes the forward order of the ranking process. This hypothesis postulates that the ranking process of the items is carried out by sequentially assigning the positions from the top (most liked) to the bottom (least liked) alternative. This assumption has been recently relaxed with the Extended Plackett-Luce model (EPL) through the introduction of the discrete reference order parameter, describing the rank attribution path. By starting from two formal properties of the EPL, the former related to the inverse ordering of the item probabilities at the first and last stage of the ranking process and the latter well-known as independence of irrelevant alternatives (or Luce's choice axiom), we derive novel diagnostic tools for testing the appropriateness of the EPL assumption as the actual sampling distribution of the observed rankings. These diagnostic tools can help uncovering possible idiosyncratic paths in the sequential choice process. Besides contributing to fill the gap of goodness-of-fit methods for the family of multistage models, we also show how one of the two statistics can be conveniently exploited to construct a heuristic method, that surrogates the maximum likelihood approach for inferring the underlying reference order parameter. The relative performance of the proposals, compared with more conventional approaches, is illustrated by means of extensive simulation studies.

中文翻译：

---

排名数据建模的诊断和推理的显着特性


排名数据的 Plackett-Luce 模型 (PL) 假定排名过程的前向顺序。该假设假设项目的排名过程是通过按顺序分配从顶部（最喜欢的）到底部（最不喜欢的）替代方案的位置来进行的。最近，通过引入描述排名归因路径的离散参考顺序参数，扩展 Plackett-Luce 模型 (EPL) 放宽了这一假设。通过从 EPL 的两个形式属性开始，前者与排序过程的第一阶段和最后阶段的项目概率的逆序相关，后者与不相关替代项的独立性（或 Luce 的选择公理）而闻名，我们推导出新颖的诊断工具，用于测试 EPL 假设作为观察到的排名的实际抽样分布的适当性。这些诊断工具可以帮助发现顺序选择过程中可能的特殊路径。除了有助于填补多阶段模型系列拟合优度方法的空白之外，我们还展示了如何方便地利用这两种统计量之一来构建启发式方法，该方法替代最大似然方法来推断基础参考订单参数。与更传统的方法相比，这些建议的相对性能通过广泛的模拟研究来说明。