The No-U-Turn sampler and its mixture-modeling revision for the 4-parameter normal ogive model

Area of Science:

• Psychometrics
• Computational Statistics
• Item Response Theory

Background:

• The No-U-Turn Sampler (NUTS) is widely used in psychometrics but lacks systematic introductions and tailored optimizations for specific Item Response Theory (IRT) models.
• The 4-parameter normal ogive (4PNO) model is a complex psychometric model requiring efficient estimation methods.

Purpose of the Study:

• To systematically explicate the NUTS algorithm for the 4PNO model.
• To propose and evaluate a novel Mixture-Modeling NUT sampler (MMNUTS) for enhanced estimation of the 4PNO model.

Main Methods:

• A simulation study comparing NUTS (Stan), MMNUTS, and Gibbs-within-Gibbs (fourPNO R package) across educational and psychological scenarios.
• An empirical analysis using a behavioral scale to assess model fit and sampler performance.

Main Results:

• All samplers demonstrated satisfactory convergence, with accuracy increasing at larger sample sizes.
• MMNUTS exhibited superior running time and upper asymptote parameter recovery in the psychological scenario.
• MMNUTS showed faster convergence and higher computational efficiency in the empirical analysis.

Conclusions:

• MMNUTS offers robust estimation accuracy and improved computational efficiency for the 4PNO model.
• This work provides a foundation for developing tailored sampling algorithms for complex psychometric models.
• MATLAB code for MMNUTS is available in the appendix.