4,343 research outputs found

    Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes

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    In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a completely random measure. We characterise the posterior distribution given data, and derive a simple and effective Gibbs sampler for posterior simulation. We then develop a Dirichlet process mixture extension of our model and apply it to investigate the clustering of preferences for college degree programmes amongst Irish secondary school graduates. The existence of clusters of applicants who have similar preferences for degree programmes is established and we determine that subject matter and geographical location of the third level institution characterise these clusters.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS717 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Modelling rankings in R: the PlackettLuce package

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    This paper presents the R package PlackettLuce, which implements a generalization of the Plackett-Luce model for rankings data. The generalization accommodates both ties (of arbitrary order) and partial rankings (complete rankings of subsets of items). By default, the implementation adds a set of pseudo-comparisons with a hypothetical item, ensuring that the underlying network of wins and losses between items is always strongly connected. In this way, the worth of each item always has a finite maximum likelihood estimate, with finite standard error. The use of pseudo-comparisons also has a regularization effect, shrinking the estimated parameters towards equal item worth. In addition to standard methods for model summary, PlackettLuce provides a method to compute quasi standard errors for the item parameters. This provides the basis for comparison intervals that do not change with the choice of identifiability constraint placed on the item parameters. Finally, the package provides a method for model-based partitioning using covariates whose values vary between rankings, enabling the identification of subgroups of judges or settings that have different item worths. The features of the package are demonstrated through application to classic and novel data sets.Comment: In v2: review of software implementing alternative models to Plackett-Luce; comparison of algorithms provided by the PlackettLuce package; further examples of rankings where the underlying win-loss network is not strongly connected. In addition, general editing to improve organisation and clarity. In v3: corrected headings Table 4, minor edit

    Epitope profiling via mixture modeling of ranked data

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    We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the raw numerical responses is difficult or subject to criticism. We review standard distance-based and multistage ranking models and in this last context we propose an original generalization of the Plackett-Luce model to account for the order of the ranking elicitation process. The usefulness of the novel model is illustrated with its maximum likelihood estimation for a real data set. Specifically, we address the heterogeneous nature of experimental units via model-based clustering and detail the necessary steps for a successful likelihood maximization through a hybrid version of the Expectation-Maximization algorithm. The performance of the mixture model using the new distribution as mixture components is compared with those relative to alternative mixture models for random rankings. A discussion on the interpretation of the identified clusters and a comparison with more standard quantitative approaches are finally provided.Comment: (revised to properly include references

    Ranking relations using analogies in biological and information networks

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    Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects S={A(1):B(1),A(2):B(2),…,A(N):B(N)}\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}, measures how well other pairs A:B fit in with the set S\mathbf{S}. Our work addresses the following question: is the relation between objects A and B analogous to those relations found in S\mathbf{S}? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org
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