Last modified: 2018-05-25
Abstract
Choice behavior and preferences typically involve numerous and subjec- tive aspects that are difficult to be identified and quantified. For this reason, their ex- ploration is frequently conducted through the collection of ordinal evidence in the form of ranking data. Multistage ranking models, including the popular Plackett- Luce distribution (PL), rely on the assumption that the ranking process is performed sequentially, by assigning the positions from the top to the bottom one (forward order). A recent contribution to the ranking literature relaxed this assumption with the addition of the discrete reference order parameter, yielding the novel Extended Plackett-Luce model (EPL). In this work, we introduce the EPL with order con- straints on the reference order parameter and a novel diagnostic tool to assess the adequacy of the EPL parametric specification. The usefulness of the proposal is illustrated with an application to a real dataset.
References
-
Alvo M, Yu PL (2014). Statistical methods for ranking data. Springer.
-
Critchlow DE, Fligner MA, Verducci JS (1991). “Probability models on rankings.†Journal of
Mathematical Psychology, 35(3), 294–318.
-
Marden JI (1995). Analyzing and modeling rank data, volume 64 of Monographs on Statistics
and Applied Probability. Chapman & Hall. ISBN 0-412-99521-2.
-
Mollica C, Tardella L (2014). “Epitope profiling via mixture modeling of ranked data.†Statis-
tics in Medicine, 33(21), 3738–3758. ISSN 0277-6715. doi:10.1002/sim.6224.
-
Mollica C, Tardella L (2017). “Bayesian mixture of Plackett-Luce models for partially ranked
data.†Psychometrika, 82(2), 442–458. ISSN 0033-3123. doi:10.1007/s11336-016-9530-0.
-
Mollica C, Tardella L (2018). “Algorithms and diagnostics for the analysis of preference rank- ings with the Extended Plackett-Luce model.†arXiv preprint: http://arxiv.org/abs/1803.02881.