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.