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Revealing Subgroup Structure in Ranked Data Using a Bayesian WAND

Lookup NU author(s): Dr Stephen Johnson, Dr Daniel Henderson, Professor Richard Boys

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Abstract

© 2019, © 2019 American Statistical Association.Ranked data arise in many areas of application ranging from the ranking of up-regulated genes for cancer to the ranking of academic statistics journals. Complications can arise when rankers do not report a full ranking of all entities; for example, they might only report their top-M ranked entities after seeing some or all entities. It can also be useful to know whether rankers are equally informative, and whether some entities are effectively judged to be exchangeable. Revealing subgroup structure in the data may also be helpful in understanding the distribution of ranker views. In this paper, we propose a flexible Bayesian nonparametric model for identifying heterogeneous structure and ranker reliability in ranked data. The model is a weighted adapted nested Dirichlet (WAND) process mixture of Plackett–Luce models and inference proceeds through a simple and efficient Gibbs sampling scheme for posterior sampling. The richness of information in the posterior distribution allows us to infer many details of the structure both between ranker groups and between entity groups (within-ranker groups). Our modeling framework also facilitates a flexible representation of the posterior predictive distribution. This flexibility is important as we propose to use the posterior predictive distribution as the basis for addressing the rank aggregation problem, and also for identifying lack of model fit. The methodology is illustrated using several simulation studies and real data examples. Supplementary materials for this article are available online.


Publication metadata

Author(s): Johnson SR, Henderson DA, Boys RJ

Publication type: Article

Publication status: Published

Journal: Journal of the American Statistical Association

Year: 2019

Issue: ePub ahead of Print

Online publication date: 24/09/2019

Acceptance date: 22/08/2019

ISSN (print): 0162-1459

ISSN (electronic): 1537-274X

Publisher: American Statistical Association

URL: https://doi.org/10.1080/01621459.2019.1665528

DOI: 10.1080/01621459.2019.1665528


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