New algorithms and goodness-of-fit diagnostics from remarkable properties of ranking models

The forward order assumption postulates that the ranking process of the items is carried out by assigning the positions from the top (most-liked) to the bottom (least-liked) alternative. This assumption has been recently relaxed in 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, we derive novel diagnostic tools for testing appropriateness of the EPL assumption.We also show how one of the two statistics can be exploited to construct a heuristic method, that surrogates the maximum likelihood approach for inferring the underlying reference order. The performance of the proposals was compared with more conventional approaches through an extensive simulation study.