A Dominance Variant Under the Multi-Unidimensional Pairwise-Preference Framework: Model Formulation and Markov Chain Monte Carlo Estimation

Forced-choice questionnaires have been proposed as a way to control some response biases associated with traditional questionnaire formats (e.g., Likert-type scales). Whereas classical scoring methods have issues of ipsativity, item response theory (IRT) methods have been claimed to accurately account for the latent trait structure of these instruments. In this article, the authors propose the multi-unidimensional pairwise preference two-parameter logistic (MUPP-2PL) model, a variant within Stark, Chernyshenko, and Drasgow's MUPP framework for items that are assumed to fit a dominance model. They also introduce a Markov Chain Monte Carlo (MCMC) procedure for estimating the model's parameters. The authors present the results of a simulation study, which shows appropriate goodness of recovery in all studied conditions. A comparison of the newly proposed model with a Brown and Maydeu's Thurstonian IRT model led us to the conclusion that both models are theoretically very similar and that the Bayesian estimation procedure of the MUPP-2PL may provide a slightly better recovery of the latent space correlations and a more reliable assessment of the latent trait estimation errors. An application of the model to a real data set shows convergence between the two estimation procedures. However, there is also evidence that the MCMC may be advantageous regarding the item parameters and the latent trait correlations.