A generative model for rank data based on insertion sort algorithm

Christophe Biernacki and Julien Jacques

Computational Statistics & Data Analysis, 2013, vol. 58, issue C, 162-176

Abstract: An original and meaningful probabilistic generative model for full rank data modelling is proposed. Rank data arise from a sorting mechanism which is generally unobservable for statisticians. Assuming that this process relies on paired comparisons, the insertion sort algorithm is known as being the best candidate in order to minimize the number of potential paired misclassifications for a moderate number of objects to be ordered. Combining this optimality argument with a Bernoulli event during a paired comparison step, a model that possesses desirable theoretical properties, among which are unimodality, symmetry and identifiability is obtained. Maximum likelihood estimation can also be performed easily through an EM or a SEM–Gibbs algorithm (depending on the number of objects to be ordered) by involving the latent initial presentation order of the objects. Finally, the practical relevance of the proposal is illustrated through its adequacy with several real data sets and a comparison with a standard rank data model.

Keywords: Full rank data; Sorting process; Insertion sort algorithm; EM algorithm; Quiz data (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947312003118
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:58:y:2013:i:c:p:162-176

DOI: 10.1016/j.csda.2012.08.008

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().