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

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Traditional questionnaires (e.g., Likert scales) suffer from response biases.
• Classical scoring methods in forced-choice questionnaires present ipsativity issues.
• Item Response Theory (IRT) methods offer potential for accurate latent trait structure analysis.

Purpose of the Study:

• To propose the multi-unidimensional pairwise preference two-parameter logistic (MUPP-2PL) model for dominance items.
• To introduce a Markov Chain Monte Carlo (MCMC) procedure for parameter estimation.
• To evaluate the performance of the MUPP-2PL model and MCMC estimation.

Main Methods:

• Development of the MUPP-2PL model within the MUPP framework.
• Implementation of a Markov Chain Monte Carlo (MCMC) procedure for parameter estimation.
• Simulation studies to assess model fit and parameter recovery.
• Comparison with a Thurstonian IRT model (Brown and Maydeu).

Main Results:

• Simulation results demonstrated appropriate goodness of recovery across conditions.
• The MUPP-2PL model and Thurstonian IRT model showed theoretical similarity.
• Bayesian estimation of MUPP-2PL potentially offers better latent space correlation recovery and error assessment.
• MCMC estimation showed advantages for item parameters and latent trait correlations in real data.

Conclusions:

• The MUPP-2PL model with MCMC provides a viable and potentially superior alternative for analyzing forced-choice data.
• The proposed Bayesian estimation procedure enhances the reliability of latent trait measurement.
• Further investigation into MCMC's advantages for item and trait parameter estimation is warranted.