Thurstonian modeling of ranking data via mean and covariance structure analysis. (original) (raw)

Analysing multiattribute ranking data: Joint and conditional approaches

British Journal of Mathematical and Statistical Psychology, 1996

Rankings, in contrast to ratings, eliminate effects of individual differences in scale usage and avoid arbitrary definitions regarding the number of response categories and category labels. However, despite the appeal and popularity of this technique, few methods are available for the analysis of rankings on several attributes. This paper presents extensions of Thurstonian and logistic models for the joint analysis of multiattribute ranking responses and for conditional analyses where rankings on one of the attributes are modelled as a hnction of the rankings on the other attributes. These extensions are based on two approaches proposed to account for associations among the ranking responses. Empirical applications of the Thurstonian and logistic ranking models indicate that one of the two approaches appears particularly promising for the analysis of multiamibute ranking data.

Structural Equation Modeling of Paired-Comparison and Ranking Data

Psychological Methods, 2005

L. L. model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone's model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently.

Structural equation modeling of paired comparisons and ranking data

L. L. Thurstone’s (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone’s model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently.

Bayesian estimation of Thurstonian ranking models based on the Gibbs sampler

British Journal of Mathematical and Statistical Psychology, 1999

This paper presents a Gibbs sampler for the estimation of Thurstonian ranking models. This approach is useful for the analysis of ranking data with a large number of options. Approaches for assessing the goodness-of-t of Thurstonian ranking models based on posterior predictive distributions are also discussed. Two simulation studies and two ranking studies are presented to illustrate that the Gibbs sam pler is a promising solution to the numerical problems that previously plagued the estimation of Thurstonian ranking models.

An R package for analyzing and modeling ranking data

BMC medical research methodology, 2013

Background: In medical informatics, psychology, market research and many other fields, researchers often need to analyze and model ranking data. However, there is no statistical software that provides tools for the comprehensive analysis of ranking data. Here, we present pmr, an R package for analyzing and modeling ranking data with a bundle of tools. The pmr package enables descriptive statistics (mean rank, pairwise frequencies, and marginal matrix), Analytic Hierarchy Process models (with Saaty's and Koczkodaj's inconsistencies), probability models (Luce model, distance-based model, and rank-ordered logit model), and the visualization of ranking data with multidimensional preference analysis.

A Rank-Ordered Logit Model with Unobserved Heterogeneity in Ranking Capabilities

In this paper we consider the situation where one wants to study the preferences of individuals over a discrete choice set through a survey. In the classical setup respondents are asked to select their most preferred option out of a (selected) set of alternatives. It is well known that, in theory, more information can be obtained if respondents are asked to rank the set of alternatives instead. In statistical terms, the preferences can then be estimated more efficiently. However, when individuals are unable to perform (part of) this ranking task, using the complete ranking may lead to a substantial bias in parameter estimates. In practice, one usually opts to only use a part of the reported ranking.

Limited information estimation and testing of Thurstonian models for preference data

Thurstonian models provide a rich representation of choice behavior that does not assume that stimuli are judged independently of each other, and they have an appealing substantive interpretation. These models can be seen as multivariate standard normal models that have been discretized using a set of thresholds and that impose certain restrictions on these thresholds and on the inter-correlations among the underlying normal variates. In this paper we provide a unified framework for modeling preference data under Thurstonian assumptions and we propose a limited information estimation and testing framework for it. Although these methods have a long tradition in psychometrics, until recently only their application to rating data has been considered. Here we shall give an overview of how these methods can be readily applied to fit not only rating data, but also paired comparison and ranking data. The limited information methods discussed here are appealing because they are extremely fast, they are able to estimate models essentially of any size, they can easily accommodate external information about the stimuli and/or respondents, and in simulations they have been found to be very robust to data sparseness.

Exploring the consistency of alternative best and/or worst ranking procedures

We apply four probabilistic ranking models to data obtained by repeated best, then worst, choices. Fits are compared across the models and latent-class analysis is used to explore how respondents naturally segregate into distinct classes determined by the best fitting best and/or worst choice ranking process. When WTP-space specifications are used we find no statistical difference in the marginal WTP distributions for three out of the four ranking models, suggesting that one may analyze currently available data that has been obtained by repeated best, then worst, choices by any one of those three models.