Remarks on the Identifiability of Thurstonian Paired Comparison Models Under Multiple Judgment

Tsai, Rung Ching

doi:10.1007/bf02294732

Cited by 18 publications

(21 citation statements)

References 17 publications

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“…will be equivalent to the estimated model (Tsai, 2003, Corollary 1). In Equation 24, c is a positive constant, and d is an n ϫ 1 vector of constants.…”

Section: Equivalent Covariance Structures and Model Interpretationmentioning

confidence: 97%

Structural Equation Modeling of Paired-Comparison and Ranking Data.

Maydeu-Olivares

Böckenholt

2005

Psychological Methods

107

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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.Keywords: Lisrel, preference data, choice models, random utility models, factor analysisThe methods of ranking and paired comparison play an essential role in the measurement of preferences, attitudes, and values. In a ranking task, respondents are presented with a set of alternatives (which, in the literature, are also referred to as options, stimuli, or items) and are asked to order them from most to least preferred. In a paired-comparison task, respondents are presented with pairs selected from the set of available alternatives and are instructed to select the more preferred alternative from each pair. The popularity of paired-comparison and ranking methods can be traced back to three reasons. First, by asking for a comparison of choice alternatives, these methods impose minimal constraints on the response behavior of a respondent. Especially when differences between choice alternatives are small, these methods are likely to provide more information about individual preferences than is obtainable by rating methods. Second, internal consistency checks are available that facilitate the identification of respondents who do not have well-defined preferences, values, or attitudes. If respondents can be shown to be consistent in their judgments, one can have much greater confidence in the obtained measurements and the predictive value of the derived scales in further applications. Third, paired-comparison and ranking data provide a rich source of information about the effects of individual differences and perceived similarity relationships among choice alternatives. This article presents two applications that illustrate this important feature.Because of their versatility, the methods of paired comparison and rankings are used in a wide range of studies.

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“…will be equivalent to the estimated model (Tsai, 2003, Corollary 1). In Equation 24, c is a positive constant, and d is an n ϫ 1 vector of constants.…”

Section: Equivalent Covariance Structures and Model Interpretationmentioning

confidence: 97%

Structural Equation Modeling of Paired-Comparison and Ranking Data.

Maydeu-Olivares

Böckenholt

2005

Psychological Methods

107

View full text Add to dashboard Cite

show abstract

“…For example, ThurstoneÕs ''Case 5'' postulates that all stimuli are judged independently of each other with equal stimulus variances. Tsai (2000Tsai ( , 2003 showed that the ''Case 5'' hypothesis cannot be tested uniquely for ranking or paired comparison data since an infinite number of different stimulus-covariance matrices yield the same predictions as the identity matrix conjectured under ''Case 5''. In contrast, the hypothesis that all stimuli are equally distant to each other (i.e., they exhibit the same similarity relations) is unique and testable.…”

Section: Discussionmentioning

confidence: 94%

Visualizing individual differences in pairwise comparison data

Böckenholt

2006

Food Quality and Preference

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“…However, other decompositions may be possible as well that may prove equally useful in understanding evaluative processes. In view of the under-parameterization of R B , it is also important to study the equivalence classes for the proposed decomposition of R B that yield the same fit but are based on a different covariance structure (Tsai, 2003). Such an analysis is valuable to improve our understanding of how to interpret a particular covariance structure under consideration.…”

Section: Discussionmentioning

confidence: 98%