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The forward order assumption postulates that the ranking process of the itemsis carried out by sequentially assigning the positions from the top(most-liked) to the bottom (least-liked) alternative. This assumption has beenrecently relaxed with the Extended Plackett-Luce model (EPL) through theintroduction of the discrete reference order parameter, describing the rankattribution path. By starting from two formal properties of the EPL, the formerrelated to the inverse ordering of the item probabilities at the first and laststage of the ranking process and the latter well-known as independence ofirrelevant alternatives (or Luce's choice axiom), we derive novel diagnostictools for testing the appropriateness of the EPL assumption as the actualsampling distribution of the observed rankings. Besides contributing to fillthe gap of goodness-of-fit methods for the family of multistage models, we alsoshow how one of the two statistics can be conveniently exploited to construct aheuristic method, that surrogates the maximum likelihood approach for inferringthe underlying reference order parameter. The relative performance of theproposals compared with more conventional approaches is illustrated by means ofextensive simulation studies.

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