  The forward order assumption 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. 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.
