Item Response Modeling of Paired Comparison and Ranking Data

Abstract

The comparative format used in ranking and paired comparisons tasks can significantly reduce the impact of uniform response biases typically associated with rating scales. Thurstone's (1927, 1931) model provides a powerful framework for modeling comparative data such as paired comparisons and rankings. Although Thurstonian models are generally presented as scaling models, that is, stimuli-centered models, they can also be used as person-centered models. In this article, we discuss how Thurstone's model for comparative data can be formulated as item response theory models so that respondents' scores on underlying dimensions can be estimated. Item parameters and latent trait scores can be readily estimated using a widely used statistical modeling program. Simulation studies show that item characteristic curves can be accurately estimated with as few as 200 observations and that latent trait scores can be recovered to a high precision. Empirical examples are given to illustrate how the model may be applied in practice and to recommend guidelines for designing ranking and paired comparisons tasks in the future.