Mixtures of distance-based models for ranking data
Computational Statistics & Data Analysis
Cranking: Combining Rankings Using Conditional Probability Models on Permutations
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Visualizing Incomplete and Partially Ranked Data
IEEE Transactions on Visualization and Computer Graphics
A latent space model for rank data
ICML'06 Proceedings of the 2006 conference on Statistical network analysis
Mixtures of weighted distance-based models for ranking data with applications in political studies
Computational Statistics & Data Analysis
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model-based clustering of high-dimensional data: A review
Computational Statistics & Data Analysis
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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.