Bayesian Thurstonian models for ranking data using JAGS

Johnson, Timothy R.; Kuhn, Kristine M.

doi:10.3758/s13428-012-0300-3

Cited by 23 publications

(14 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While calculating the exact posterior distribution is generally intractable, Markov Chain Monte Carlo (MCMC) algorithms can provide a robust approximation of the posterior (J. K. Kruschke, 2015). It has been shown that MCMC algorithms can be used to fit BTMs (Yao and Böckenholt, 1999;Yu, 2000;and Johnson and Kuhn, 2013), and can be implemented in probabilistic programming frameworks such as JAGS (Johnson and Kuhn, 2013). MCMC algorithms work by indirectly taking a representative sample from the joint posterior distribution.…”

Section: Bayesian Estimation and Markov Chain Monte Carlomentioning

confidence: 99%

“…MCMC algorithms have previously been applied to Thurstonian models using a "rank censoring constraint" which obviates the need to analytically evaluate the likelihood function. The rank censoring constraint essentially ensures that the Markov Chain has zero probability of transitioning to locations in parameter space where does not have the same rank as (see Johnson and Kuhn, 2013, for an overview). Popular MCMC algorithms, such as the Metropolis algorithm (Hastings, 1970;Metropolis, Rosenbluth, Rosenbluth, Teller, & Teller, 1953) work by first proposing a transition in parameter space, and then accepting the transition according to a probabilistic acceptance criterion…”

Section: Bayesian Estimation and Markov Chain Monte Carlomentioning

confidence: 99%

“…Of particular note is the Thurstonian model, developed by Thurstone (1931). Thurstonian models map discrete ranking data to a set of latent continuous variables, allowing the model to be easily extended to include covariates (Johnson & Kuhn, 2013). Thus Thurstonian models allow us to estimate an aggregate ranking from a set of rankings provided by individuals, as well as compare aggregate rankings between experimental conditions and populations, or even predict an aggregate ranking given a set of covariates.…”

Section: Introductionmentioning

confidence: 99%

“…While the Thurstonian model of ranking data have existed for almost a century, it has not seen widespread use in data analysis. This is largely because of difficulty fitting the models parameters using tradition optimisation methods, as the likelihood function cannot be analytically evaluated when there are more than two items being ranked (see Johnson & Kuhn (2013) for an overview).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian analysis of subjective ranking data using Thurstonian Models: Tutorial, novel methods, and an open-source library

Giles¹,

Romano²,

Markkula³

2018

Preprint

View full text Add to dashboard Cite

Subjective ranking data are ubiquitous in behavioural research, design and marketing. Subjective ranking data arise when subjects are asked to order a set of items or stimuli according to some criteria. For example, a psychologist may ask subjects to order a set of faces according to their perceived 'friendliness', while an automotive engineer may rank a set of vehicle prototypes according to their subjectively perceived stability. Thurstonian models provide a powerful framework for analysing ranking data, but have not seen widespread use in the behavioural sciences. By modelling discrete rankings as arising from a set of continuous latent variables, Thurstonian models can extend the flexibility of generalised linear models to ranking data. This allows us to estimate aggregate (or "consensus") ranks for a group of participants, incorporate covariates into the models, test for differences between conditions and populations, and assess the degree of agreement between rankings from multiple subjects. Here we provide an introduction to Thurstonian models, and illustrate how these, when coupled with Bayesian estimation approaches, can provide a powerful tool for analysing ranking data. Specifically, using three example datasets, including both simulated data and data from our own research on subjective impressions of driving simulators, we illustrate how we can fit and interpret Thurstonian models. We demonstrate a number of novel approaches for summarising the Bayesian Thurstonian model fits using distance metrics, and provide an open source code library which allows users to flexibly specify and fit Thurstonian models. This implementation uses a novel reformulation of the Thurstonian model, which admits the use of Hamiltonian Monte Carlo, a fast and efficient algorithm for fitting Bayesian models.

show abstract

Section: Bayesian Estimation and Markov Chain Monte Carlomentioning

confidence: 99%

Section: Bayesian Estimation and Markov Chain Monte Carlomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian analysis of subjective ranking data using Thurstonian Models: Tutorial, novel methods, and an open-source library

Giles¹,

Romano²,

Markkula³

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…8], [91]. Other possible software are JAGS [86, p. 214], [50,78,108]; SAS (SAS Institute, Cary NC) [86,Ch. 8], [128]; etc.…”

Section: Random Coefficients and Bayesian Inferencementioning

confidence: 99%

Computational methods for random differential equations: probability density function and estimation of the parameters

Gregori¹

View full text Add to dashboard Cite

Mathematical models based on deterministic differential equations do not take into account the inherent uncertainty of the physical phenomenon (in a wide sense) under study. In addition, inaccuracies in the collected data often arise due to errors in the measurements. It thus becomes necessary to treat the input parameters of the model as random quantities, in the form of random variables or stochastic processes. This gives rise to the study of random ordinary and partial differential equations. The computation of the probability density function of the stochastic solution is important for uncertainty quantification of the model output. Although such computation is a difficult objective in general, certain stochastic expansions for the model coefficients allow faithful representations for the stochastic solution, which permits approximating its density function. In this regard, Karhunen-Loève and generalized polynomial chaos expansions become powerful tools for the density approximation. Also, methods based on discretizations from finite difference numerical schemes permit approximating the stochastic solution, therefore its probability density function. The main part of this dissertation aims at approximating the probability density function of important mathematical models with uncertainties in their formulation. Specifically, in this thesis we study, in the stochastic sense, the following models that arise in different scientific areas: in Physics, the model for the damped pendulum; in Biology and Epidemiology, the models for logistic growth and Bertalanffy, as well as epidemiological models; and in Thermodynamics, the heat partial differential equation. We rely on Karhunen-Loève and v generalized polynomial chaos expansions and on finite difference schemes for the density approximation of the solution. These techniques are only applicable when we have a forward model in which the input parameters have certain probability distributions already set. When the model coefficients are estimated from collected data, we have an inverse problem. The Bayesian inference approach allows estimating the probability distribution of the model parameters from their prior probability distribution and the likelihood of the data. Uncertainty quantification for the model output is then carried out using the posterior predictive distribution. In this regard, the last part of the thesis shows the estimation of the distributions of the model parameters from experimental data on bacteria growth. To do so, a hybrid method that combines Bayesian parameter estimation and generalized polynomial chaos expansions is used.

show abstract

Elementary Signal Detection and Threshold Theory

Kellen

Klauer

2018

Stevens' Handbook of Experimental Psychology and Cognitive Neuroscience

View full text Add to dashboard Cite

Signal detection and threshold model classes are important measurement tools that disentangle the contribution of different factors such as discriminability and response/guessing‐bias based on observed categorical responses. This chapter provides an introduction to both model classes by discussing their theoretical foundations and different measures that can be derived from them. Measures and tests are exemplified with previously published data from the fields of perception and memory.

show abstract

Bayesian Thurstonian models for ranking data using JAGS

Cited by 23 publications

References 39 publications

Bayesian analysis of subjective ranking data using Thurstonian Models: Tutorial, novel methods, and an open-source library

Bayesian analysis of subjective ranking data using Thurstonian Models: Tutorial, novel methods, and an open-source library

Computational methods for random differential equations: probability density function and estimation of the parameters

Elementary Signal Detection and Threshold Theory

Contact Info

Product

Resources

About