1,720,994 research outputs found
Extending parametric models for ranked data
Full text linkThe thesis deals with the problem of analyzing ranking data and focuses, in particular, on the probabilistic modeling of complete/partial rankings drawn from populations with an underlying group composition. After a structured review of the literature on statistical ranking models, the dissertation concentrates on the stagewise parametric modeling and, in this context, develops some original extensions of the popular Plackett-Luce model, aimed at accounting for the order in the ranking elicitation process. The thesis further generalizes such contributions to the finite mixture framework to address heterogeneous configurations of the target population. Corresponding inferential procedures are detailed and rely on a hybrid iterative technique that, in order to efficiently solve the likelihood optimization over a mixed-type parameter space, combines the ordinary EM scheme with Minorization-Maximization algorithm. As additional contribution the dissertation illustrates a Bayesian finite mixture of Plackett-Luce models, that extends a Bayesian device recently introduced in the literature. It describes an efficient way to incorporate the latent group structure in the data augmentation approach and how to interpret existing maximum likelihood procedures as special instances of the proposed Bayesian analysis. Bayesian inference is conducted with the combination of the EM algorithm for maximum a posteriori estimation and the Gibbs sampling procedure, paying special attention on the identifiability problems that can affect the results of the MCMC technique. The practical relevance of the methodological proposals are illustrated with applications to both simulated and real data sets
PLMIX: Bayesian Analysis of Finite Mixtures of Plackett-Luce Models for Partial Rankings/Orderings
No full textFit finite mixtures of Plackett-Luce models for partial top rankings/orderings within the Bayesian framework. It provides MAP point estimates via EM algo- rithm and posterior MCMC simulations via Gibbs Sampling. It also fits MLE as a special case of the noninformative Bayesian analysis with vague priors. In addition to inferential techniques, the package assists other fundamental phases of a model-based analysis for par- tial rankings/orderings, by including functions for data manipulation, simulation, descriptive summary, model selection and goodness-of-fit evaluation
Bayesian binary quantile regression for the analysis of Bachelor-Master transition
No full textThe multi-cycle organization of the modern university systems stimulates
the interest in studying the progression to higher level degree courses during the
academic career. In particular, after the achievement of the first level qualification
(Bachelor degree), students have to decide whether to continue their university studies,
by enrolling in a second level (Master) programme, or to conclude their training
experience. In this work we propose a binary quantile regression approach to analyse
the Bachelor-Master transition adopting the Bayesian inferential perspective.
Quantile regression represents a well-established and useful device to gain a more
in-depth understanding of the relation between the outcome of interest and the explanatory
variables. By using the data augmentation strategy, quantile regression
modeling for continuous responses has been recently extended for the treatment of
binary response variables. We illustrate the utility of the Bayesian binary quantile
regression approach to characterize the non-continuation decision with an application
to administrative data of Bachelor graduates at the Faculty of Economics of
“’Sapienza” University of Rome
Bayesian mixture of Extended Plackett-Luce models for the analysis of preference rankings
No full textChoice behavior and preferences typically involve numerous and subjective
aspects that are difficult to be identified and quantified. For this reason their
exploration is frequently conducted through the collection of ordinal evidence in the
form of ranking data. A ranking is an ordered sequence resulting from the comparative
evaluation of a given set of items according to a specific criterion. 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 reference order
parameter, yielding the novel Extended Plackett-Luce model (EPL). Inference on the
EPL and its generalization into a finite mixture framework was originally addressed
from the frequentist perspective. In this work we propose the Bayesian estimation
of the EPL mixture. The Bayesian extension benefits from the data augmentation
strategy and the conjugacy of the PL with the Gamma prior distribution, by making
use of a Metropolis-Hastings step within the Gibbs Sampling scheme to simulate
the discrete reference order parameter. The usefulness of the proposal is illustrated
with applications to simulated and real datasets
Bayesian analysis of ranking data with the Extended Plackett-Luce model
Full text linkMultistage 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-valued reference order parameter, yielding the novel Extended Plackett-Luce model (EPL). Inference on the EPL and its generalization into a finite mixture framework was originally addressed from the frequentist perspective. In this work, we propose the Bayesian estimation of the EPL in order to address more directly and efficiently the inference on the additional discrete-valued parameter and the assessment of its estimation uncertainty, possibly uncovering potential idiosyncratic drivers in the formation of preferences. We overcome initial difficulties in employing a standard Gibbs sampling strategy to approximate the posterior distribution of the EPL by combining the data augmentation procedure and the conjugacy of the Gamma prior distribution with a tuned joint Metropolis-Hastings algorithm within Gibbs. The effectiveness and usefulness of the proposal is illustrated with applications to simulated and real datasets
Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition
Full text linkThe multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary respons
Bayesian mixture of Plackett-Luce models for partially ranked data
No full textThe Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze partial top-rankings of a finite set of items. A Bayesian finite mixture of Plackett-Luce models is illustrated, that extends a Bayesian device recently introduced in the literature in order to account for unobserved sample heterogeneity. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and how to interpret existing maximum likelihood procedures as special instances of the proposed Bayesian analysis. Bayesian inference is conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure, with a focus on the identifiability problems that can affect the results of the MCMC technique. The novel Bayesian Plackett- Luce mixture is illustrated with an analysis of real preference partially ranked data, which discusses the application of several relabeling algorithms to solve the label-switching issue and the resulting posterior estimates
Remarkable properties for diagnostics and inference of ranking data modelling
Full text linkThe Plackett‐Luce model (PL) for ranked data assumes the forward order of the ranking process. This hypothesis postulates that the ranking process of the items is carried out by sequentially assigning the positions from the top (most liked) to the bottom (least liked) alternative. This assumption has been recently relaxed with the Extended Plackett‐Luce model (EPL) through the introduction of the discrete reference order parameter, describing the rank attribution path. By starting from two formal properties of the EPL, the former related to the inverse ordering of the item probabilities at the first and last stage of the ranking process and the latter well‐known as independence of irrelevant alternatives (or Luce's choice axiom), we derive novel diagnostic tools for testing the appropriateness of the EPL assumption as the actual sampling distribution of the observed rankings. These diagnostic tools can help uncovering possible idiosyncratic paths in the sequential choice process. Besides contributing to fill the gap of goodness‐of‐fit methods for the family of multistage models, we also show how one of the two statistics can be conveniently exploited to construct a heuristic method, that surrogates the maximum likelihood approach for inferring the underlying reference order parameter. The relative performance of the proposals, compared with more conventional approaches, is illustrated by means of extensive simulation studies
Epitope profiling via mixture modeling of ranked data
No full textWe 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 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 the 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 then compared with 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
Mixture models for ranked data classification
No full textAnalysis of ranking data is required in several research fields. In the present work we review statistical models for random rankings and propose an original generalization of a popular parametric distribution, that we name extended Plackett-Luce model, to account for the order of the ranking elicitation process. We illustrate the validity of the novel model with its successful maximum likelihood estimation from the real data set of the Large Fragment Phage Display (LFPD) ex- periment, where the epitope mapping of a specific human protein is the main goal. In particular we address the heterogeneous nature of theexperimental units via a finite mixture model approach and compare the performances when alternative ranking models are employed as mixture component
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