Bayesian analysis of order-statistics models for ranking data

Yu, Philip L. H.

doi:10.1007/bf02296147

Cited by 37 publications

(31 citation statements)

References 52 publications

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“…Others have proposed fullinformation maximum likelihood methods using Monte Carlo expectation-maximization algorithms (Poon & Lu, 2009;Xu, Poon, & Lee, 2008). Yao and Böckenholt (1999) and Yu (2000) showed that Bayesian Thurstonian ranking models are amenable to Markov chain Monte Carlo (MCMC) algorithms by using data augmentation with Gibbs sampling (Gelfand & Smith, 1990;Tanner & Wong, 1987). Using this approach, the unobserved differences are specified as missing data in a complete-data likelihood function to create the Bayesian probability model:…”

Section: Estimation Methodsmentioning

confidence: 99%

“…The mean and variance are often specified as being constant over observations, although some researchers have discussed letting the mean μ i vary over observations, due to its dependence on covariates (e.g., Yu, 2000). This is not a major extension of the model, but it is worth discussion since, in practice, covariates are common and there are some important considerations in terms of how their effects are specified and identified.…”

Section: Including Covariatesmentioning

confidence: 99%

“…Our recommendation is to limit inferences to this covariance matrix. Although there are various constraints that can be imposed on Σ so that it is identified (see Yu, 2000), these constraints, while technically convenient, are not particularly meaningful. The scale of the latent responses is not set, meaning that the probability of a given rank order does not change if μ i and CΣC 0 are multiplied by d and ffiffiffi d p , respectively, for any d > 0.…”

Section: Parameter Identificationmentioning

confidence: 99%

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Bayesian Thurstonian models for ranking data using JAGS

Johnson

Kuhn

2013

Behav Res

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A Thurstonian model for ranking data assumes that observed rankings are consistent with those of a set of underlying continuous variables. This model is appealing since it renders ranking data amenable to familiar models for continuous response variables-namely, linear regression models. To date, however, the use of Thurstonian models for ranking data has been very rare in practice. One reason for this may be that inferences based on these models require specialized technical methods. These methods have been developed to address computational challenges involved in these models but are not easy to implement without considerable technical expertise and are not widely available in software packages. To address this limitation, we show that Bayesian Thurstonian models for ranking data can be very easily implemented with the JAGS software package. We provide JAGS model files for Thurstonian ranking models for general use, discuss their implementation, and illustrate their use in analyses.

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Section: Estimation Methodsmentioning

confidence: 99%

Section: Including Covariatesmentioning

confidence: 99%

Section: Parameter Identificationmentioning

confidence: 99%

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Bayesian Thurstonian models for ranking data using JAGS

Johnson

Kuhn

2013

Behav Res

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“…The issues of leniency and central tendency are well known in psychology: it is often observed that individuals have a tendency to place objects in the middle of the scale and to avoid extreme positions. Similar problems have also been studied by Poon and Chan (2002), Fligner and Verducci (1990), and Yu (2000). The mathematics of these methods has been described by Alvo and Yu (2014), Marden (1995), andCritchlow et al (1991).…”

Section: Introductionmentioning

confidence: 91%

A statistical approach to calibrating the scores of biased reviewers of scientific papers

Kuhlisch

Roos

Rothe

et al. 2015

Metrika

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Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by individual reviewers to papers, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. A similar procedure is part of the selection process of grant applications and, among other fields, in sports. It is well known that the reviewing process suffers from measurement errors due to a lack of agreement among multiple reviewers of the same paper. And if not all papers are reviewed by all reviewers, the naive approach of averaging the scores is biased. Several statistical methods are proposed for aggregating review scores, which all can be realized by standard statistical software. The simplest method uses the well-known fixed-effects two-way classification with identical variances, while a more advanced method assumes different variances. As alternatives a mixed linear model and a generalized linear model are employed. The application of these methods implies an evaluation of the reviewers, which may help to improve reviewing processes. An application example with real conference data shows the potential of these statistical methods.

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“…Models based on orderstatistics are discussed in Thurstone (1927), Yellot (1977), Critchlow (1980), Daniels (1950), Mosteller (1951) and Yu (2000). Order-statistics based models consider a latent utility y i , of ith item, i = 1, .…”

Section: Introductionmentioning

confidence: 99%

A novel sandwich algorithm for empirical Bayes analysis of rank data

Laha

Dutta

Roy

2017

Statistics and Its Interface

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Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the items are ranked. In this paper we analyze rank data using a purely probabilistic model where the observed ranks are assumed to be perturbed versions of the true rank and each perturbation has a specific probability of occurring. We consider the general case when covariate information is present and has an impact on the rankings. An empirical Bayes approach is taken for estimating the model parameters. The Gibbs sampler is shown to converge very slowly to the target posterior distribution and we show that some of the widely used empirical convergence diagnostic tools may fail to detect this lack of convergence. We propose a novel, fast mixing sandwich algorithm for exploring the posterior distribution. An EM algorithm based on Markov chain Monte Carlo (MCMC) sampling is developed for estimating prior hyperparameters. A real life rank data set is analyzed using the methods developed in the paper. The results obtained indicate the usefulness of these methods in analyzing rank data with covariate information.

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Bayesian analysis of order-statistics models for ranking data

Abstract: data augmentation, Gibbs sampling, order-statistics model, ranking data,

Cited by 37 publications

References 52 publications

Bayesian Thurstonian models for ranking data using JAGS

Bayesian Thurstonian models for ranking data using JAGS

A statistical approach to calibrating the scores of biased reviewers of scientific papers

A novel sandwich algorithm for empirical Bayes analysis of rank data

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