Comparing Approaches to Estimating Person Parameters for the MUPP Model

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Accurate person scoring is crucial for educational and psychological assessments.
• The Multi-Unidimensional Pairwise Preference Model (MUPPM) offers a flexible framework for preference data.
• Comparing different computational approaches for MUPPM person parameters is essential for practical application.

Purpose of the Study:

• To compare the accuracy and efficiency of Maximum a Posteriori (MAP), Expected a Posteriori (EAP), and Markov Chain Monte Carlo (MCMC) methods for person score estimation in the MUPPM.
• To evaluate the impact of dimensionality on the performance of these scoring methods.
• To investigate the influence of the number of items per dimension on parameter recovery.

Main Methods:

• Employed three distinct person scoring approaches: MAP, EAP with fully crossed quadrature, and MCMC using the No-U-Turn sampling (NUTS) algorithm.
• Simulated data from the MUPPM under varying conditions of dimensionality and number of items per dimension.
• Assessed parameter recovery accuracy and computational performance.

Main Results:

• The EAP method with fully crossed quadrature and the NUTS algorithm demonstrated superior performance compared to MAP, particularly in lower-dimensional settings.
• The NUTS algorithm yielded the most accurate person parameter estimates in higher-dimensional conditions.
• The number of items per dimension was identified as the most influential factor affecting person parameter recovery.

Conclusions:

• Both EAP with fully crossed quadrature and NUTS are effective methods for person score estimation in the MUPPM, with NUTS showing an advantage in complex, high-dimensional scenarios.
• The MUPPM's performance is sensitive to the number of items available per dimension, highlighting the importance of test design.
• These findings provide valuable guidance for researchers and practitioners selecting appropriate scoring methods for MUPPM-based assessments.