Remarkable properties for diagnostics and inference of ranking data modelling

Abstract

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.